Answer:
600kW
Explanation:
Power= Workdone/ time
= 1500/8*320
= 1500*40
= 60000J/s
= 600kW
Workdone= Fd
= 3000*1*1/16
= 1500/8
= 750/4
= 137. 5Nm
3000F/320
=150F/16
s=ut+1/2at^2
3000= 1/2at^2
6000= at^2
6000/a=t^2
F=ma
20m/t=ma
20/t= a
20m=Ft
20m=F(320)
m= 8F
F=ma
= 20/tm
20m/t= 20/tm
m= 1/m
m=1kg
6000/a= 400/a^2
16= 1/a
a= 1/16ms-2
t= 20/1/16
t= 320 s
(v-u)/t=a
v= 20ms-1
1.1 Determine whether the following equations are dimensionally correct, if NOT, how
can you make them dimensionally correct?
(i)
Answer:
You have not provided any equation for me to evaluate. Please provide the equation(s) in question so that I can determine whether they are dimensionally correct or not.
A 80kg stone falls from the top of the 360 meter cliff. Neglecting friction, how fast will the stone be moving just before it hits the ground?
The stone will be moving at a speed of approximately 84.4 meters per second just before it hits the ground, neglecting friction.
To find how fast will the stone be moving just before it hits the ground?This problem can be solved using the laws of kinematics and conservation of energy. The potential energy of the stone at the top of the cliff is converted to kinetic energy as it falls. We can equate the potential energy at the top of the cliff to the kinetic energy just before hitting the ground.
Potential energy = mgh,
Where
m is the mass of the stone g is the acceleration due to gravity (9.8 m/s^2) h is the height of the cliff (360 meters)Kinetic energy = (1/2)mv^2,
Where
v is the velocity of the stone just before hitting the ground.Equating these two expressions and solving for v, we get:
mgh = (1/2)mv^2
v^2 = 2gh
v = sqrt(2gh)
Plugging in the given values, we get:
v = sqrt(2 x 9.8 m/s^2 x 360 m) = 84.4 m/s
Therefore, the stone will be moving at a speed of approximately 84.4 meters per second just before it hits the ground, neglecting friction.
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The voltage of a battery is V and the current is I. If the voltage is doubled to 2V, what is the new current?
O 1/4
O 21
O 1/2
041
Answer:The current in a lightbulb with a voltage of 35.0 V and a resistance of 175 ohm is 0.2 A.
Find the current in a lightbulb?
Given:
The voltage in a lightbulb is given by the equation V=IR
V is the voltage, I is current, and R is the resistance.
The voltage of the lightbulb is given as 35.0 V.
The resistance of the lightbulb is given as 175 Ohm.
As the equation is given,
V= IR
where I is current, R is resistance and V is the voltage.
Now, I = V/R
As the value of Voltage and resistance of the lightbulb is given, we will put in the above equation, we get;
I = 35.0/ 175 A
I = 0.2 A.
Hence, the current of the lightbulb is 0.2 A.
Therefore, Option C is the correct answer.
To learn more about Current, refer to:
Explanation:
A block of mass m1=3.0kg rests on a frictionless horizontal surface. A second block of m2=2.0kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block . the blocks are released from rest . determine the displacement of the velocity of the first block 1.2 s after the release of the blocks, assuming the first block doesn't run out of the room on the table and the second block doesn't land on the floor?
A) 23.5m/s
B) 12m/s
C) 33.7m/s
D) 6.7m/s
To solve this problem, we can use the principles of Newton's laws of motion and the conservation of energy.
At the moment of release, the second block will start to accelerate downwards due to gravity, and the first block will start to move to the right due to the tension in the rope. Since the surface is frictionless, there is no horizontal force acting on the first block once it starts moving.
Using the free-body diagrams for the two blocks, we can write the following equations of motion:
For the second block:
m2g - T = m2a
where g is the acceleration due to gravity, T is the tension in the rope, a is the acceleration of the second block, and m2 is the mass of the second block.
For the first block:
T = m1a
where m1 is the mass of the first block and a is its acceleration.
