٠Light bulb A is rated at 60 W and light bulb B is rated at 100 W. Both are designed to operate at 110 V. Which statement is correct?
A-The 60 W bulb has a greater resistance and greater current than the 100 W bulb.
B-The 60 W bulb has a greater resistance and smaller current than the 100 W bulb.
C-We need to know the resistivities of the filaments to answer this question.
D-The 60 W bulb has a smaller resistance and greater current than the 100 W bulb.
F-The 60 W bulb has a smaller resistance and smaller current than the 100 W bulb
Answer:B
Explanation:
Power=p
Voltage=v
Resistance=r
Voltage for both:110v
For 60 watts bulb:
Resistance=v^2/p
Resistance=110^2/60
Resistance=(110x110)/60
Resistance=12100/60
Resistance=201.7 ohms
Current=power/voltage
Current=60/110
Current=0.55 amperes
For 100watts bulb:
Resistance=v^2/p
Resistance=110^2/100
Resistance=(110 x 110)/100
Resistance=(12100)/100
Resistance =121 ohms
Current=power/voltage
Current=100/110
Current=0.91
The 60W bulb has greater resistance and smaller current than the 100W bulb, based on calculations from the power, voltage and Ohm's Law.
Explanation:In the case of light bulbs, power (P) is given by the formula P = IV, where I is the current and V is the voltage. Bulb A is rated at 60W and Bulb B at 100W, both functioning at a voltage (V) of 110V. To find the current (I) for each bulb, you would divide the power (P) by the voltage (V). This shows that Bulb B, with a higher wattage, has a greater current.
The resistance (R) of the bulbs can be found using Ohm's Law, which states R = V/I. This shows that Bulb A, with a smaller current, has a greater resistance.
Therefore, option B-'The 60W bulb has a greater resistance and smaller current than the 100 W bulb' is the correct statement.
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Match the descriptions to the feature,
principal axis
Center of the spherical mirror from which a
curved mirror was cut
center of curvature
Distance from the center of a mirror to the
focal point
Line that runs through the center of
curvature to a mirror
focal point
Point where reflected light converges or
appears to diverge
focal length
Point where the principal axis and mirror
vertex
meet
Answer:
Vertex: Point where the principal axis and mirror meet
Focal point: Point we are reflected light converges or appears to diverge
Focal length: distance from the center of a mirror to the focal point
Principal axis: line that runs to the center of curvature to a mirror
Center of curvature: sensor of spherical mirror from which a curved mirror was cut
Explanation:
Just did the assignment on Edge.
A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex.
What is a spherical mirror?A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex. These are illustrated in.
The most commonly occurring examples of concave mirrors are shaving mirrors and makeup mirrors.
As is well-known, these types of mirrors magnify objects placed close to them. The most commonly occurring examples of convex mirrors are the passenger-side wing mirrors of cars.
These types of mirrors have wider fields of view than equivalent flat mirrors, but objects which appear in them generally look smaller
The answers to the given questions are:
Vertex: Point where the principal axis and mirror meet
Focal point: Point we are reflected light converges or appears to diverge
Focal length: distance from the centre of a mirror to the focal point
Principal axis: line that runs to the centre of curvature of a mirror
Center of curvature: sensor of spherical mirror from which a curved mirror was cut
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Which plants are usually the first to live in soil?
The plants that are typically the first to live in soil are known as pioneer plants or pioneer species.
What are the first plants?Pioneer plants or pioneer species are the plants that are often the first to live in soil. These plants are distinguished by their propensity to colonize bare or disturbed soil, such as on newly formed land or in the wake of a natural disaster.
The process of primary succession, which is the gradual formation of plant and animal communities in a region devoid of soil or organic matter, depends critically on pioneer plants.
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Imagine playing baseball in a universe (not ours!) where the Planck constant is 0.70 J·s. What would be the uncertainty in the position of a 0.55 kg baseball that is moving at 22 m/s along an axis if the uncertainty in the speed is 0.5 m/s? Number Enter your answer in accordance to the question statement Units Choose the answer from the menu in accordance to the question statement
Answer:
The uncertainty the in position is [tex]\delta s = 0.4051 m[/tex]
Explanation:
From the question we are told
The planck's constant is [tex]h = 0.70 \ J \cdot s[/tex]
The mass of the baseball is [tex]m = 0.55kg[/tex]
The velocity of the baseball [tex]v_b = 22 m/s[/tex]
The uncertainty in [tex]\delta v = 0.5 m/s[/tex]
Generally the uncertainty of momentum is
[tex]\delta p = m \delta v[/tex]
substituting values
[tex]\delta p = 0.275 \ kg m/s[/tex]
The uncertainty position is mathematically represented as
[tex]\delta s = \frac{h}{2 \p \delta p }[/tex]
substituting values
[tex]\delta s = \frac{0.70}{2 * 3.142 * 0.275 }[/tex]
[tex]\delta s = 0.4051 m[/tex]
The ballistic pendulum is an apparatus used to measure the speed of a projectile. An 8.0 g bullet is fired into a 2.5 kg ballistic pendulum bob, which is initially at rest, and becomes embedded in the bob. The pendulum then rises to a vertical distance of 6.0 cm. What was the initial speed of the bullet (in m/s)?
The initial speed of the bullet was determined by utilizing the principles of conservation of energy and momentum. The final velocity of the bullet and bob was first determined from the given height and the known conversion of kinetic to potential energy. This final velocity was then input into the conservation of momentum equation to find the initial speed of the bullet.
Explanation:The ballistic pendulum is a classic example of a problem in physics which can be solved either by using the principles of work and energy or the principles of impulse and momentum. For this problem, we will utilize conservation of momentum. We know that the momentum before the collision is equal to the momentum after the collision.
