The given standing wave on a string has a wavelength (λ) of 0.55 m, a frequency (f) of 24.54 Hz, a wave number (k) of 11.46 rad/m, and an angular frequency (ω) of 154.3 rad/s. The displacement of the bead at its position is given by the wave equation, and the maximum transverse speed (vy_max) is estimated to be approximately 0.4 m/s.
Length of the string (L) = 1.65 m
Amplitude of the traveling wave (A) = 3.65 mm
Speed of the traveling wave (vx) = 13.5 m/s
Distance of the first antinode from the left end (x) = 27.5 cm
Distance of the bead from the first antinode (d) = 13.8 cm
2. Finding the wavelength (λ):
Since the antinode is the point of maximum displacement, the first antinode is located at half the wavelength from the fixed end. Therefore,
λ = 2 * x = 2 * 0.275 m = 0.55 m
3. Finding the frequency (f):
We can use the relationship between wave speed, wavelength, and frequency:
v = λf
f = v / λ = 13.5 m/s / 0.55 m = 24.54 Hz
4. Finding the wave equation:
The equation for a standing wave on a string can be written as:
y(x, t) = A sin(kx) cos(ωt)
where:
k = wave number (k = 2π/λ)
ω = angular frequency (ω = 2πf)
5. Finding the wave number (k):
k = 2π/λ = 2π / 0.55 m = 11.46 rad/m
6. Finding the angular frequency (ω):
ω = 2πf = 2π * 24.54 Hz = 154.3 rad/s
7. Finding the displacement of the bead at its position:
The bead is located at x = x1 + d, where x1 is the distance of the first antinode from the left end (0.275 m) and d is the distance of the bead from the first antinode (0.138 m).
x1 + d = 0.275 m + 0.138 m = 0.413 m
Substitute this value of x in the wave equation:
y(0.413 m, t) = 3.65 mm * sin(11.46 rad/m * 0.413 m) * cos(154.3 rad/s * t)
8. Finding the maximum transverse speed (vy):
The maximum transverse speed occurs when the derivative of the displacement with respect to time (dy/dt) is at its maximum.
vy(t) = dy/dt = -Aω * cos(kx) sin(ωt)
The maximum value of sin(ωt) is 1, and the maximum value of cos(kx) depends on the position of the bead. Since the bead is not at a node or antinode, cos(kx) will not be 0 or 1.
Therefore, the maximum transverse speed (vy_max) can be estimated as:
vy_max ≈ Aω ≈ 3.65 mm * 154.3 rad/s ≈ 0.4 m/s
How much force is required to accelerate a 50 kg with a mass at 4 m/s2?
Answer:200N
Explanation:
Mass=50kg
Acceleration=4m/s^2
Force=mass x acceleration
Force=50 x 4
Force=200N
A charge of 4.5 × 10-5 C is placed in an electric field with a strength of 2.0 × 104 StartFraction N over C EndFraction. If the charge is 0.030 m from the source of the electric field, what is the electric potential energy of the charge?
Answer:
0.027 J
Explanation:
The electric potential energy of the charge is given by:
[tex]U=qEd[/tex]
where:
q is the magnitude of the charge
E is the strength of the electric field
d is the distance of the charge from the source of the field
In this problem, we have:
[tex]q=4.5\cdot 10^{-5}C[/tex] is the charge
[tex]E=2.0\cdot 10^4 V/m[/tex] is the strength of the field
d = 0.030 m is the distance of the charge
So, its electric potential energy is
[tex]U=(4.5\cdot 10^{-5})(2.0\cdot 10^4)(0.030)=0.027 J[/tex]
Answer:
.027 J
Explanation:
Does reflection occur when a wave bounces off a surface that cannot pass through
Answer: yes
Explanation: bc
Based on the idea of isostasy, which of these statements is NOT correct?
A) Continental crust is less dense than oceanic crust.
B) The depth at which a crustal plate sits is a function of its mass.
C) When more weight is added to the crust, through a process like mountain building, it slowly sinks deeper into the mantle.
D) The formation ice sheets cause the Earth's surface to sink so much that when the ice melts, the crust and mantle does not rebound.
The formation ice sheets cause the Earth's surface to sink so much that when the ice melts, the crust and mantle does not rebound.
Explanation:
The above-mentioned statement is the only false statement
During the Ice ages, large continental parts were covered under thick ice sheets. This imposed a superincumbent additional load on the Earth's crust.
