(a) -1.208 m
The position of the particle at time t is given by
[tex]x(t) = x_0 + v_0 t + \frac{1}{2}at^2[/tex]
where:
[tex]x_0 = 0.250 m[/tex] is the initial position
[tex]v_0 = 0.050 m/s[/tex] is the initial velocity
[tex]a=-0.240 m/s^2[/tex] is the acceleration
Substituting into the equation t=3.70 s, we find the position after 3.70 seconds:
[tex]x(3.70 s) = 0.250 m + (0.050 m/s)(3.70 s) + \frac{1}{2}(-0.240 m/s^2)(3.70 s)^2=-1.208 m[/tex]
(b) -0.838 m/s
The velocity of the particle at time t is given by:
[tex]v(t) = v_0 + at[/tex]
where
[tex]v_0 = 0.050 m/s[/tex] is the initial velocity
[tex]a=-0.240 m/s^2[/tex] is the acceleration
Substituting t = 3.70 s, we find the velocity after 3.70 seconds:
[tex]v(3.70 s) = 0.050 m/s + (-0.240 m/s^2)(3.70 s)=-0.838 m/s[/tex]
How does weight change as the gravitational acceleration changes and why?
Answer
The correct formula for weight is F = m*g where g is the gravitational acceleration.
All over the earth's surface, g is slightly different. The mass does not change no matter where you are. We should be measuring out weights in Newtons, not in kg. So the unit of weight in the metric system is 9.8 about * mass in kg.
Stop reading. This is your answer.
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Notes
It was hard enough to get people to change over to kg never mind newtons. Canada, which is on the metric system, still gives the price of food in pounds. Or if not, in grams if the container is small enough.
Cashews cost 19$ Canadian per 906 grams which is roughly 2 pounds.
Oranges are $1.27 a pound and that is the way they are listed in Walmart.
10 pounds of potatoes are 4.95 dollars.
I'm sure you get the point. We use kg for certain things and retain pounds for others.
A negatively charged particle is moving to the right, directly above a wire have a current flowing to the right. In which direction is the magnetic force exerted on the particle?A) into the pageB) downwardC) upwardD) out of the page
Answer:
C) upward
Explanation:
The problem can be solved by using the right-hand rule.
First of all, we notice at the location of the negatively charged particle (above the wire), the magnetic field produced by the wire points out of the page (because the current is to the right, so by using the right hand, putting the thumb to the right (as the current) and wrapping the other fingers around it, we see that the direction of the field above the wire is out of the page).
Now we can apply the right hand rule to the charged particle:
- index finger: velocity of the particle, to the right
- middle finger: direction of the magnetic field, out of the page
- thumb: direction of the force, downward --> however, the charge is negative, so we must reverse the direction --> upward
Therefore, the direction of the magnetic force is upward.
The magnetic force exerted on a negatively charged particle, moving in the same direction as the current, would be downward according to the left-hand rule in Physics.
Explanation:In this scenario, we can use the left-hand rule, as it's relevant to the movement and force applied on negatively charged particles in a magnetic field. To apply the left-hand rule, point your thumb in the direction of the particle's velocity (right), and your fingers in the direction of the current (also right). This should make your palm face downward. Hence, a negatively charged particle moving right, with the current also flowing right, would experience a magnetic force directed downward. So, the correct answer is B) Downward.
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How are limiting factors related to carrying capacity
Limiting factors are resources or other factors in the environment that can lower the population growth rate. ... The carrying capacity (K) is the maximum population size that can be supported in a particular area without destroying the habitat. Limiting factors determine the carrying capacity of a population.
Limiting factors are environmental conditions that hinder the increase of a certain population in an ecosystem. On the other hand, carrying capacity is the highest population size that an environment can sustain. These two are related in that the limiting factors determine an environment's carrying capacity.
Explanation:In biology, limiting factors are conditions in an environment that limit the growth or survival of a population within an ecosystem. Examples include scarcity of food, insufficient habitat space, or occurrence of diseases. Carrying capacity, denoted as K, on the other hand, is the maximum population size that a particular environment can sustain indefinitely, given the food, habitat, water, and other necessities available in that environment.
Warehousing factors and carrying capacity are intimately connected: the occurrence of limiting factors affects the carrying capacity of an environment. When a given population reaches its carrying capacity, the limiting factors cause the growth rate to slow down and eventually settle at a plateau. Therefore, these limiting factors play a critical role in determining and regulating an environment's carrying capacity. Summer weather conditions, for example, might lead to the proliferation of a particular resource, boosting an environment's carrying capacity for that year.
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A ____ is the time required for one half of the nuclei in a radio- ____ isotope to decay.
Answer:
A half-life is the time required for one half of the nuclei in a radio- active isotope to decay.
Explanation:
A radio-active isotope is an isotope which undergoes radioactive decay.
Radioactive decay is a spontaneous process in which the nucleus of an atom changes its state (turning into a different nucleus, or de-exciting), emitting radiation, which can be of three different types: alpha, beta or gamma.