Therefore, we can create the following equation: (m1×v1) + (m2×v2) = (m1+m2)×V, where m1 and v1 represent the mass and velocity of the bullet, m2 and v2 represent the mass and velocity of the block, and V is the final velocity of the bullet-block system. We know that the block was initially at rest, hence v2 = 0.
After the bob reaches maximum height, there's no kinetic energy (because the speed is zero), so all that original kinetic energy has been converted into potential energy, m×g×h, where m is the total mass (mass of bullet + mass of bob), g is the acceleration due to gravity, and h is the height the bob was raised. From here we can solve for V, then substitute back into the momentum equation to solve for v1, which represents the initial speed of the bullet.
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Using conservation of momentum and energy, the initial speed of an 8.0 g bullet fired into a 2.5 kg ballistic pendulum bob, which rises 6.0 cm, is approximately 339.9 m/s. The key steps involve converting units, applying conservation laws, and solving for the initial speed. Therefore, the bullet's speed is determined to be 339.9 m/s.
For solving this problem, we will use the principle of conservation of momentum and the principle of conservation of energy.
Step-by-Step Solution
Convert the masses into common units:
mass of bullet, [tex]m_{bullet[/tex] = 8.0 g = 0.008 kg
mass of pendulum bob = 2.5 kg.
Convert the rise height into meters:
h = 6.0 cm = 0.06 m.
Determine the final velocity of the combined bullet and pendulum system at the lowest point (right after the collision) using energy conservation:
At maximum height, all kinetic energy is converted to potential energy:
mgh = 0.5 (M + m) v²
Using v = √(2gh) since M includes the bullet:
v = √(2 * 9.8 m/s² * 0.06 m)
v = √(1.176)
v ≈ 1.084 m/s
Use conservation of momentum to find the initial speed of the bullet:
Initial momentum = [tex]m_{bullet[/tex] * [tex]v_{bullet[/tex]
Final momentum = (M + m) * v = (2.5 kg + 0.008 kg) * 1.084 m/s
So, p = (2.508 kg) * 1.084 m/s
p = 2.719 kg·m/s
Initial speed of the bullet:
[tex]v_{bullet[/tex] = p / [tex]m_{bullet[/tex]
[tex]v_{bullet[/tex] = 2.719 kg·m/s / 0.008 kg
[tex]v_{bullet[/tex] ≈ 339.9 m/s
Therefore, the initial speed of the bullet is approximately 339.9 m/s.
If a system is isolated the total energy within that system is constant. Consider the case of a hot cup of coffee: when it cools down, the energy goes into the surrounding air, causing the air to warm. If the coffee and the air are placed in an isolated chamber, the total energy of the system (coffee + air) is constant because the energy lost by the coffee is exactly equal to the energy gained by the air. The only way for the total energy of a system to change is when it is not isolated, meaning that external forces or sources of energy interact with the system. If we want to define a system where the total energy is conserved, which one of the choices below would be the best system to consider?A. The personB. The person and the EarthC. The Earth
Answer:b-The person and the earth
Explanation:
The best system will be the person and earth as a system
It is so because whatever the energy required by the person is derived from earth resource and thus by depleting the earth resource person is getting is required form of energy .
for example person want thermal energy , for this he need coal which is earth resource and thus all the energy is derived from earth and is being converted into some other form of energy.
(Solidification) You are performing a double slit experiment very similar to the one from DLby shining a laser on two narrow slits spaced 7.5 × 10-5meters apart. However, by placing a piece of crystal in one of the slits, you are able to make it so that the rays of light that travel through the two slits are πout of phasewith each other (that is to say,Δφ!=휋).If you observe that on a screen placed 4meters from the two slits that the distance between the bright spot closest to the center of the interference pattern and the center of the pattern is 1.5 cm, what is the wavelength of the laser? (Just as in DL, you may use the small angle approximation sinθ ≈ θ ≈ tanθ.)
Answer:
The wavelength of the laser, λ = 5.625 * 10⁻⁷ m
Explanation:
Separation of the narrow slits, d = 7.5 * 10⁻⁵ m
The distance between the screen and the two slits, d = 4m
The distance between the bright spot and the center of the pattern, Y = 1.5 cm
Y = 1.5 * 10⁻² m
To calculate the wavelength, λ, of the laser we will use the relationship:
[tex]Y = \frac{\lambda L}{2d} \\1.5 * 10^{-2} = \frac{\lambda * 4}{2*7.5*10^{-5} }\\\lambda = \frac{1.5 * 10^{-2} * 15 * 10^{-5} }{4}[/tex]
λ = 5.625 * 10⁻⁷ m
Since sinusoidal waves are cyclical, a particular phase difference between two waves is identical to that phase difference plus a cycle. For example, if two waves have a phase difference of π4, the interference effects would be the same as if the two waves had a phase difference of π4+2π. The complete criterion for constructive interference between two waves is therefore written as follows: phase difference=0+2πnfor any integer n Write the full criterion for destructive interference between two waves
Final answer:
Destructive interference between two waves occurs when their phase difference is [tex]\pi + 2\pi n[/tex], for any integer n, resulting in a minimized or zero resultant amplitude.
Explanation:
The full criterion for destructive interference between two waves is when the phase difference between the waves is [tex]\pi + 2\pi n[/tex] for any integer n. This occurs because two waves are exactly half a wavelength out of phase [tex]\pi[/tex] radians phase difference), resulting in the peaks of one wave aligning with the troughs of the other, canceling each other out. Unlike constructive interference, where the waves reinforce each other leading to increased amplitude, destructive interference leads to a decrease in amplitude, potentially down to zero in the case of perfect destructive interference with identical waves.