Isostasy refers to the balance that exists between parts of Earth's mantle and crust. Isostatic adjustments are a common phenomenon. As a result of isostatic adjustments, several parts of the world have risen by as much as 900 feet as an adjustment to superincumbent load since ice ages. E.g. Parts of Scandinavian countries have witnessed these activities and also undergoing this process.
Answer: d
Explanation:
The circumference of the earth is 40,000 km. The distance from the
North Pole to the equator is 1/4 of the circumference of the earth, which equals __ m.
Answer:
The distance from the North Pole to the equator is [tex]1*10^{7}[/tex]m.
Explanation:
Circumference of Earth = 40,000 km ......................(1)
Distance from the North Pole to the Equator is = 1/4th of the Circumference of Earth ...................... (2)
Let Distance from the North Pole to the Equator be d ,
the equation formed will be ,
d = 1/4 * Circumference of Earth ........(3)......... ( from equation 1 )
put the value of Circumference of Earth in equation (3),
d = 1/4 * 40,000 km
d = 10,000 km
converting km to m ,
d = 10,000 * [tex]10^{3}[/tex] m
d = 1 * [tex]10^{7}[/tex] m
The distance from the North Pole to the equator is [tex]1*10^{7}[/tex]m.
The distance from the North Pole to the equator is 1/4 of the Earth's circumference, which equals 10,000,000 meters.
Explanation:The distance from the North Pole to the equator is 1/4 of the circumference of the earth. Given that the circumference of the earth is 40,000 kilometers, we can calculate this by dividing the circumference by 4. So, 40,000 km ÷ 4 = 10,000 km. To convert this into meters, we multiply by 1,000 (since there are 1,000 meters in a kilometer), thus 10,000 km × 1,000 = 10,000,000 meters. The distance from the North Pole to the equator is 1/4 of the circumference of the earth. The circumference of the earth is 40,000 km, so 1/4 of that distance would be 10,000 km.
gravity has traditionally been defined as a force of attraction between things that have
The gravity has traditionally been defined as a force of attraction between things that have masses.
Explanation:
Gravitational force is a type of attractive force. It is because of this force, that we are able to walk on this Earth. Also due to gravitational force, the solar system and the galaxies are existing in the universe. Sir Issac Newton first discovered this force. He postulated the universal law of gravity. And according to this law, the gravitational force will be acting between the objects having masses and separated by a distance. So in this law, it states that gravitational law is directly proportional to the product of masses and inversely proportional to the square of the distance between them.
Thus, the gravity has traditionally been defined as a force of attraction between things that have masses.
What are the advantages of parallel circuits? Check all that apply.
If one bulb goes out, the other bulbs go out.
If one bulb goes out, the other bulbs stay lit.
If there is a break in one branch of the circuit, current can still flow through the other branches.
If there is a break in one branch of the circuit, current cannot flow at all.
Parallel circuits are simple to design and build,
O Parallel circuits are complicated to design and build.
The correct answer is option (1) and (2). The advantages of parallel circuits include If one bulb goes out, the other bulbs stay lit and If there is a break in one branch of the circuit, current can still flow through the other branches.
Parallel circuits offer several advantages, and you should check the statements that accurately reflect these benefits.
Here are the advantages of parallel circuits:
1. If one bulb goes out, the other bulbs stay lit.
Correct. In a parallel circuit, each component is connected across the same voltage source. Therefore, if one component fails, the others continue to function.2. If there is a break in one branch of the circuit, current can still flow through the other branches.
Correct. In a parallel circuit, each branch operates independently. A break in one branch does not affect the operation of the other branches.3. Parallel circuits are simple to design and build.
Incorrect. While parallel circuits offer certain advantages in terms of reliability and consistent voltage, they are not necessarily simpler to design compared to series circuits. The complexity can increase with the number of branches and components.4. Parallel circuits are complicated to design and build.
Correct. Parallel circuits can be more complex to design and build than series circuits, especially as the number of branches increases. The design must ensure proper connections and consider the current distribution across each branch.5. If one bulb goes out, the other bulbs go out.
Incorrect. This statement applies to series circuits, not parallel circuits. In a series circuit, if one component fails, the entire circuit is interrupted.6. If there is a break in one branch of the circuit, current cannot flow at all.