The half-life of a radio-active isotope is the time required for half of the nuclei of the initial sample to decay.
The law of radio-active decay can be expressed as follows:
[tex]N(t) = N_0 (\frac{1}{2})^{t/t_{1/2}}[/tex]
where
N(t) is the number of undecayed nuclei left at time t
N0 is the initial number of nuclei
t is the time
[tex]t_{1/2}[/tex] is the half-life
We see that when [tex]t=t_{1/2}[/tex] (that means, when 1 half-life has passed), the number of undecayed nuclei left is
[tex]N(t) = N_0 (\frac{1}{2})^{t_{1/2}/t_{1/2}}=N_0 (\frac{1}{2})^1=\frac{N_0}{2}[/tex]
So, half of the initial nuclei.
Theory that many different realities are happening at once True or false
Well, there is string theory, which proposes many ideas, one of them pertaining to the idea that there’s multiple universes. Though they’re still trying to figure out whether it’s true, which is difficult.
That's a hypothesis. So far, it hasn't been possible to test it, so it hasn't become a theory yet.
Which of the following statements are true regarding electromagnetic waves traveling through a vacuum? (Select all that apply.) All waves have the same wavelength. All waves have the same frequency. All waves travel at 3.00 108 m/s. The electric and magnetic fields associated with the waves are perpendicular to each other and to the direction of wave propagation. The speed of the waves depends on their frequency.
Correct choices:
- All waves travel at 3.00 108 m/s.
- The electric and magnetic fields associated with the waves are perpendicular to each other and to the direction of wave propagation.
Explanation:
Let's analyze each statement:
- All waves have the same wavelength. --> FALSE. Electromagnetic waves have a wide range of wavelengths, from less than 10 picometers (gamma rays) to hundreds of kilometers (radio waves)
- All waves have the same frequency. --> FALSE. As for the wavelength, electromagnetic waves have a wide range of frequencies also.
- All waves travel at 3.00 108 m/s. --> TRUE. This value is called speed of light, and it is one of the fundamental constant: it is the value of the speed of all electromagnetic waves in a vacuum.
- The electric and magnetic fields associated with the waves are perpendicular to each other and to the direction of wave propagation. --> TRUE. Electromagnetic waves are transverse waves, which means that their oscillations (represented by the electric field and the magnetic field) occurs perpendicularly to the direction of motion of the wave.
- The speed of the waves depends on their frequency. --> FALSE. In a vacuum, the speed of ALL electromagnetic waves is always equal to c, regardless of the frequency.
Answer:
option C and D
Explanation:
Electromagnetic waves can travel in vacuum as well as in a medium. The different waves have different frequency and wavelength but have same speed in vacuum (3.00 x 10⁸ m/s).
These waves carry the energy via oscillating electric and magnetic fields. The electric and magnetic fields oscillate perpendicular to each other and to the direction of motion of the wave.
A bumblebee flying through the air picks up a net charge of +40 pC, due in part to the triboelectric effect (charge transfer by friction) from collision with small dust particles*. The presence of this positive charge on their bodies helps the bumblebees locate negatively charged flowers when foraging for pollen and nectar**. The natural electric field near the surface of the Earth has an average magnitude of 120 N/C and is directed downward. The mass of a typical bumblebee is 0.10 grams. Calculate the ratio of the Coulomb force on the bee to the gravitational force on the bee. Note that (1pC = 10^{-12} C)(1pC=10 −12 C). [For small number answers, use the scientific “E” notation : 0.0076 = 7.6E-3 ]
Answer:
[tex]4.9\cdot 10^{-6}[/tex]
Explanation:
The Coulomb force on the bee is:
[tex]F_E=qE[/tex]
where
[tex]q=40 pC=40\cdot 10^{-12} C[/tex] is the charge of the bee
[tex]E=120 N/C[/tex] is the magnitude of the electric field
Substituting into the formula,
[tex]F_E=(40\cdot 10^{-12} C)(120 N/C)=4.8\cdot 10^{-9} N[/tex]
The gravitational force on the bee is
[tex]F_G = mg[/tex]
where
[tex]m=0.10 g=1\cdot 10^{-4}kg[/tex] is the bee's mass
[tex]g=9.8 m/s^2[/tex] is the gravitational acceleration
Substituting into the formula,
[tex]F_G = mg=(1\cdot 10^{-4}kg)(9.8 m/s^2)=9.8\cdot 10^{-4} N[/tex]
So, the ratio between the two forces is
[tex]\frac{F_E}{F_G}=\frac{4.8\cdot 10^{-9} N}{9.8\cdot 10^{-4} N}=4.9\cdot 10^{-6}[/tex]
If the pressure acting on a given sample of an ideal gas at constant temperature is tripled, what happens to the volume of the gas? a)The volume is reduced to one-third of its original value. b)The volume is reduced to one-ninth of its original value. c) The volume remains constant. d)The volume is increased by a factor of three times its original value. e) The volume is increased by a factor of nine times its original value.
Answer:
a)The volume is reduced to one-third of its original value.