Since the two blocks are connected by a rope, they must have the same acceleration, so we can set the two equations for acceleration equal to each other:
m2g - T = m1a
T = m1a
m2g - m1a = T = m1a
Solving for a, we get:
a = (m2/m1 + m2)g
We can also use the conservation of energy to find the final velocity of the first block after 1.2 seconds. At the moment of release, the total mechanical energy of the system is given by:
E = m1gh
where h is the initial height of the second block. As the blocks move, the potential energy of the second block is converted into the kinetic energy of both blocks. At the end of the 1.2 seconds, all of the potential energy will be converted into kinetic energy, so we can write:
E = (1/2)m1v^2 + (1/2)m2v^2
where v is the final velocity of the first block.
Solving for v, we get:
v = sqrt(2gh(m1+m2)/m1)
Plugging in the given values, we get:
a = (2/5)g ≈ 3.92 m/s^2
v = sqrt(2gh(m1+m2)/m1) ≈ 2.36 m/s
Therefore, the displacement of the velocity of the first block 1.2 s after the release of the blocks is approximate:
vt + (1/2)at^2 = 2.361.2 + (1/2)3.92(1.2)^2 ≈ 5.52 m/s
So the answer is not given in the options.
Question 14 of 16
When is work negative?
OA. When an object goes from high to low potential energy
O B. When an object goes from low to high potential energy
O C. When an object slows down
O D. When an object speeds up
Work is negative when A. When an object goes from high to low potential energy.
When can work be said to be negative ?Work is defined as the transfer of energy that occurs when a force is applied to an object, causing it to move a certain distance. When the force and displacement are in the same direction, the work is positive.
When an object moves from a higher to a lower potential energy state, it loses potential energy. In this case, the negative work done by gravity is equal to the loss of potential energy of the ball.
When an object slows down, the force acting on it is in the opposite direction to its velocity, so work is done in the opposite direction to the displacement, and the work is negative.
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why the ocean near Christchurch is a different temperature than we’d expect for its latitude
Why the ocean near Christchurch is a different temperature than we'd expect for its latitude (distance from the equator)? Water moving from the equator is warmer than would be expected based on latitude, and so is warmer than the air it passes.
Changes to prevailing winds affect ocean currents. Changes to ocean currents affect how much energy is brought to (or taken away from) a location. In El Niño years, the prevailing winds that normally drive a warm current from the Equator past New Zealand are disrupted and may stop or even reverse.
Please!
I need the answer for question 2.
Thank you.
(i) The vector 2r is 2.0i + 26.0j - 4.0e12j + 6.0e12k
(ii) The velocity vector is v = r'(t) = 24.0e12j.
(iii) The acceleration vector is zero, meaning the particle is not accelerating at t=3 seconds.
(iv) The magnitude of the vector r is approximately 3.605e12 m.
How did we get the values?(i) To find the vector 2r, we simply multiply the position vector r by 2:
2r = 2(1.0i + 13.0j - 2.0e12j + 3.0e12k)
= 2.0i + 26.0j - 4.0e12j + 6.0e12k
(ii) To find the velocity vector, we take the derivative of the position vector with respect to time:
r'(t) = (1.0i + 13.0j - 2.0e12j + 3.0e12k)'
= 0i + 0j + 24.0e12j + 0k
= 24.0e12j
So the velocity vector is v = r'(t) = 24.0e12j.
(iii) To find the acceleration vector at time t=3 seconds, we take the derivative of the velocity vector with respect to time:
a(t) = v'(t) = 0i + 0j + 0k = 0
So the acceleration vector is zero, meaning the particle is not accelerating at t=3 seconds.
(iv) The magnitude of the vector r is given by:
|r| = √(1.0^2 + 13.0^2 + (-2.0e12)^2 + 3.0e12^2)
= √(1 + 169 + 4e24 + 9e24)
= √(13e24 + 170)
So the magnitude of the vector r is approximately 3.605e12 m.
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The question in text format:
The position of an object is given by 1.0 13 -2.0 12j+3.0 12 k. m (with t in s econds). Determine;
(i) vector" such that 2r="
(ii) the derivative of position and hence the velocity of the particle. [4]
(iii) the acceleration of the particle for 3 seconds.