Incorrect. In a parallel circuit, a break in one branch does not stop current from flowing through the other branches. Each branch operates independently of the others.The complete question is:
What are the advantages of parallel circuits? Check all that apply.
1. If one bulb goes out, the other bulbs go out.
2. If one bulb goes out, the other bulbs stay lit.
3. If there is a break in one branch of the circuit, current can still flow through the other branches.
4. If there is a break in one branch of the circuit, current cannot flow at all.
5. Parallel circuits are simple to design and build,
6. Parallel circuits are complicated to design and build.
name the three basic types of playing positions used in a basketball game.
Answer:
point guard, center, middle
Explanation:
The magnitudes of the vertical and horizontal components of a vector are 11 and 17 centimeters respectively. Find the magnitude of the vector and the angle from the horizontal axis.
Explanation:
let the magnitude of the vector be |A|
|A| = ✓11^2 + 17^2 =
|A| =✓410
|A| = 20.23
theta =Tan^-1(11/17) =32.91°
Explanation: edmentum answer
A car accelerates from 20mi/hr to 60mi/hr. How many times greater is the car's kinetic energy at the higher speed compared to the kinetic energy at the slower speed
Answer:
9 times
Explanation:
Kinetic energy is:
KE = ½ mv²
When we triple the velocity, the kinetic energy increases by a factor of 9.
9KE = ½ m(3v)²
The kinetic energy of the car at 60 m/hr is 9 times greater than the kinetic energy at 20 m/hr.
What do you mean by kinetic energy?Kinetic energy is a form of energy that an object possesses by virtue of its motion and is dependent on the mass and velocity of the object.
The kinetic energy of an object is given by the equation:
KE = (1/2)mv²
Where
KE = is the kinetic energy,
m = is the mass of the object,
v = its velocity.
Here in this question,
The kinetic energy of an object is proportional to the square of its velocity, so if a car accelerates from 20 km/hr to 60 km/hr, its kinetic energy at the higher speed will be:
KE(higher) = 1/2 ×m × v(higher)²
And at the lower speed, the kinetic energy will be:
KE(lower) = 1/2 ×m × v(lower)²
Where
m = the mass of the car.
Now for ratio, we have to divide the two equations:
KE(higher) / KE(lower) = [1/2× m ×v(higher)²] / [1/2 × m × v(lower)²]
The mass of the car cancels out, leaving us with:
KE(higher) / KE(lower) = (v(higher)²) / (v(lower)²)
Now, we get:
KE(higher) / KE(lower) = (60²) / (20²) = 9
Therefore, the kinetic energy of the car which is moving at a speed of 60 m/hr is 9 times greater than the kinetic energy of the car which is moving at 20 m/hr.
To learn about the conversion of Kinetic energy click:
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Compare the magnitude of the electromagnetic and gravitational force between two electrons separated by a distance of 2.00 m. Assume the electrons have a mass of 9.11 × 10–31 kg and a charge of 1.61 × 10–19 C. Round to two decimal places
Answer:
1) 5.83
2) 1.38
3) 4.22
Explanation:
The electrostatic force exerted tow electrons on each other is equal to 5.83 × 10⁻²⁹ N. The gravitational force is 1.38 × 10⁻⁷¹ N.
What is coulomb's law?According to this law, the force of attraction between two charged particles can be written as the product of their charges on them and is the inverse of the square of the distance by which they are separated.
The magnitude of the electrostatic force between charges is given by:
[tex]\displaystyle F = k\frac{q_1q_2}{r^2}[/tex]
where k has a value of 8.99 × 10⁹ N.m²/C².
Given the charge on one electron, q₁ = q₂ = 1.61 × 10⁻¹⁹
The distance between these two electrons, r = 2.00 m
The magnitude of electric force between the electrons will be:
F = 8.99 × 10⁻⁹ × (1.61 × 10⁻¹⁹)²/ (2.00)²
F = 5.83 × 10⁻²⁹ N
The gravitational force between two electrons is equal to:
[tex]\displaystyle F = G\frac{m_1m_2}{r^2}[/tex]
F' = 6.674 × 10⁻¹¹ × (9.1 × 10⁻³¹)²/ (2.00)²
F' = 1.38 × 10⁻⁷¹ N
F/F' = 4.23 × 10⁴² N
Learn more about Coulomb's law, here:
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what is the resistance of a conductor
Opposition for the current flow
Explanation:
Resistance is defined as the ability pf the conductor to oppose the flow of electrons through it. It is usually represented in Ohm.Resistance is an important parameter in a circuit design and it should be properly designed.Resistance of a conductor depends upon the material nature, length of the conductor and area of cross section. In conductor, Resistance is low. It is due to that charges flow through the conductor freely.