Explanation:
For a gas at constant temperature, we can apply Boyle's law, which states that the product between pressure and volume is constant:
[tex]pV=const.[/tex]
where p is the pressure and V the volume.
In our case, this law can also be rewritten as
[tex]p_1 V_1 = p_2 V_2[/tex]
where the labels 1 and 2 refer to the initial and final conditions of the gas.
For the gas in the problem, the pressure of the gas is tripled, so
[tex]p_2 = 3p_1[/tex]
And re-arranging the equation we find what happens to the volume:
[tex]V_2 = \frac{p_1 V_1}{p_2}=\frac{p_1 V_1}{3p_1}=\frac{V_1}{3}[/tex]
so, the volume is reduced to 1/3 of its original value.
Examine the scenario.
A car starts from rest and uniformly accelerates to a speed of 40 km/h in 5 s. The car moves south the entire time.
Which option correctly lists a vector quantity from the scenario?
distance: 40 km
velocity: 5 km/h north
acceleration 8 km/h/s south
speed: 40 km/h
Answer:
acceleration 8 km/h/s south
Explanation:
First of all, let's remind that a vector quantity is a quantity which has both a magnitude and a direction.
Based on this definition, we can already rule out the following two choices:
distance: 40 km
speed: 40 km/h
Since they only have magnitude, they are not vectors.
Then, the following option:
velocity: 5 km/h north
is wrong, because the car is moving south, not north.
So, the correct choice is
acceleration 8 km/h/s south
In fact, the acceleration can be calculated as
[tex]a=\frac{v-u}{t}[/tex]
where
v = 40 km/h is the final velocity
u = 0 is the initial velocity
t = 5 s is the time
Substituting,
[tex]a=\frac{40 km/h-0}{5 s}=8 km/h/s[/tex]
And since the sign is positive, the direction is the same as the velocity (south).
What is the main action and reaction forces at work when a person leans against a car? * 3 points A. The person pushes against the car and the car pushes back B. The person is pushed away and the car stays still. C. The person pushes against the car and the car pulls the person back on it. D. The car pushes the person.
Anytime an object applies a force to another object, there is an equal and opposite force back on the original object. This is known as an action-reaction.
A. The person pushes against the car and the car pushes back
Suppose an ice hockey puck strikes a hockey stick that lies flat on the ice and is free to move in any direction. Which
quantities are likely to be conserved: angular momentum, linear momentum, or kinetic energy (assuming the puck and stick are
very resilient)?
Answer:
Linear momentum
Explanation:
The most likely conservation candidate is the linear momentum. The law of momentum conservation states that the sum of momenta before and after an (elastic or inelastic) collision will remain constant.
The kinetic energy is another possible, but less likely suspect. It is conserved in elastic collisions (i.e., those with no kinetic energy loss), but we are not told this collision is assumed elastic. In fact the real setup would be nowhere close to an elastic collision, as the stick lies on ice, which hasn't be zambonied for an entire period of rough skating, there's rough surface and the stick's shaft is also slightly stuck to the surface through frost. So when the puck hits the stick, a portion of its kinetic energy is spent to unstick the stick and get it moving. And so, kinetic energy is not conserved.
Angular momentum is not applicable with the puck-stick scenario.
In the described scenario, both angular and linear momentum are likely to be conserved, while kinetic energy may not be due to potential energy conversion during the impact.
Explanation:In this scenario regarding an ice hockey puck hitting a hockey stick on ice, both angular momentum and linear momentum would likely be conserved. The conservation of angular momentum comes into play as the hockey puck changes its direction, and linear momentum is conserved as long as there are no external forces acting on it, as is the case in this scenario. On the other hand, kinetic energy would not necessarily be conserved because some energy might be converted into other forms such as heat or sound during the impact.
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How can you measure the amplitude of a longitudinal wave
Answer:
In longitudinal waves, such as sound, the vibration is parallel to the propagation direction of the wave itself. These disturbances are due to the successive compressions of the medium, where the particles move back and forth in the same direction as the wave.
If we want to measure the amplitude of this type of wave we need to know the distance between particles of the medium that is being compresed by the perturbation. So, the closer together the particles are, the greater the amplitude of the wave.
The amplitude of a longitudinal wave may be measured by comparing the height of its compressions and rarefactions. This is the variation from the equilibrium or rest position of the wave. If you have a wave equation, you can determine the amplitude directly from it.
Explanation:In Physics, you can measure the amplitude of a longitudinal wave, which is a measure of the maximum displacement of the medium from its equilibrium position, by comparing the heights of its compressions (peaks) and rarefactions (troughs). The equilibrium position, in scenario of a water wave for example, is the height of the water if there were no waves moving through it. The crest of the wave is a distance +'A' above the equilibrium position, and the trough is a distance -'A' below it.
Remember that the amplitude of a sound wave decreases with distance from its source, as the energy of the wave gets spread over a larger area. The compression of a longitudinal wave is analogous to the peak of a transverse wave, and the rarefaction to the trough of a wave. Just as a transverse wave alternates between peaks and troughs, a longitudinal wave alternates between compression and rarefaction.