(iv) the magnitude of vector r
In the arrangement described in Sample Problem B, how much would the water’s internal energy increase if the mass fell 6.69 m?
If a mass fell into water, the water's internal energy would increase due to the conversion of the kinetic energy of the falling mass into thermal energy.
How to explain the informationWhen the mass hits the water, it will experience a force from the water, and this force will cause the mass to decelerate and eventually come to a stop. During this process, the kinetic energy of the mass is converted into thermal energy of the water, which increases the water's internal energy.
The amount by which the water's internal energy increases will depend on several factors, including the mass of the falling object, its velocity, and the properties of the water, such as its specific heat capacity and temperature. Additionally, the temperature of the water may rise due to the energy transfer from the falling object, which would further increase its internal energy.
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HELP ME!!!!If a researcher is designing an electromagnet for a life-saving medical application, which properties of the magnet will she need to take into account?
Select two answers!!
Wether or not magnetic field is constant.
Number of could of conducting wire.
Wether or not domains are present in iron core.
Metal composition of conducting wire.
Answer:
Number of coils of conducting wire and whether or not domains are present in iron core are the two properties of the electromagnet that the researcher will need to take into account.
Explanation:
The number of coils of conducting wire affects the strength of the magnetic field produced by the electromagnet. More coils will produce a stronger magnetic field, while fewer coils will produce a weaker magnetic field. The researcher will need to determine the appropriate number of coils to produce the desired strength of the magnetic field for the medical application.
The presence of domains in the iron core is also an important consideration. The iron core of the electromagnet helps to concentrate the magnetic field and increase its strength. The domains in the iron core align with the magnetic field produced by the current flowing through the wire, and this alignment reinforces the magnetic field. If the iron core does not have domains, the magnetic field produced by the electromagnet will be weaker. Therefore, the researcher will need to ensure that the iron core has domains to maximize the strength of the magnetic field for the medical application.
Mitchell dropped a basketball and watched it bounce a few times. It bounced highest the first time. The next time, it did not move as
fast or bounce as high.
What happened to some of the ball's energy?
OA. It was changed into heat.
B.
It was transferred to Mitchell,
OC. It was changed into light
OD. It disappeared.
Answer:
A. It was changed into heat
Explanation:
Some of the kinetic energy the ball has when it strikes the floor is retained, but other is transformed to heat energy, so each time the ball bounces it loses a bit of its kinetic energy, and after several bounces it has so little of it left that it ceases to bounce.
As shown in the figure, a light inextensible string is passing around a smooth light pulley and it is attached to a spring having spring constant K. When a mass is suspended to the pulley, the pulley moved downwards through a distance of x and attained equilibrium. The mass attached to the pulley is given by :
1) Kx/g
2) 2Kx/g
3) 3Kx/g
4) 4Kx/g
5) 5Kx/g
Please show me how you worked it out, along with a brief explanation.
The mass attached to the pulley is Kx/g.
option 1.
What is the mass attached to the pulley?Assuming there is no friction, the tension in the string will be constant throughout, and the net force on the pulley-mass system will be the weight of the mass.
Let the mass of the hanging weight be m, then the weight of the mass is mg.
The spring will be extended by the same distance x, as the string is inextensible, and it will exert a force of Kx in the upward direction.
Since the pulley is in equilibrium, the net force on the pulley-mass system must be zero.
Therefore, the tension in the string must be equal to the force exerted by the spring:
T = Kx
Using the fact that the tension in the string is equal to the weight of the mass, we can write:
mg = Kx
Therefore, the mass attached to the pulley is:
m = Kx/g
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Pls awnser
I Need help
The two correct answers are:
Patterns of rain and snow are changing.Ocean waters are becoming warmer.What is the hydrosphere?The hydrosphere is described as the combined mass of water found on, under, and above the surface of a planet, minor planet, or natural satellite.
Increasing levels of carbon dioxide in the atmosphere leads to global warming, which in turn affects the hydrosphere in various ways.
One of the impacts is that changing climate patterns lead to changes in precipitation patterns, resulting in alterations in the amount and timing of rainfall and snowfall.