A certain microwave has a
wavelength of 0.032 meters. Calculate the frequency of this
microwave
Answer:
[tex]9.375\times 10^{9} Hz[/tex]
Explanation:
Frequency is mathematically defined as the quotient of speed divided by wavelength.
[tex]Frequency= \frac {v}{W}[/tex]
where
v-is the speed of light
-w is wavelength.
Given the speed of the wave as [tex]V=300000000 \ m/s[/tex] and the wavelength [tex]\lambda= 0.032\ m[/tex], we substitute these values in the Frequency function to solve for frequency:
[tex]Frequency=\frac {300000000}{0.032}=9375000000 Hz=9.375\times 10^{9} Hz[/tex]
Hence, the wave's frequency is [tex]9.375\times 10^9\ Hz[/tex]
Microwave has the wavelength of 0.032 meters so, the frequency is [tex]\rm 9.375\times 10^9 \; Hz[/tex] and this will be determined by using the frequency formula.
Given :
Wavelength = 0.032 m
The Formula of Frequency can be used to determine the wavelength of the microwave:
[tex]\rm Frequency = \dfrac{c}{w}[/tex] --- (1)
where, [tex]\rm c = 3 \times 10^8\;m/sec[/tex] is the speed of light and w is the wavelength.
Now, put the values of speed of light (c) and wavelength (w) in equation (1).
[tex]\rm Frequency = \dfrac{3\times 10^8}{0.032}[/tex]
[tex]\rm Frequency = 9.375\times 10^9 \; Hz[/tex]
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Based on the Law of Conservation of Matter, describe the relationship between the mass of the reactants and the mass of the products.
The truck’s motor is creating 500 N of thrust, but air resistance is placing 500 N in the opposite direction
A tuning fork vibrating at 512 Hz is held near one end of a tube of length that is open at both ends, as shown above. The column of air in the tube resonates at its fundamental frequency. The speed of sound in air is 340 m/s. Calculate the length of the tube.
Answer:
Length of the pipe is 33.2 cm
Explanation:
As we know that the frequency of the sound in open end pipe is given as
[tex]f = \frac{v}{2L}[/tex]
so here we will have
f = 512 Hz
v = 340 m/s
so now we have
[tex]512 = \frac{340}{2L}[/tex]
[tex]L = \frac{170}{512}[/tex]
[tex]L = 33.2 cm[/tex]
Final answer:
To calculate the length of a tube open at both ends with a given frequency and speed of sound, we can rearrange the formula ν = v / (2L) and solve for L, giving a length of 0.332 m for a 512 Hz tuning fork.
Explanation:
A tuning fork vibrating at 512 Hz is held near one end of a tube of length that is open at both ends. The tube resonates at its fundamental frequency. To calculate the length of the tube given the speed of sound in air is 340 m/s, we use the formula for the fundamental frequency of a tube open at both ends, which is ν = v / (2L), where ν is the frequency (512 Hz), v is the speed of sound (340 m/s), and L is the length of the tube we are looking for.
Rearranging the formula, we get L = v / (2ν). Plugging in the numbers, L = 340 m/s / (2 × 512 Hz) = 0.33203125 meters, which can be rounded to 0.332 m or 33.2 cm.
g of potassium reacts with 16 g of oxygen to produce 94 g of potassium oxide
Answer:
78g
Explanation:
Given parameters:
Mass of oxygen gas = 16g
Mass of potassium oxide = 94g
Unknown:
Mass of reacting potassium = ?
Solution:
To solve this problem, we need to obtain a balanced reaction equation. Then determine the number of moles of the reactant and use it to find that of the other one.
Balanced equation:
4K + O₂ → 2K₂O
Number of moles of reacting oxygen;
Number of moles = [tex]\frac{mass}{molar mass}[/tex]
molar mass of O₂ = 2 x 16 = 32g/mole
Number of moles = [tex]\frac{16}{32}[/tex] = 0.5mole
From the reaction equation;
4 mole of K reacted with 1 mole of O₂;
x mole of K will react with 0.5 mole of O₂
Therefore, 4 x 0.5 = 2 moles of potassium.