If you have a wave equation, you can decipher the amplitude, wave number, and angular frequency directly. For example, in the equation y(x, t) = A sin (kx — wt), the amplitude is read straight from the equation and is equal to 'A'.
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What is the speed of a beam of electrons when the simultaneous influence of an electric field of 1.56×104v/m and a magnetic field of 4.62×10−3t
Answer:
[tex]3.38\cdot 10^6 m/s[/tex]
Explanation:
Assuming the electron is moving in a straight line, it means that the electric force and the magnetic force acting on the electron are balanced:
[tex]F_E = F_B\\qE = qvB[/tex]
where
q is the electron charge
E is the electric field
v is the electron speed
B is the magnetic field
Re-arranging the equation and solving for v, we find the electron's speed:
[tex]v=\frac{E}{B}=\frac{1.56\cdot 10^4 V/m}{4.62\cdot 10^{-3} T}=3.38\cdot 10^6 m/s[/tex]
The type of lens that spreads out parallel light is a
the answer is concave lens
The type of lens that spreads out parallel light is a concave lens. Concave lenses are thicker at the edges than they are in the middle.
How does concave lens work?This causes the light rays to bend outwards, or diverge, as they pass through the lens. Convex lenses, on the other hand, are thicker in the middle than they are at the edges. This causes the light rays to bend inwards, or converge, as they pass through the lens. Convex lenses are used to magnify objects, while concave lenses are used to spread out light.
The parallel light rays are shown as blue lines. As they pass through the lens, they bend outwards and are spread out. The image of the object is shown as a red line. Concave lenses are used in a variety of applications, including microscopes, telescopes, and magnifying glasses. They are also used in some eyeglasses to correct nearsightedness.
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A motor and generator perform opposite functions, but their fundamental structure is the same. Their structure is a coil mounted on an axel within a magnetic field. How do they differ? Question 6 options: Motors convert electrical energy into mechanical energy. Generators convert mechanical energy into electrical energy. Generators convert electrical energy into mechanical energy. Motors convert mechanical energy into electrical energy. Motors convert mechanical energy into solar energy. Generators convert wind energy into mechanical energy. Motors convert kinetic energy into potential energy. Generators convert potential energy into mechanical energy.
Answer :
correct choice is option A
Motors convert electrical energy into mechanical energy. Generators convert mechanical energy into electrical energy.
Explanation :
Their difference is described as;
Premise MOTOR
The Motor Converts Electrical imperatives into vitality . It uses control. (power)In partner degree motor this is to be given to the curl winding The Shaft of the motor is driven by the drawing in power made among loop and field. Engine seeks after Fleming's left guideline.GENERATOR
Generator changes over Mechanical essentialness to Electrical imperatives . It produces control (electricity)In the generator current is conveyed inside the curl winding. The Shaft is associated with the rotor and is driven by mechanical power. Generator seeks after Fleming's correct guideline. .Final answer:
Motors convert electrical energy into mechanical energy, while generators convert mechanical energy into electrical energy.
Explanation:
Motors and generators are similar in structure but have opposite functions. A motor converts electrical energy into mechanical energy, while a generator converts mechanical energy into electrical energy. Both motors and generators have a coil mounted on an axel within a magnetic field.
When the coil of a motor rotates, the change in magnetic flux induces an electromotive force (emf) according to Faraday's law of induction. Thus, a motor also acts as a generator when its coil rotates.
On the other hand, a generator works by sending a current through a loop of wire located in a magnetic field. The magnetic field exerts torque on the loop, causing it to rotate and generate mechanical work out of the electrical current initially sent in.
A nylon guitar string vibrates in a standing wave pattern shown below. 2.7 m what is the wavelength of the wave? answer in units of m.
In this case the wavelength would be 3.14 m.
The wavelength of the wave formed by guitar string is 1.8 m.
What is wavelength?The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave. The wavelength is the reciprocal of the frequency of the wave.
One wavelength is 2/3 of the length of the string. The wavelength related to the length of string by
λ = 2/3 L
A nylon guitar string vibrates in a standing wave pattern. Harmonics only occur in 1/2 wavelength increments, so the third harmonic would be 3/2 wavelengths on the2.7 m string.
Substitute the value, we get
λ = 2/3 x 2.7
λ = 1.8 m
Thus, wavelength of the wave formed by guitar string is 1.8 m.
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If the voltage impressed across a circuit is held constant while the resistance is halved, what change occur?
Answer:
The current doubles
Explanation:
In a circuit, Ohm's law gives the relationship between voltage, current and resistance:
[tex]V=RI[/tex]
where
V is the voltage
R is the resistance
I is the current
In this problem,
V is held constant
R is halved: [tex]R'=\frac{R}{2}[/tex]
Therefore, the new current is
[tex]I'=\frac{V}{R'}=\frac{V}{R/2}=2\frac{V}{R}=2I[/tex]
So, the current doubles.
The wavelength of red helium-neon laser light in air is 632.8 nm.(a) What is its frequency?(b) What is its wavelength in glass that has an index of refractionof 1.48?(c) What is its speed in the glass?