Another impact is the warming of the ocean waters due to the absorption of excess heat from the atmosphere. Warmer ocean water can lead to a variety of negative impacts on marine ecosystems, including coral bleaching, altered patterns of marine life migration, and the potential extinction of some marine species.
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Which of the choices correctly shows the result of the interference of waveforms I and II?
The interference of waves would lead to the combination of the both waves as shown
What is the interference of waves?The question is incomplete but I will discuss the idea of the interference of waves.
The interference of waves is a phenomenon in which two or more waves meet and combine to produce a new wave. Depending on the relative phase and amplitude of the waves, the resulting wave may be either reinforced or canceled out.
When two waves are in phase (i.e., their crests and troughs align), they produce constructive interference, resulting in a wave with an amplitude that is the sum of the amplitudes of the individual waves. Conversely, when two waves are out of phase (i.e., their crests and troughs are misaligned), they produce destructive interference, resulting in a wave with an amplitude that is the difference between the amplitudes of the individual waves.
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Contamination of food in a storage area can be reduced by: making sure that the temperature is kept at 98°F removing all wrapping from food before storage putting cardboard on the floor of the store room to keep food off the floor keeping raw and ready to eat food separated
Of the options provided, keeping raw and ready-to-eat food separated is likely the most effective way to reduce contamination of food in a storage area.
When raw meat and ready-to-eat foods come into contact with each other, there is a risk of cross-contamination, which can lead to foodborne illness. This can happen if bacteria from the raw meat are transferred to the ready-to-eat food, where they can grow and cause illness.
Keeping raw and ready-to-eat food separated helps to reduce this risk by preventing direct contact between the two types of food. This can be done by storing raw meat on the bottom shelf of a refrigerator or in a separate area from ready-to-eat food in a storage room.
While keeping the temperature at 98°F can help prevent the growth of some types of bacteria, it may not be effective in preventing contamination from other sources. Removing wrapping from food before storage and putting cardboard on the floor can also help with cleanliness and organization, but may not directly address the issue of cross-contamination.
Overall, it is important to use a combination of food safety practices to prevent contamination of food in a storage area. This includes proper storage, handling, and preparation of food, as well as maintaining a clean and organized storage environment.
Pulse transfers a
disturbance. while wave is a
disturbance that transfers energy.
Answer:
Pulse transfers a single disturbance, while wave is a continuous disturbance that transfers energy.
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The designers of a large, tethered pollution-sampling balloon wish to know what the drag will be on the balloon for the maximum anticipated wind speed of 5 m/s (the air is assumed to be at 20°C). A 1/20-scale model is built for testing in water at 20°C. What water speed is required to model the prototype? At this speed the model drag is measured to be 2 kN. What will be the corresponding drag on the prototype?
Answer:
The drag on the prototype at a wind speed of 5 m/s is 5 N.
Explanation:
what component of fitness does tennis not fall under?
Answer:
Play tennis, nothing can train you better for the sport than the sport itself. However, tennis is one of those unique sports that combine nearly all components of fitness including power, agility, speed, flexibility, reaction time, balance, coordination, cardiovascular endurance and muscular endurance.
Explanation:
A 208g sample of sodium-24 decays to 13.0g of sodium-24 within 60.0 hours. What is the half life of this radioactivity isotope?
Answer:
15 hours
Explanation:
formula: f(a) = a(0.5)^(T/t)
fill in known values: 13=208(0.5)^(60/t)
use natural log to isolate t: ln(13/208)=ln(0.5)(60/t)
solve for t: t=15
If 10 A of current flows through a 2 ohm resistor, what is the voltage of the battery?
20 V
0.2 V
OS V
12 V
The voltage of the battery would be 20 volts. Option I.
Voltage calculationAccording to Ohm's law, the voltage (V) across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R). Mathematically,
V = I × R
In this case, the current (I) flowing through the resistor is given as 10 A and the resistance (R) of the resistor is given as 2 ohms. Substituting these values into the above formula, we get:
V = 10 A × 2 ohms = 20 volts
Therefore, the voltage of the battery is 20 volts.