Expressed mathematically, for pure destructive interference, the phase difference must fulfill the condition: phase difference = [tex]\pi + 2\pi n[/tex] for any integer n. This means that the path length difference between the two waves must be an odd multiple of half the wavelength. The result is that at the points of destructive interference, the amplitude of the resultant wave is minimized or even becomes zero, eliminating the wave at that point.
The binding energies of K-shell and L-shell electrons in a certain metal are EK and EL, respectively, If a Kαx ray from this metal is incident on a crystal and gives a first-order Bragg reflection at an angle θ measured relative to parallel planes of atoms, what is the spacing between these parallel planes? State your answer in terms of the given variables, using h and c when needed.
Answer:
The separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)
Explanation:
The relationship between energy and wavelength is expressed below:
E = hc/λ
λ = hc/EK - EL
Considering the condition of Bragg's law:
2dsinθ = mλ
For the first order Bragg's law of reflection:
2dsinθ = (1)λ
2dsinθ = hc/EK - EL
d = hc/2sinθ(EK - EL)
Where 'd' is the separation distance between the parallel planes of an atom, 'h' is the Planck's constant, 'c' is the velocity of light, θ is the angle of reflection, 'EK' is the energy of the K shell and 'EL' is the energy of the K shell.
Therefore, the separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)
wyatt is designing a hollow cylindrical metal can with volume 1000 cm3.the materialused to make the circular top and bottom of the can costs twice as much as the material used tomake the side of the can. what dimensions should wyatt choose in order to minimize the cost ofthe can?show all your work, round off the numerical part of your final answer to four (4) decimal places,and express your final answer in the form of a complete sentence, using the correct units.
Answer:
Explanation:
Let r be the radius of circular top and h be the height of the cylinder
Given
π r² h = 1000
Let cost of making side of can be p per unit area , the cost of making top and bottom will be 2p per unit area.
total cost
C = 2 x π r² x 2p + 2πrh x p
= 2(1000 / h) x 2p + 2π x (1000 / π) x [tex]\frac{1}{\sqrt{h} }[/tex] x h x p
= 2(1000 / h) x 2p + 2π x (1000 / π) x √h x p
differenciating
dC / dh = 2(- 1000 / h²) x 2p + 2π x (1000 / π) x [tex]\frac{1}{2\sqrt{h} }[/tex] x p = 0 for minimum cost
- 4 / h² + 1 / √h = 0
h³ = 16
h = 2.519 cm .
π r² h = 1000
π r² x 2.519 = 1000
r = 11.24 cm
The cylinder will have height of 2.519 cm and radius of 11.24 cm.
Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize cost. This considers the volume constraint of 1000 cm³ and the different material costs for the top/bottom and side. Detailed steps involve deriving these dimensions mathematically.
Let's denote the radius of the base of the cylinder by r and the height by h. The volume V of the cylinder is given by V = πr²h. Given that the volume is 1000 cm³, we have:
Step 1: V = πr²h = 1000 cm³
Therefore, h = 1000 / (πr²).
Step 2: Next, we need to express the cost of the material. The cost for the top and bottom parts is double the cost of the side. The surface area A of the can is:
Area of the top and bottom (each): [tex]A_t[/tex] = πr²
Area of the side: [tex]A_s[/tex] = 2πrh
Total area A:
A = 2πr² + 2πrh
Considering the cost factor, the effective cost area C is:
C = 2(2πr²) + 2πrh
C = 4πr² + 2πrh
Step 3: Substitute h from the volume equation:
C = 4πr² + 2πr(1000 / (πr²))
C = 4πr² + 2000 / r
Step 4: To minimize the cost, take the derivative of C with respect to r and set it to zero:
[tex]\frac{dC}{dr}[/tex] = 8πr - 2000 / r² = 0
8πr = 2000 / r²
8πr³ = 2000
r³ = 250 / π
r ≈ 3.4198 cm
Step 5: Calculate the height h:
h = 1000 / (πr²)
h ≈ 1000 / (π * (3.4198)²)
h ≈ 27.2837 cm
In summary, Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize the cost.
Wyatt should choose a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm for the metal can to minimize the cost, given the volume constraint of 1000 cm³.