(a) [tex]4.74 \cdot 10^{14}Hz[/tex]
The frequency of a wave is given by:
[tex]f=\frac{v}{\lambda}[/tex]
where
v is the wave's speed
[tex]\lambda[/tex] is the wavelength
For the red laser light in this problem, we have
[tex]v=c=3\cdot 10^8 m/s[/tex] (speed of light)
[tex]\lambda=632.8 nm=632.8\cdot 10^{-9} m[/tex]
Substituting,
[tex]f=\frac{3\cdot 10^8 m/s}{632.8 \cdot 10^{-9} m}=4.74 \cdot 10^{14}Hz[/tex]
(b) 427.6 nm
The wavelength of the wave in the glass is given by
[tex]\lambda=\frac{\lambda_0}{n}[/tex]
where
[tex]\lambda_0 = 632.8\cdot 10^{-9} m[/tex] is the original wavelength of the wave in air
n = 1.48 is the refractive index of glass
Substituting into the formula,
[tex]\lambda=\frac{632.8\cdot 10^{-9}m}{1.48}=427.6\cdot 10^{-9}m=427.6 nm[/tex]
(c) [tex]2.02\cdot 10^8 m/s[/tex]
The speed of the wave in the glass is given by
[tex]v=\frac{c}{n}[/tex]
where
[tex]c = 3\cdot 10^8 m/s[/tex] is the original speed of the wave in air
n = 1.48 is the refractive index of glass
Substituting into the formula,
[tex]v=\frac{3\cdot 10^8 m/s}{1.48}=2.02\cdot 10^8 m/s[/tex]
The frequency of a red helium-neon laser light in air is approximately 4.74 x 10¹⁴ Hz. Its wavelength in a glass medium with refractive index 1.48 is about 427.6 nm, and it travels through the glass at an estimated speed of 2.03 x 10⁸ m/s.
Explanation:(a) The frequency of the light can be calculated using the formula for the speed of light: c = λf, where c is the speed of light (3 x 10⁸ m/s), λ is the wavelength, and f is the frequency. We rearrange the formula to solve for f: f = c/λ. Given the wavelength of 632.8 nm, we first convert it to meters (632.8 x 10⁻⁹ m). So, the frequency f = (3 x 10⁸ m/s) / (632.8 x 10⁻⁹ m), or approximately 4.74 x 10¹⁴ Hz.
(b) The wavelength within a medium is given by λ/n, where n is the index of refraction. So in glass with an index of refraction 1.48, the new wavelength would be (632.8 nm) / 1.48 = approx. 427.6 nm.
(c) The speed of light in a medium is its speed in vacuum divided by the refractive index, i.e., v = c/n. So, in glass, the speed would be (3 x 10⁸ m/s) / 1.48 = approximately 2.03 x 10⁸ m/s.
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A freight train rolls along a track with considerable momentum. If it were to roll at the same speed but had twice as much mass, it's momentum would be
Answer:
The momentum would be doubled
Explanation:
The magnitude of the momentum of the freight train is given by:
[tex]p=mv[/tex]
where
m is the mass of the train
v is its speed
In this problem, we have that the speed of the train is unchanged, while the mass of the train is doubled:
[tex]m'=2m[/tex]
therefore, the new momentum is
[tex]p'=m'v=(2m)v=2(mv)=2p[/tex]
so, the momentum has also doubled.
If a freight train rolls at the same speed but has twice as much mass its momentum would be doubled as momentum is the product of mass and velocity.
Explanation:The question asks what would happen to the momentum of a freight train if it rolls at the same speed but has twice its current mass. Momentum is a concept in physics, and it is defined as the product of an object's mass and velocity. Therefore the momentum of the train would be directly proportional to its mass. If the mass of the train is doubled while the speed remains constant the momentum of the train would also be doubled.
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When energy is transferred between substances what happens to their temperatures?
Energy cannot be created nor destroyed, only change forms (the 1st law of thermodynamics). This means that when energy is transferred to another substance it has to lose some energy someway, because no energy transfer is 100% efficient. It loses it by converting in thermal energy. The temperature will increase in both substances but more likely in the substance that the energy is transfer to.
What happens to a low-mass star after helium flash?
The Luminosity Decreases.
What is the current in a 100.-ohm resistor connected to a 0.40-volt source of potential diffrence
Current = (voltage) / (resistance) Ohm's law
Current = (0.4 v) / (100 ohms)
Current = 0.004 Ampere
Current = 4 milliamperes
The current in a 100.-ohm resistor connected to a 0.40-volt source of potential diffrence will be 0.004Ampere
What is potential difference?Potential difference is the difference in the amount of energy that charge carriers have between two points in a circuit.
The potential difference (which is the same as voltage) is equal to the amount of current multiplied by the resistance.
A potential difference of one Volt is equal to one Joule of energy being used by one Coulomb of charge when it flows between two points in a circuit.