Mass of potassium = number of moles x molar mass
Molar mass of potassium = 39g
Mass of potassium = 2 x 39 = 78g
Circuit that has only one path for the current to follow
Answer:
Series circuit
Explanation:
The type of circuit can be divided into series and parallel. In the series circuit, there is only one loop/path. If the path is cut or stopped, the current of the circuit will be stopped completely. A parallel circuit has more than one loops. This means the circuit has alternative paths that it can travel in case that one path is blocked or cut. This alternative path makes the parallel circuit have a lower resistance compared to the series.
Need help pls (projectiles)
A) 13.13 m (4.13 m above the top of the ramp)
B) 0.92 s, 30.0 m (14.4 m from the top of the ramp)
Explanation:
A)
The motion of the projectile consists of two independent motions:
- A uniform motion along the horizontal direction (constant horizontal velocity)
- A uniformly accelerated motion along the vertical direction (constant downward acceleration)
To find the maximum height, we just analyze the vertical motion.
The initial vertical velocity of the projectile is given by:
[tex]u_y = u sin \theta = (18)(sin 30^{\circ})=9 m/s[/tex]
Where
u = 18 m/s is the initial velocity
[tex]\theta=30^{\circ}[/tex] is the angle of projection
Since this is a uniformly accelerated motion, we can use the following suvat equation:
[tex]v_y^2-u_y^2=2as[/tex]
where:
[tex]v_y=0[/tex] is the final vertical velocity when the projectile reaches the maximum height
[tex]a=-g=-9.8 m/s^2[/tex] is the acceleration due to gravity (negative because it is downward)
s is the vertical displacement
Re-arranging, we find s:
[tex]s=\frac{v_y^2-u_y^2}{2a}=\frac{0^2-(9)^2}{2(-9.8)}=4.13 m[/tex]
However, this is the vertical displacement above the top of the ramp. We see that the ramp is [tex]d=15.6 m[/tex] long in the horizontal direction, so the height of the ramp is
[tex]h=d tan \theta=(15.6)(tan 30^{\circ})=9m[/tex]
So, the maximum height of the projectile is:
[tex]H=h+s=9+4.13 = 13.13 m[/tex]
B)
To find the time at which the projectile reaches the maximum height, we use another suvat equation:
[tex]v_y=u_y + at[/tex]
where:
[tex]v_y=0[/tex] is the vertical velocity at the maximum height
[tex]a=-9.8 m/s^2[/tex] is the acceleration due to gravity
[tex]u_y = 9 m/s[/tex] is the initial vertical velocity
Solving for t, we find the time:
[tex]t=\frac{v_y-u_y}{a}=\frac{0-9}{-9.8}=0.92 s[/tex]
The horizontal position of the projectile instead is given by the equation for uniform motion:
[tex]x(t)=v_x t[/tex]
where:
[tex]v_x = u cos \theta = (18)(cos 30^{\circ})=15.6 m/s[/tex] is the initial horizontal velocity
Substituting t = 0.92 s, we find:
[tex]x=(15.6)(0.92)=14.4 m[/tex]
So, this is the horizontal distance covered from the top of the ramp at the instant of maximum height; and therefore, the horizontal distance from the beginning of the ramp is
[tex]d=15.6+14.4=30.0 m[/tex]
Please need help on this one
Answer:
B) 5
Explanation:
Pedigree charts can be read like family trees, and you can trace a trait through families. Squares usually refer to males, and circles refer to females. Shaded shapes usually refer to the presence of a specific trait, whereas blank shapes are those who do not possess the trait of interest.
The horizontal line between 1 and 2 shows that these individuals have had offspring.
If you follow that vertical line down to the next level, you can see it forms 5 branches - to individuals 3, 5, 7, 8 and 10. Therefore, 1 and 2 had five offspring.
Then, individual 3 had two children with individual 4 (see the horizontal line) - individuals 11 and 12.
Individual 5 had three children with individual 6 - individuals 13, 14, and 15.
Individual 7 did not have any children. Neither did individual 8
Individual 10 had four children with individual 9 - individuals 16, 17, 18 and 19.
2 characteristics of constant speed
Answer:
it has no acceleration
Explanation:
What is the acceleration of the object?