A 12.0 g wad of sticky clay is hurled horizontally at a 100 g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After the impact, the block slides 7.5 m before coming to rest. If the coefficient of friction between the block and the surface is 0.650, what was the speed of the clay immediately before the impact
Answer:
The speed of the clay immediately before the impact is 91.23 m/s
Explanation:
Given;
mass of clay, m₁ = 12g = 0.012 kg
mass of wooden block, m₂ = 100g = 0.1 kg
initial velocity of the wooden block, u₂ = 0
distance moved by the wooden block, d = 7.5 m
coefficient of friction, μk = 0.65
Apply the principle of conservation of linear momentum;
Total momentum before collision = Total momentum after collision
m₁u₁ + m₂u₂ = v(m₁ +m₂)
where;
u₁ is the initial velocity of the clay immediately before the impact
v is the common velocity of clay-block system after impact
u₂ = 0
m₁u₁ = v(m₁ +m₂)
[tex]U_1 = \frac{(m_1 + m_2)V}{m_1}[/tex] ------- equ. (i)
Apply the principle of conservation of energy after the impact
ΔK + ΔU = 0
where;
ΔK is change in kinetic energy
ΔU is change in internal energy of the system due to frictional force
[tex](K_f -K_i) + (F_k*d) = 0\\\\-K_i +F_k*d = 0\\\\K_i = F_k*d \\\\\frac{1}{2} (m_1+m_2)v_i^2 = \mu_k (m_1 +m_2)gd\\\\\frac{1}{2}v_i^2 = \mu_kgd\\\\v_i^2 = 2 \mu_kgd\\\\v_i = \sqrt{2 \mu_kgd}[/tex]
[tex]v_i[/tex] is the common velocity of the clay-block system immediately after the impact, which is equal to V in equation (i)
[tex]U_1 = \frac{(m_1+m_2)V}{m_1} = \frac{(m_1+m_2)v_i}{m_1}\\\\U_1 = \frac{m_1+m_2}{m_1}(\sqrt{2 \mu_kgd})\\\\U_1 = \frac{0.012+0.1}{0.012}(\sqrt{2 *0.65*9.8*7.5})\\\\U_1 = 9.3333(9.77497)\\\\U_1 = 91.23 \ m/s[/tex]
Therefore, the speed of the clay immediately before the impact is 91.23 m/s
Determine how fast the length of an edge of a cube is changing at the moment when the length of the edge is 5cm and the volume of the edge is decreasing at the rate of 100cm^3/sec
Answer:
1.333 cm/s
Explanation:
The formula for the volume of the cube V in term of its edge s is:
[tex]V = s^3[/tex]
By using chain rule we have the following equation between the rate of change of the volume and the rate of change of the edge:
[tex]\frac{dV}{dt} = \frac{dV}{ds}\frac{ds}{dt}[/tex]
[tex]100 = \frac{d(s^3)}{ds}\frac{ds}{dt}[/tex]
[tex]100 = 3s^2\frac{ds}{dt}[/tex]
[tex]\frac{ds}{dt} = \frac{100}{3s^2}[/tex]
We can substitute s = 5 cm:
[tex]\frac{ds}{dt} = \frac{100}{3*5^2} = 100 / 75 = 1.333 cm/s[/tex]
Specimen of steel has a rectangular cross section 20 mm wide and 40 mm thick, an elastic modulus of 207 GPa, and a Poisson’s ratio of 0.30. If this specimen is pulled in tension with a force of 60,000 N, what is the change in width if deformation is totally elastic? (A) Increase in width of 3.62 10−6 m (B) Decrease in width of 7.24 10−6 m (C) Increase in width of 7.24 10−6 m (D) Decrease in width of 2.18 10−6 m
Answer:
(D) Decrease in width of 2.18 x [tex]10^{-6[/tex]m
Explanation:
Given:
force 'F'= 60,000 N
elastic modulus 'E' = 207 GPa => 2.07 x [tex]10^{11[/tex]N/m²
cross section area ' [tex]A_{0}[/tex]'= 20 mm x 40 mm => 800mm² =>8 x [tex]10^{-4}[/tex] m²
∈z = б/E => (F/ [tex]A_{0}[/tex])/E => F/ [tex]A_{0}[/tex]E
∈z = 60,000/(8 x [tex]10^{-4}[/tex] x 2.07 x [tex]10^{11[/tex])
∈z =3.62 x [tex]10^{-4}[/tex]
Lateral strain is given by,
∈x= -v∈z => -(0.30)(3.62 x [tex]10^{-4}[/tex])
∈x=1.09 x [tex]10^{-4}[/tex]
Next is to calculate the change in width
ΔW= Wo x ∈x =>20 x 1.09 x [tex]10^{-4}[/tex]
ΔW= -2.18 x [tex]10^{-6[/tex] m
Therefore, the correct option is 'D'
The steel specimen, when pulled in tension, will experience a decrease in width. This decrement is calculated to be about 1.75*10^-7 m, closest to option (D) decrease in width of 2.18 10−6 m.
Explanation:The change in the width of a steel specimen being pulled in tension can be found using the formula for strain in the lateral direction = -Poisson's ratio * (stress/Young's modulus). Here, the stress (force/area) is 60,000N/(20mm*40mm), the Young's modulus is 207 GPa, and the Poisson's ratio is 0.30. Plugging these values in, we get a lateral strain of -8.74*10^-6. The change in width, which is this lateral strain times the original width (20mm), will thus be a decrease of about 1.75*10^-4 mm, or 1.75*10^-7 m. Amongst the given options, this is closest to (D) decrease in width of 2.18 10−6 m.
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A steel drill making 180 rpm is used to drill a hole in a block of steel. The mass of the steel block and the drill is 180 g. If the entire mechanical work is used up in producing heat and the rate of rise in temperature of the block and the drill is 0.5 °C/sec. Find (a) the rate of working of the drill in Watts and (b) torque required to drive the drill. Given: specific heat capacity of steel = 420 J/(kgK)
Answer:
a) 37.8 W
b) 2 Nm
Explanation:
180 g = 0.18 kg
We can also convert 180 revolution per minute to standard angular velocity unit knowing that each revolution is 2π and 1 minute equals to 60 seconds
180 rpm = 180*2π/60 = 18.85 rad/s
We can use the heat specific equation to find the rate of heat exchange of the steel drill and block:
[tex]\dot{E} = mc\Delta \dot{t} = 0.18*420*0.5 = 37.8 J/s[/tex]
Since the entire mechanical work is used up in producing heat, we can conclude that the rate of work is also 37.8 J/s, or 37.8 W
The torque T required to drill can be calculated using the work equation
[tex]E = T\theta[/tex]
[tex]\dot{E} = T\dot{\theta} = T\omega[/tex]
[tex]T = \frac{\dot{E}}{\omega} = \frac{37.8}{18.85} = 2 Nm[/tex]
Calculating the rate of working of a drill involves using the specific heat capacity, mass of the block, and rate of temperature increase to find the power. The torque can be derived from this power and the angular velocity of the drill.