The formula for potential difference is :
[tex]V=IR[/tex]
[tex]I=\dfrac{V}{R}[/tex]
[tex]I=\dfrac{0.4}{100}=0.0004 \ Amp[/tex]
Thus the current in a 100.-ohm resistor connected to a 0.40-volt source of potential diffrence will be 0.004Ampere
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A 0.20 kg plastic cart and a 20 kg lead cart can roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a time of 1 , starting from rest. After the force is removed at t = 1s is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Explain.
Answer:
The have equal momentum
Explanation:
The change in momentum of each cart is equal to the impulse given to the cart:
[tex]\Delta v = I = F \Delta t[/tex]
where
F is the average force exerted on the cart
[tex]\Delta t[/tex] is the contact time
In this case, the force F applied to both carts is the same, and the contact time is the same for both carts (1 s). Therefore, the change in momentum of the two carts is the same.
However, both carts at the beginning have a momentum of zero (because they start from rest): this means that their final momentum will be equal, since they gain the same amount of momentum [tex]\Delta p[/tex].
Due to the relationship in the momentum equation, (p = mv) and equal forces applied on the two carts, both the plastic and the lead cart will have equal momentum irrespective of their mass differences.
Explanation:The momentum of the plastic cart and the lead cart will be equal. This is because momentum is the product of mass and velocity (p = mv). As equal forces are applied for the same duration, according to Newton's second law of motion, the acceleration a = F/m is equal for both carts. As the smaller plastic cart has less mass, it will have a greater velocity, while the larger lead cart, having more mass, will have a lesser velocity. However, because of the relationship in the momentum equation (p = mv), these different velocities will effectively cancel out the mass differences, resulting in equal momentum for the two carts.
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Batteries are rated in terms of ampere-hours (A·h). For example, a battery that can produce a current of 2.00 A for 3.00 h is rated at 6.00 A·h.
(a) What is the total energy stored in a 9.0 V battery rated at 47.0 A·h?
(b) At $0.0660 per kilowatt-hour, what is the value of the electricity produced by this battery? NOTE: Enter your response with hundredths precision.
(a) 423 J
The power of the battery is the ratio between the total energy stored (E) and the time elapsed (t):
[tex]P=\frac{E}{t}[/tex]
However, the power is also the product of the voltage (V) and the current (I):
[tex]P=VI[/tex]
Linking the two equations together,
[tex]\frac{E}{t}=VI\\E=VIt[/tex]
Since we know:
V = 9.0 V
[tex]I \cdot t = 47.0 A\cdot h[/tex]
We can calculate the total energy:
[tex]E=(9.0 V)(47 A \cdot h)=423 J[/tex]
(b) [tex]7.79\cdot 10^{-6}[/tex] dollars
The battery has a total energy of E = 423 J. (2)
1 Watt (W) is equal to 1 Joule (J) per second (s):
[tex]1 W = \frac{1 J}{1 s}[/tex]
so 1 kW corresponds to 1000 J/s:
[tex]1 kW = \frac{1000 J}{1 s}[/tex]
Multiplying both side by 1 hour (1 h):
[tex]1 kW \cdot h = \frac{1000 J}{1 s} 1 h[/tex]
and [tex]1 h = 3600 s[/tex], so
[tex]1 kWh = \frac{1000 J}{1 s}\cdot 3600 s =3.6\cdot 10^6 J[/tex]
So we find the conversion between kWh and Joules. So now we can convert the energy from Joules (2) into kWh:
[tex]1 kWh = 3.6\cdot 10^6 J = x : 423 J\\x=\frac{1 kWh \cdot 423 J}{3.6\cdot 10^6 J}=1.18\cdot 10^{-4}kWh[/tex]
And since the cost is $0.0660 per kilowatt-hour, the total cost will be
[tex]C=$0.0660\cdot 1.18\cdot 10^{-4} kWh=7.79\cdot 10^{-6}[/tex] dollars
The total energy stored in a 9.0 V battery rated at 47.0 A·h is 423.0 Wh. The value of the electricity produced by this battery at $0.0660 per kWh is approximately $0.03.
The total energy stored in a 9.0 V battery rated at 47.0 A·h can be calculated by multiplying the voltage by the charge capacity. The energy (E) in watt-hours (Wh) can be found using E = V * Q, where Q is the charge in ampere-hours (A·h) and V is the voltage in volts (V).
For the provided battery:
Voltage (V) = 9.0 V
Charge Capacity (Q) = 47.0 A·h
Energy (E) = V * Q = 9.0 V * 47.0 A·h = 423.0 Wh
For part (b), we convert the watt-hours into kilowatt-hours by dividing by 1000:
Energy in kilowatt-hours (kWh) = 423.0 Wh / 1000 = 0.423 kWh
The value of the electricity produced by this battery, at $0.0660 per kWh, can be calculated by multiplying the energy in kWh by the cost per kWh:
Value of electricity = Energy in kWh * Cost per kWh
Value of electricity = 0.423 kWh * $0.0660 = $0.027918, which rounds to $0.03 when rounded up to the nearest cent.