Answer:
Explanation:
Velocity is changing by a constant amount -10 m/s-in second of time.Anytime an object's velocity is changing,the object is said to be accelerating;it has an acceleration.
Answer:
[tex]\boxed{\mathrm{view \ explanation}}[/tex]
Explanation:
[tex]\displaystyle Acceleration =\frac{change \ in \ velocity}{elapsed \ time}[/tex]
[tex]\displaystyle A=\frac{V_f-V_i}{t}[/tex]
Explain how water freezing and thawing causes weathering and the type of weathering it would be considered.
Final answer:
Water freezing and thawing causes weathering through a process called frost or ice wedging. This leads to the physical weathering of rocks or soil. In areas with frequent freeze-thaw cycles, such as Iceland, this process can gradually break down rocks into smaller pieces.
Explanation:
Water freezing and thawing can cause weathering through a process called frost or ice wedging. When water freezes, it expands by about 9%, exerting pressure on the rocks or soil in which it is trapped. This pressure can cause the rocks to crack or break apart, leading to physical weathering. As the ice thaws, water seeps into the cracks and when it freezes again, it widens the cracks further, gradually breaking down the rock. This type of weathering is known as mechanical weathering. It is a significant process in areas with frequent freeze-thaw cycles.
Example: In regions with colder climates, such as Iceland, freezing and thawing of water can weather rocks over time. The repeated cycles of freezing and thawing cause the rocks to deteriorate and break down into smaller pieces, contributing to the formation of gravel, sand, and clay.
WILL GIVE BRAINIEST! Considered together, kinetic and potential energy on a macroscopic scale are known as what
A mechanical energy
B light energy
C internal energy
D thermal energy
This is may mastering physics homework and I just need help solving the question.
Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can be modeled as a 4.0-m-diameter disk with a weight of 1500 N. Luc's body can be modeled as a uniform 40-cm-diameter cylinder with massless arms extending to hands that are 85 cm from his center. The merry-go-round is coasting at a steady 27 rpm when Luc brings his hands in to his chest.
Answer:
Angular speed of the disc after he fold his hands is given as
[tex]\omega_f = 27.5 rpm[/tex]
Explanation:
As we know that the moment of inertia of the solid cylinder is given as
[tex]I_1 = \frac{m_1r_1^2}{2}[/tex]
so we have
[tex]I_1 = \frac{(950/9.81)(0.20)^2}{2}[/tex]
[tex]I_1 = 1.94 kg m^2[/tex]
now moment of inertia of two dumbbell in his hand is given as
[tex]I_2 = 2(m_2 r_2^2)[/tex]
[tex]I_2 = 2(4)(0.85)^2[/tex]
[tex]I_2 = 5.78 kg m^2[/tex]
Now moment of inertia of the disc is given as
[tex]I_3 = \frac{1}{2}MR^2[/tex]
[tex]I_3 = \frac{1}{2}(1500/9.81)(2^2)[/tex]
[tex]I_3 = 305.8 kg m^2[/tex]
Now we can use angular momentum conservation as there is no external torque on it
[tex](I_1 + I_2 + I_3) \omega_i = (I_1 + I_3)\omega_f[/tex]
[tex](1.94 + 5.78 + 305.8) 27 = (1.94 + 305.8) \omega_f[/tex]
[tex]\omega_f = 27.5 rpm[/tex]
Answer: Hello above answerer, Why didn't you add I2 on the other side of the equation?
You just added I1 and I3
Explanation:
one cubic foot of water can store 312btu. a home requires 100,000 what is the volume
Volume of water required to store 100,000 Btu of thermal energy is [tex]320.51foot^{3}[/tex] .
Explanation:
The complete question is : One cubic foot of water can store 312 Btu of thermal energy. On a cold winter day a well-constructed home may require 100,000 Btu of nighttime space heating. What is the volume of water required to store this energy? In this question , it's given that One cubic foot of water can store 312 Btu of thermal energy or 312 Btu takes 1 cubic foot of water ,So
1 Btu takes [tex]\frac{1}{312}[/tex] cubic foot of water
Therefore, 100,000 Btu takes:
⇒ [tex]volume = \frac{1}{312}(100,000)[/tex] [tex]foot^{3}[/tex]
⇒ [tex]volume = \frac{100,000}{312}[/tex] [tex]foot^{3}[/tex]
⇒ [tex]volume = 320.51[/tex] [tex]foot^{3}[/tex]
∴ Volume of water required to store 100,000 Btu of thermal energy is [tex]320.51foot^{3}[/tex] .