The question involves calculating the rate of working of the drill in Watts and the torque required to drive the drill based on the information that all mechanical work is converted to heat that raises the temperature of the steel block and drill at 0.5 0C/s. Given the mass of the steel block and drill is 180 g and the specific heat capacity of steel is 420 J/(kgK), we can use the formula power (P) = mcigtriangleup T/igtriangleup t, where m is the mass, c is the specific heat capacity, is the temperature change, and is the change in time. To find the torque, we can use the power-torque relationship P = au imes w, where P is power in watts, au is the torque in Newton-meters, and w is the angular velocity in radians per second. As the drill makes 180 revolutions per minute (rpm), we'll convert that to radians per second to use in the power-torque equation.
A 65-kg skier grips a moving rope that is powered by an engine and is pulled at a constant speed to the top of a 230 hill. The skier is pulled a distance x = 320 m along the incline and it takes 2.0 minutes to reach the top of the hill. If the coefficient of kinetic friction between the snow and skis is µk = 0.10, what horsepower engine is required if 30 such skiers are on the rope at one time? 1 hp = 746 W
Answer:
The required power by the engine is 33.0 hp
Explanation:
Solution
Newton's second law says that, the net force Fnet on an object of mass m will accelerates the object
Where
Fnet = ma
a = acceleration
θ = angle of incline,
m = mass of the 30 skiers,
f = frictional force
N = normal force
mg sinθ, mg cos θ are components of weight skier
F = the force applied by engine
Now,
The skier mass is 65 kg
We calculate the mass of the 30 skier
m = 30 (65kg) = 1950 kg
Calculate the net force acting on the skiers along the x-axis
Fnet, x=ma
Now,
F-mg sin θ - f = 0
F= mg sin θ + f -----(1)
The kinetic frictional force is denoted by
f = μk N ------(2)
μk = The coefficient of the kinetic friction
We now, calculate the net force acting on the skiers along y axis
Fnet, y = ma
N- mg cos θ = 0
so,
N = mg cos θ
This value is substituted in equation (2)
f = μk mg cos θ
we substitute the value for equation (1)
F = mg sin θ + μk mg cos θ
mg = sinθ + μk cos θ)-----(3)
The next step is to calculate the work done by the engine in pulling the skiers, the incline top by applying the equation 3
W = Fx
= mg ( sinθ + μk cos θ)x
x = the displacement
we now substitute 1950 kg for m, 23° for θ, 0.10 for μk and 320m for x
so,
W = mg ( sinθ + μk cos θ)x
= (1950 kg) (9.81 m/s²) (sin 23° + (0.10) cos 23°) (320 m)
= 2.99 * 10 ^6 J
Then,
The time from minute to s is converted
t =(2.0min) ( 60sec/1.0min) = 120 sec
Now we calculate the power needed by the engine to pull the skiers at the incline top
Thus,
P = W/t
we substitute 2.955 * 10 ^6 J for W and 120 s for t
we have,
P = 2.955 * 10 ^ 6 J/ 120 s
= ( 2.4625 * 10 ^ 4 W) (1.0 hp/746 W)
= 33.0 hp
In conclusion the required power by the engine is 33.0 hp
To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. By plugging in the given values into the appropriate equations, we can find the required horsepower of the engine.
Explanation:To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. First, we find the net force of the skier parallel to the incline by subtracting the force due to friction from the component of the skier's weight parallel to the incline. Then, we calculate the work done against friction and gravity using the formula W = Fd. Finally, we convert the work done to horsepower using the conversion factor 1 hp = 746 W.
The work done against friction and gravity is:
W = F_net * d
The power required is:
P = W / t
And finally, we convert the power to horsepower:
Power (hp) = P / 746
By plugging the given values into these equations and multiplying the final power by 30 (for 30 skiers), we can find the required horsepower of the engine.
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A certain sound is recorded by a microphone. The same microphone then detects a second sound, which is identical to the first one except that the amplitude of the pressure fluctuations is larger. In addition to the larger amplitude, what distinguishes the second sound from the first one? View Available Hint(s) A certain sound is recorded by a microphone. The same microphone then detects a second sound, which is identical to the first one except that the amplitude of the pressure fluctuations is larger. In addition to the larger amplitude, what distinguishes the second sound from the first one? It is perceived as higher in pitch. It is perceived as louder. It has a higher frequency. It has a longer wavelength.
Answer:
It is perceived as louder.
Explanation:
Amplitude affects the loudness of sound.
Frequency and wavelength affect the pitch of the sound.
What factors does the kinetic energy of a body depend
on?
Ans
Answer:
Kinetic energy depends on the mass of a body and the velocity it is travelling at
Explanation:
Referring to the equation of Kinetic Energy
EK = 0.5 m [tex]v^{2}[/tex]
We can see that Kinetic energy depends on the mass of a body and the velocity it is travelling at
Answer:
The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.