A 41 g ball rolls around a 64-cm-diameter L-shaped track at 55 rpm. What is the magnitude of the net force that the track exerts on the ball? Rolling friction can be neglected.
Using Newton's Second Law for Rolling Motion and centripetal force formulas, the magnitude of the net force exerted on a 41 g ball rolling at 55 rpm on a 64-cm-diameter track is calculated to be approximately 0.4307 Newtons.
To find the magnitude of the net force that the track exerts on the ball, we apply Newton's Second Law to Rolling Motion. We begin by converting the rotational speed to angular velocity: 55 rpm (revolutions per minute) is equivalent to 55 × 2π rad/60s ≈ 5.7596 rad/s. The radius (r) of the circular path is half the diameter, hence r = 64 cm / 2 = 32 cm = 0.32 m.
The ball experiences centripetal force due to its circular motion, which is defined as F = m × ω² × r, where m is the mass, ω is the angular velocity, and r is the radius. Plugging in the values, we get F = 0.041 kg × (5.7596 rad/s)² × 0.32 m ≈ 0.4307 N.
Therefore, the magnitude of the net force that the track exerts on the ball, considering rolling friction is neglected, is 0.4307 Newtons.
The net force exerted by the track on the ball is 0.435 N, calculated using the ball's mass, track radius, and angular velocity. This force is derived by finding the centripetal force required for circular motion.
To find the magnitude of the net force that the track exerts on a ball, we first identify the necessary parameters. The mass of the ball is 41 g, which we convert to kg (0.041 kg). The diameter of the track is 64 cm, giving us a radius of 0.32 m. The ball moves with a frequency of 55 rpm, which we convert to angular velocity.
Convert RPM to radians per second:Therefore, the magnitude of the net force that the track exerts on the ball is 0.435 N.
what type of device is a car engine?
A.A heat pump that uses heat to do work
B.A heat engine that uses work to move heat
C.A heat pump that uses work to move heat
D.A heat engine that uses heat to do work
D A heat engine that uses heat to do work
In a model AC generator, a 505 turn rectangular coil 8.0 cm by 30 cm rotates at 120 rev/min in a uniform magnetic field of 0.59 T.
(a) What is the maximum emf induced in the coil?
(b) What is the instantaneous value of the emf in the coil at t = (π/32) s? Assume that the emf is zero at t = 0.
(c) What is the smallest value of t for which the emf will have its maximum value? s
The maximum emf in the coil depends on
the maximum flux linkage through the coil, andthe angular velocity of the coil.Maximum flux linkage in the coil:
[tex]\phi_\text{max} = B\cdot A\cdot N = 0.59\;\text{T}\times(0.08 \times 0.30)\;\text{m}^{2} \times 505 = 7.2\;\text{Wb}[/tex].
Frequency of the rotation:
[tex]f = 120\;\text{rev}\cdot\text{min}^{-1} = 2 \;\text{rev}\cdot\text{s}^{-1}[/tex].
Angular velocity of the coil:
[tex]\omega = 2\;\pi\;\text{rev}^{-1}\times 2\;\text{rev}\cdot\text{s}^{-1} = 4 \pi \;\text{s}^{-1}[/tex].
Maximum emf in the coil:
[tex]\epsilon_\text{max} = \omega\cdot\phi_\text{max} = 4\;\pi \times 7.2\;\text{Wb} = 90\;\text{V}[/tex].
(b)Emf varies over time. The trend of change in emf over time resembles the shape of either a sine wave or a cosine wave since the coil rotates at a constant angular speed. The question states that emf is "zero at t = 0." As a result, a sine wave will be the most appropriate here since [tex]\sin{0} = 0[/tex].
[tex]\displaystyle \epsilon(t) = \epsilon_\text{max}\cdot \sin{(\omega\cdot t)}[/tex].
Make sure that your calculator is in the radian mode.
[tex]\displaystyle \epsilon\left(\frac{\pi}{32}\right) = 90\;\text{V}\times \sin\left(4\;\pi\times \frac{\pi}{32}\right) = 85\;\text{V}[/tex].
(c)Consider the shape of a sine wave. The value of [tex]\displaystyle \sin\left(\omega \cdot t\right)[/tex] varies between -1 and 1 as the value of [tex]t[/tex] changes. The value of [tex]\epsilon[/tex] at time [tex]t[/tex] depends on the value of [tex]\sin(\omega \cdot t)[/tex].
[tex]\sin(\omega \cdot t)[/tex] reaches its first maximum for [tex]t\ge 0[/tex] when what's inside the sine function is equal to [tex]\pi/2[/tex].
In other words, the first maximum emf occurs when
[tex]\omega \cdot t = \dfrac{\pi}{2}[/tex],
where
[tex]\sin{\omega \cdot t} = 1[/tex],
and
[tex]\epsilon = \epsilon_\text{max}[/tex].
[tex]\displaystyle t = \frac{\pi}{2}/\omega = \frac{1}{8} = 0.125\;\text{s}[/tex].
Final answer:
The maximum emf induced in the coil is 9.67 V. The instantaneous value of the emf at t = π/32 s is 4.67 V. The smallest value of t for which the emf will have its maximum value is approximately 0.395 seconds.