1. Identify whether the following statements describe a change in acceleration. Explain your response.
a. A car stopped at a stop sign.
b. A boat traveling east at 10 knots.
c. An airplane traveling north 600 miles per hour.
d. A person running at 5 meters/second along a curving path.
Answers:
a. Change in acceleration
b. Not change in acceleration.
c. Not change in acceleration.
d. Change in acceleration
Explanation:
Let's begin by explaining what acceleration is:
Acceleration [tex]a[/tex] is initially defined as the variation of Velocity [tex]\Delta V[/tex] in time [tex]\Delta t[/tex]:
[tex]a=\frac{\Delta V}{\Delta t}[/tex]
However, we cannot forget acceleration is a vector quantity as well (like velocity) and as a vector it has magnitude and direction.
So, when one of these aspects changes (or both) acceleration changes as well.
In other words: A change in acceleration implies the change in velocity, or a change in direction, or both.
Having this clear, we can identify the statements that describe a change in acceleration:
a. A car stopped at a stop sign.
Change in acceleration, since the car changed its velocity.
b. A boat traveling east at 10 knots.
Not a change in acceleration, since the boat is travelling at a constant velocity and is not changing its direction.
c. An airplane traveling north 600 miles per hour.
Not a change in acceleration, since the airplane is travelling at a constant velocity and is not changing its direction.
d. A person running at 5 meters/second along a curving path
Change in acceleration, since the person is changing its direction in the curving path.
Which of the following materials offer the least electrical resistance? Pure water, wood, salt water, glass
Salt water offers the least electrical resistance.
Explanation:
Least electrical resistance indicates that any material which readily allows the electric current through itself, and shows more conductivity.
Here pure water doesn't contain any ions, so it is a bad conductor.
Wood and glass are also bad conductors of electricity.
Salt water contains ions, which conducts electricity which means it shows least electrical resistance.
Answer:
salt water
Explanation:
If an object's mass is decreasing while a constant force is applied to the object, would its acceleration decrease, increase, or remain the same?
Answer:
increase
Explanation:
We need to find what change takes place to the acceleration of the object in the given situation.
The acceleration of the object would increase.
m = Mass of the object
a = Acceleration of the object
Force is given by
[tex]F=ma[/tex]
Acceleration would be
[tex]a=\dfrac{F}{m}[/tex]
It is given that force is constant so
[tex]a\propto \dfrac{1}{m}[/tex]
This means that acceleration is inversely proportional to mass.
Here, the mass is decreasing so the acceleration will increase.
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Jo lifts a 330 N cement block 3.6 m (using a system of pulleys) by pulling 16 m of rope with a force of 121 N.
a. What is the mechanical advantage of the pulley system?
b. What is the work input?
c. What is the work output?
d. What is the efficiency of the machine?
Answer:
a) Mechanical advantage: 2.7b) Work input: 1,936Jc) Work ouput: 1,188Jd) Efficieny: 0.61Explanation:
a. Mechanical advantage
The mechanical advantage of a system of pulleys is the ratio of the ouput force (weight of the object) to the input force (pulling force):
Mechanical advantage = output force / input forceMechanical advantage = 330N/ 121N = 2.727 ≈ 2.7b. Work input
Work is the product of the force applied by the distance traveled in the same direction:
Work input = Input force × input distance = 121N × 16m = 1,936Jc. Work output
Using the law of conservation of energy, the work output is equal to the change in the potential energy of the block:
ΔPotential energy = mass × g × heightΔPotential energy = weight × height = 330N × 3.6m = 1,188JWork output = 1,188Jd. Efficiency
The efficiency is the ratio of the work output to the work input:
Efficiency = Work input / Work outputEfficiency = 1,188J / 1,936J = 0.61You can check that the efficiency is also the ratio of the mechanical advantage to the ideal mechanical advantage
The ideal mechanical advantage is equal to the ratio of the input distance (pulling distance) to the output distance (lift distance):
Ideal mechanical advantage = 16m/3.6m = 4.444Efficiency = mechanical advantage / ideal mechanical advantageEfficiency = 2.727 / 4.444 = 0.61