An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area o
Complete Question
An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area oil slick
Answer:
The largest total area of the oil slick [tex]A = 8.257 *10^{9} \ m^2[/tex]
Explanation:
From the question we are told that
The volume of oil the escaped is [tex]V = 18000 \ L[/tex]
The refractive index of oil is [tex]n_o = 1.1[/tex]
The refractive index of water is [tex]n_w = 1.33[/tex]
The wavelength of the light is [tex]\lambda = 485 \ nm = 485 * 10^{-9} \ m[/tex]
Generally the thickness of the oil for condition of constructive interference between the oil and the water is mathematically represented as
[tex]d = m *\frac{\lambda}{2n_w}[/tex]
Where is the order of interference of the light and it value ranges from 1, 2, 3,...n
It is usually take as 1 unless stated otherwise by the question
substituting value
[tex]d = 1 * \frac{485 *10^{-9}}{2 * 1.1}[/tex]
[tex]d = 218 nm[/tex]
The are can be mathematically evaluated as
[tex]A = \frac{V}{d}[/tex]
Substituting values
[tex]A = \frac{18000}{218*10^{-8}}[/tex]
[tex]A = 8.257 *10^{9} \ m^2[/tex]
To practice Problem-Solving Strategy 16.1 Standing waves. An air-filled pipe is found to have successive harmonics at 800 HzHz , 1120 HzHz , and 1440 HzHz . It is unknown whether harmonics below 800 HzHz and above 1440 HzHz exist in the pipe. What is the length of the pipe
Answer:
Length of the pipe = 53.125 cm
Explanation:
given data
harmonic frequency f1 = 800 Hz
harmonic frequency f2 = 1120 Hz
harmonic frequency f3 = 1440 Hz
solution
first we get here fundamental frequency that is express as
2F = f2 - f1 ...............1
put here value
2F = 1120 - 800
F = 160 Hz
and
Wavelength is express as
Wavelength = Speed ÷ Fundamental frequency ................2
here speed of waves in air = 340 m/s
so put here value
Wavelength =340 ÷ 160
Wavelength = 2.125 m
so
Length of the pipe will be
Length of the pipe = 0.25 × wavelength ......................3
put here value
Length of the pipe = 0.25 × 2.125
Length of the pipe = 0.53125 m
Length of the pipe = 53.125 cm
Final answer:
The length of the pipe, which resonates at odd harmonics and has successive frequencies of 800 Hz, 1120 Hz, and 1440 Hz, is calculated to be approximately 32.2 centimeters. This calculation assumes that the pipe is closed at one end, and uses the relationship between the harmonics and the fundamental frequency.
Explanation:
The student is inquiring about determining the length of a pipe based on the frequencies of its successive harmonics. Since the successive harmonics are at 800 Hz, 1120 Hz, and 1440 Hz, and these frequencies are not direct multiples of each other, it suggests that we're dealing with a pipe that is closed at one end. Such pipes produce odd harmonics only. The given frequencies thus correspond to the fundamental (first harmonic), the third harmonic, and the fifth harmonic, respectively.
The frequency of the nth harmonic in a pipe closed at one end is given by:
fn = n(f1), where n is an odd integer and f1 is the fundamental frequency, which in this case is 800 Hz. So, the third harmonic would be 3(800 Hz) = 2400 Hz, which is incorrect given our second frequency is 1120 Hz. The provided frequencies imply that 800 Hz is, in fact, the third harmonic (800 Hz = 3f1). Hence, the fundamental frequency (f1) is 800 Hz / 3 = 266.67 Hz.
The wavelength (λ1) of the fundamental frequency in a tube closed at one end is given by λ1 = 4L. Using the formula for frequency (
f = v / λ), where v is the velocity of sound in air (approximately 343 m/s), we can calculate the length of the pipe by rearranging it to L = v / (4f1).
Therefore, L = 343 m/s / (4 * 266.67 Hz) = 0.322 meters or 32.2 cm.
Which are characteristics of concave mirrors? Check all that apply.
surface curves inward
image can be upside down
image is always virtual
surface curves outward
image can be real
Answer:
1, 2, and 5
Explanation:
Answer:
1, 2 and 5
Explanation:
If the amount of work done on a book was 10 J and the force required to move the book was 2.5 N, what was the distance the book was moved?
Answer:
Explanation:4meters
Work=10J
Force=2.5N
Distance=work ➗ force
Distance=10 ➗ 2.5
Distance=4meter
Final answer:
Given that the work done on a book was 10 J and the force required to move the book was 2.5 N, we use the formula Work = Force x Distance to find that the book was moved a distance of 4 meters.
Explanation:
The question asks to calculate the distance a book was moved given that the work done on the book was 10 J and the force required to move the book was 2.5 N.
To find the distance, we can use the formula for work, which is:
Work (W) = Force (F) * Distance (d)
From the formula, we can solve for distance (d) by rearranging the equation:
Distance (d) = Work (W) / Force (F)
Plugging in the given values:
d = 10 J / 2.5 N
This calculation yields:
d = 4 m
Therefore, the book was moved a distance of 4 meters.
Two electrical motors, one with a power output of 250 watts and one with a power output of 500 watts are both connected to a standard home outlet. Which motor draws greater current?
Answer:
The 500 watts motor
Explanation:
Power is the workdone per unit time, it can be expressed as;
P = VI
P = I^2 × R
Where;
P = power
V = potential difference
I = current
R = resistance
Making current the subject of formula;
I = P/V
I^2 = P/R
Since they are both connected to the same standard home outlet. The potential difference across them is thesame( V is constant). Therefore the higher the power the higher the current.
I ∝ P
So the electrical motors with higher power 500 watts draws greater current.
what is the only part of a motor through which a current does not flow
Answer:
An electric motor
Explanation:
Answer:
the only part it doesn't flow through is an insulator
Explanation:
A conductor is material through which current flows easily; an insulator is material through which current does not flow easily.
An "emergency blow" is a procedure used by military submarines to quickly rise to the surface in case of trouble. It involves using compressed air to pump out ballast water from its tanks.Suppose the submarine SSN Cthulhu has a displacement volume when fully submerged of 32000 m3. It is submerged with neutral buoyancy at a periscope depth of 30m when an emergency arises disabling its propulsion and other critical systems.Neglecting the pumped air’s density (much lower than that of water) and water resistance, what mass of water would this submarine have to pump out suddenly to make it to the surface in 30 seconds?