Explanation:
Answer:
(a) To find the maximum emf induced in the coil, we can use the formula: emf = NABω, where N is the number of turns, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity of the coil.
Given:
N = 505 turnsA = 8.0 cm × 30 cm = 240 cm² = 0.024 m²B = 0.59 Tω = 120 rev/min × (2π rad/rev) × (1 min/60 s) = 12.57 rad/sSubstituting these values into the formula, we can calculate the maximum emf:
emf = 505 × 0.024 m² × 0.59 T × 12.57 rad/s = 9.67 V
Therefore, the maximum emf induced in the coil is 9.67 V.
(b) To find the instantaneous value of the emf at t = π/32 s, we can use the equation: emf = emfmaxsin(ωt), where emfmax is the maximum emf and ω is the angular velocity of the coil.
Given:
emfmax = 9.67 Vt = π/32 sω = 12.57 rad/sSubstituting these values into the equation, we can calculate the instantaneous emf:
emf = 9.67 V × sin(12.57 rad/s × π/32 s) = 4.67 V
Therefore, the instantaneous value of the emf in the coil at t = π/32 s is 4.67 V.
(c) The smallest value of t for which the emf will have its maximum value can be found by solving the equation: ωt = π/2, where ω is the angular velocity of the coil.
Given:
ω = 12.57 rad/sSolving for t:
t = π/2ω = π/2(12.57 rad/s) ≈ 0.395 s
Therefore, the smallest value of t for which the emf will have its maximum value is approximately 0.395 seconds.
Two wires are stretched between two fixed supports and have the same length. One wire A there is a second-harmonic standing wave whose frequency is 660 Hz. However, the same frequency of 660 Hz is the third harmonic on wire B. (a) Is the fundamental frequency of wire A greater than, less than, or equal to the fundamental frequency of wire B? Explain. (b) How is the fundamental frequency related to the length L of the wire and the speed v at which individual waves travel back and forth on the wire? (c) Do the individual waves travel on wire A with a greater, smaller, or the same speed as on wire B? Give your reasoning.
(a) Greater
The frequency of the nth-harmonic on a string is an integer multiple of the fundamental frequency, [tex]f_1[/tex]:
[tex]f_n = n f_1[/tex]
So we have:
- On wire A, the second-harmonic has frequency of [tex]f_2 = 660 Hz[/tex], so the fundamental frequency is:
[tex]f_1 = \frac{f_2}{2}=\frac{660 Hz}{2}=330 Hz[/tex]
- On wire B, the third-harmonic has frequency of [tex]f_3 = 660 Hz[/tex], so the fundamental frequency is
[tex]f_1 = \frac{f_3}{3}=\frac{660 Hz}{3}=220 Hz[/tex]
So, the fundamental frequency of wire A is greater than the fundamental frequency of wire B.
(b) [tex]f_1 = \frac{v}{2L}[/tex]
For standing waves on a string, the fundamental frequency is given by the formula:
[tex]f_1 = \frac{v}{2L}[/tex]
where
v is the speed at which the waves travel back and forth on the wire
L is the length of the string
(c) Greater speed on wire A
We can solve the formula of the fundamental frequency for v, the speed of the wave:
[tex]v=2Lf_1[/tex]
We know that the two wires have same length L. For wire A, [tex]f_1 = 330 Hz[/tex], while for wave B, [tex]f_B = 220 Hz[/tex], so we can write the ratio between the speeds of the waves in the two wires:
[tex]\frac{v_A}{v_B}=\frac{2L(330 Hz)}{2L(220 Hz)}=\frac{3}{2}[/tex]
So, the waves travel faster on wire A.
How long does it take to get to the moon in a spaceship
It would take about 3 days
Hope this helps have a good day....
It takes about 3 days or less than a week
PLEASE ANSWER ASAP
What is the difference between a newtonian and a galilean telescope?
Galilean Telescope or Refracting Telescope uses a convergent (plano-convex or bi-convex) objective lens and a divergent (plano-concave or bi-concave) eyepiece lens. Galilean telescopes produce upright images.Galileo’s best telescope magnified objects about 30 times. Because of flaws in its design, such as the shape of the lens and the narrow field of view, the images were blurry and distorted. Despite these flaws, the telescope was still good enough for Galileo to explore the sky. The Galilean telescope could view the phases of Venus, and was able to see craters on the Moon and four moons orbiting Jupiter.
The Newtonian telescope is a type of reflecting telescope invented by the British scientist Sir Isaac Newton using a concave primary mirror and a flat diagonal secondary mirror. Newton’s first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope. The Newtonian telescope's simple design makes them very popular with amateur telescope makers.Newtonian telescopes are usually less expensive for any given aperture than comparable quality telescopes of other types. And a short focal ratio can be more easily obtained, leading to wider field of view.
The eyepiece is located at the top end of the telescope. Combined with short f-ratios this can allow for a much more compact mounting system, reducing cost and adding to portability, Which was not in the Case of Galilean Telescope.