Answer:
Check the explanation
Explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
The chart shows data for a moving object.
Which conclusion is best supported by the information in
the chart?
The object has negative displacement
The object has negative acceleration
The object does not have displacement
The object is not accelerating
Answer:the object is not accelerating
Explanation:
There object is not accelerating since there's no increase in velocity
Final answer:
Based on the descriptions of graphical data, we can conclude that the object has negative acceleration because its velocity is decreasing over time while it is moving in the positive direction, or its negative velocity is increasing over time. Also, since the object is moving in the negative direction, it experiences a negative displacement.
Explanation:
The question asks about the motion of an object based on different graphical representations. To determine the nature of this motion, we can analyze the provided diagrams. In this case, we have descriptions of how the velocity changes over time, which allows us to infer acceleration, and acceleration is defined as the change in velocity over time. According to the information, the object experiences a decrease in positive velocity, which indicates a negative acceleration, as acceleration is in the opposite direction to the velocity. Furthermore, it is mentioned that the object has a negative velocity which increases in magnitude, coherently resulting in negative acceleration as well.
Acceleration is a vector quantity, meaning it has both direction and magnitude. Since we are discussing a coordinate system where to the right is considered positive, any acceleration towards the left will be considered negative. The graphs that indicate an object having a constant negative velocity also imply that the object has negative displacement over the time period, because it's moving in the negative direction of the coordinate system.
What is the gravitational potential energy of a 2.5kg object that is 300m above the surface of the earth? g=10m/s
Answer:
7350 J
Explanation:
Gravitational Potential Energy: This is defined as the energy possessed by a body due to it's position in the gravitational field. The S.I unit is Joules(J).
Applying,
E.p = mgh..................... Equation 1
Where E.p = Gravitational potential Energy, m = mass of the object, h = height of the object above the surface of the earth, g = acceleration due to gravity.
Given: m = 2.5 kg, h = 300 m
Constant: g = 9.8 m/s²
Substitute these values into equation 1
E.p = 2.5(300)(9.8)
E.p = 7350 J.
Lightning bolts can carry currents up to approximately 20 kA. We can model such a current as the equivalent of a very long, straight wire. You may want to review (Pages 926 - 929) . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Magnetic field of a single wire. Part A If you were unfortunate enough to be 4.9 m away from such a lightning bolt, how large a magnetic field would you experience? Express your answer using two significant figures. B1 = nothing T Request Answer Part B How does this field (B1) compare to one (B2) you would experience by being 4.9 cm from a long, straight household current of 10 A? Express your answer using two significant figures.
Given Information:
Current due to Lightning bolt = I₁ = 20 kA
Current of household = I₂ = 10 A
Distance = r₁ = 4.9 m
Distance = r₂ = 4.9 cm = 0.049 m
Required Information:
a) Magnetic field due Lightning bolt = B₁ = ?
b) Magnetic field due to household current = B₂ = ?
Answer:
a) Magnetic field due Lightning bolt = B₁ = 8.16×10⁻⁴ T
b) Magnetic field due to household current = B₂ = 4.08×10⁻⁵ T
B₁ = 20B₂
Explanation:
The magnetic field produced in a long straight wire carrying a current (I) at distance r is given by
B = μ₀I/2πr
Where μ₀ is the permeability of free space and its value is 4π×10⁻⁷
a) The magnetic field produced due to the lightning bolt current is
B₁ = μ₀I₁/2πr₁
B₁ = (4π×10⁻⁷*20,000)/2π*4.9
B₁ = 0.000816
B₁ = 8.16×10⁻⁴ T
Therefore, the strength of magnetic field due to the lightning bolt current is 8.16×10⁻⁴ T
b) The magnetic field produced due to the household current is
B₂ = μ₀I₂/2πr₂
B₂ = (4π×10⁻⁷*10)/2π*0.049
B₂ = 0.00004081
B₂ = 4.08×10⁻⁵ T
Therefore, the strength of magnetic field due to the household current is 4.08×10⁻⁵ T
The ratio of magnetic field produced by the lightning bolt current to the magnetic field produced by the household current is
B₁/B₂ = 8.16×10⁻⁴/4.08×10⁻⁵
B₁/B₂ = 20
B₁ = 20B₂
Which means that the magnetic field produced by the lightning bolt current is 20 time greater than the magnetic field produced by the household current.
a) The magnetic field due Lightning bolt will be 8.16×10⁻⁴ T
b)The magnetic field due to household current will be 4.08×10⁻⁵ T
What is a magnetic field?
It is the type of field where the magnetic force is obtained. With the help of a magnetic field. The magnetic force is obtained it is the field felt around a moving electric charge.
The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength .it is denoted by B.
a) The magnetic field due Lightning bolt will be 8.16×10⁻⁴ T
The magnetic field produced in a long straight wire carrying a current (I) at distance r is given by
B = μ₀I/2πr
Where μ₀ is the permeability of free space and its value is 4π×10⁻⁷
[tex]\rm B_1= \frac{\mu_0i_1}{2 \pi r} \\\\ \rm B_1= \frac{4 \pi \times 10^{-7} \times 20,00}{2 \times 3.14 4.9} \\\\ \rm B_1= 8.16 \times 10^{-4} \ T[/tex]
b) Magnetic field due to household current will be 4.08×10⁻⁵ T
[tex]\rm B_2= \frac{\mu_0i_2}{2 \pi r} \\\\ \rm B_2= \frac{4 \pi \times 10^{-7} \times 10}{2 \times 3.14 0.049} \\\\ \rm B_2= 4.08\times 10^{-5} \ T[/tex]
Hence the magnetic field due to household current will be 4.08×10⁻⁵ T
The magnetic field created by lightning bolt current divided by the magnetic field produced by home electricity equals
[tex]\rm \frac{B_1}{B_2} = \rm \frac{8.16 \times 10^{-4}}{4.08 c\times 10^{-5}} \\\\ \rm \frac{B_1}{B_2} = 20 \\\\[/tex]
That is, the magnetic field created by a lightning bolt current is 20 times stronger than the magnetic field produced by a home current.
Hence the magnetic field due to the Lightning bolt will be 8.16×10⁻⁴and the magnetic field due to household current will be 4.08×10⁻⁵ T.
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How do magnets act when they are near each other?
Answer:
Either repel or attract.
Explanation:
The hydraulic oil in a car lift has a density of 8.53 x 102 kg/m3. The weight of the input piston is negligible. The radii of the input piston and output plunger are 5.43 x 10-3 m and 0.135 m, respectively. What input force F is needed to support the 22600-N combined weight of a car and the output plunger, when (a) the bottom surfaces of the piston and plunger are at the same level, and (b) the bottom surface of the output plunger is 1.20 m above that of the input plunger
Answer:
(a) the input force is 36.56 N
(b) the input force is 37.49 N
Explanation:
Given;
density of hydraulic oil, ρ = 8.53 x 10² kg/m³
radius of plunger, r₁ = 0.135 m
radius of piston, r₂ = 5.43 x 10⁻³ m
Part (a) The input force needed to support 22600-N weight, when the bottom surfaces of the piston and plunger are at the same level;
[tex]P =\frac{F}{A}[/tex]
Where;
P is pressure
F is force
A is circular area = πr²
[tex]\frac{F_1}{A_1} =\frac{F_2}{A_2} \\\\F_2 = \frac{F_1*A_2}{A_1} =\frac{F_1* \pi r_2^2}{\pi r_1^2} = \frac{F_1* r_2^2}{ r_1^2} \\\\F_2 = \frac{22600*(5.43*10^{-3})^2 }{(0.135)^2}\\\\F_2 = 36.56 \ N[/tex]
Part (b) The input force needed to support 22600-N weight, when the bottom surface of the output plunger is 1.20 m above that of the input plunger
[tex]P_2 = P_1 + \rho gh[/tex]
But, F = PA and A = πr²
[tex]F_2 = F_1(\frac{A_2}{A_1} ) + \rho gh*A_2\\\\F_2 = F_1(\frac{r_2^2}{r_1^2} )+\rho gh(\pi r_2^2)\\\\F_2 = 22600(\frac{5.43*10^{-3}}{0.135})^2 \ + 853*9.8*1.2*\pi (5.43*10^{-3})^2\\\\F_2=36.56 + 0.93\\\\F_2 = 37.49 \ N[/tex]
The solution of this problem involves the use of Pascal's principle and a concept known as hydrostatic pressure.
First, let's identify the given parameters:
- The density (ρ) of the hydraulic oil is 8.53 x 10ˆ2 kg/m³
- The radius of the input piston is 5.43 x 10ˆ-3 m
- The radius of the output plunger is 0.135 m
- The total weight (W) being lifted is 22600 N
- The acceleration due to gravity (g) is approximately 9.81 m/s²
- The height difference (Δh) between the pistons is 1.2 m
We will use these in our calculations.
We begin by determining the areas of the input piston and the output plunger using the formula for the area of a circle A = πr². We denote the area of the input piston as Ain and the area of the output plunger as Aout.
Let's now focus on when the pistons are at the same level.
Part (a) requires us to find the input force (F) needed to support the weight of the car and output plunger. This is governed by Pascal's principle, which states that for an incompressible, non-viscous fluid in a hydraulic system, pressure is transmitted undiminished throughout the fluid and acts with equal force on all areas. Using Pascal's principle, the force required on the input piston is equal to the weight divided by the ratio of the areas. F = W * (Ain / Aout). After performing the calculation, we find that F equivales to approximately 36.562893827160494 N.
Next, let's turn to when the bottom surface of the output plunger is 1.2 m above the input piston.
Part (b) of the problem asks us to calculate the input force needed in this scenario. We must consider not only Pascal's principle but the additional hydrostatic pressure due to the height difference between the pistons. Firstly, we calculate the hydrostatic pressure difference (ΔP): ΔP = ρ * g * Δh. We then add this pressure difference to the force required when pistons were at the same level. Remember that pressure is force divided by area, thus when we add pressure we need to multiply it by the area of the input piston to maintain the units consistent. F = F_same_level + ΔP * Ain. The result of this calculation yields an input force of approximately 37.49208673165364 N.
In conclusion, the input force required to support the specified weight when the bottom surfaces of the pistons are at the same level is about 36.56 N. This force increases to roughly 37.49 N when the output plunger is pushed 1.2 m above the input piston due to the added hydrostatic pressure.
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At the bottom, deep bodies of water always measure 4°C, because at that temperature water has its highest [...] (fill in the physical quantity in question)
Answer:density
Explanation:
At the bottom, deep bodies of water always measure [tex]4^{\circ}C[/tex] because at that temperature water has it highest density .
In water bodies like lake warm water rises up due to convection and at higher depths there is cold water, which is found to be at highest density of water.
When water molecules acquired heat energy it become widely spread at the same volume and thus posses low density but at low temperature water molecule occupy less space therefore posses maximum density at [tex]4^{\circ}C[/tex]