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A crate of mass
m = 26 kg
rides on the bed of a truck attached by a cord to the back of the cab as in the figure below. The cord can withstand a maximum tension of 69 N before breaking. Neglecting friction between the crate and truck bed, find the maximum acceleration the truck can have before the cord breaks. (Enter the magnitude of the maximum acceleration in the forward direction.)
m/s2
Answer:
Explanation:
The maximum tension the cord can withstand is 69 N, so we know that the tension in the cord cannot exceed this value. The tension in the cord is related to the acceleration of the truck through Newton's second law:
ΣF = ma
where ΣF is the net force on the crate, m is the mass of the crate, and a is the acceleration of the truck.
In this case, the only force acting on the crate in the horizontal direction is the tension in the cord. Therefore, we can write:
ΣF = T = ma
where T is the tension in the cord.
We can solve this equation for the acceleration:
a = T/m
We know that the tension cannot exceed 69 N, so the maximum acceleration the truck can have before the cord breaks is:
a = 69 N / 26 kg
a ≈ 2.65 m/s^2
Therefore, the maximum acceleration the truck can have before the cord breaks is 2.65 m/s^2.
explain using diagram how to burn a paper using concave mirror
Explanation:
B.C.ghmll h ffghklhgfjlA golf ball has one-tenth the inertia and three times the speed of a baseball.
what is the ratio of the magnitudes of their moomenta
We are aware that the impulse is equal to the change in the object's momentum. As a result, the ball's momentum change and the club's momentum change are equal.
What is a brief explanation of inertia?A body's ability to fight against attempts by outside forces to set it in motion A body's inertia is a passive characteristic that prevents it from doing anything other than opposing active agents like forces and torques.
What does momentum and inertia mean?A body's propensity to continue moving is called momentum, which is a vector quantity. The resistance a body offers to any acceleration shift makes inertia a scalar quantity.
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An archer shoots an arrow at an 82.0 m distant target; the bull's-eye of the target is at same height as the release height of the arrow.
(a)
At what angle in degrees must the arrow be released to hit the bull's-eye if its initial speed is 40.0 m/s?
Answer:
Explanation:
We can use the following kinematic equation to solve this problem:
y = y0 + tanθ(x - x0) - (gx²)/(2v₀²cos²θ)
where
y = 0 (since the target is at the same height as the release height)
y0 = 0
x0 = 0
x = 82.0 m
v₀ = 40.0 m/s
g = 9.81 m/s²
We want to solve for θ.
Rearranging the equation and substituting the values, we get:
tanθ = (xg)/(2v₀²)
θ = tan⁻¹[(xg)/(2v₀²)]
θ = tan⁻¹[(82.0 m)(9.81 m/s²)/(2(40.0 m/s)²)]
θ ≈ 18.1°
Therefore, the archer must release the arrow at an angle of approximately 18.1 degrees to hit the bull's-eye.
x
X
Number of Paper Clips Picked up
Electromagnet Strength
25
4x D
20
15
10
s
5
This chart measures how many paper clips were picked up by an electromagnet based on its number of coils.
Based on the graph, which statement is true?
A
The more coils of wire on an electromagnet, the more paperclips that it is likely to pick up.
10
15
Number of Coils of Wire
B At least one electromagnet in this study did not pick up any paperclips at all.
20
C
The less coils of wire wrapped around an electromagnet, the more magnetic it becomes.
The most paperclips picked up by an electromagnet in this study is 20.
Answer:
Explanation:
X
Number of Paper Clips Picked up
Electromagnet Strength
25
4x D
20
15
10
s
5
This chart measures how many paper clips were picked up by an electromagnet based on its number of coils.
Based on the graph, which statement is true?
A
The more coils of wire on an electromagnet, the more paperclips that it is likely to pick up.
10
15
Number of Coils of Wire
B At least one electromagnet in this study did not pick up any paperclips at all.
20
C
The less coils of wire wrapped around an electromagnet, the more magnetic it becomes.
The most paperclips picked up by an electromagnet in this study is 20.
How could you use the game of baseball to explain the difference between
inertia and momentum?
Explanation:
Inertia refers to the tendency of an object to resist changes in its motion. In baseball terms, a baseball that is at rest on the ground has a high level of inertia because it is resistant to moving until an external force, such as a player's bat, acts on it.
Momentum, on the other hand, is the product of an object's mass and velocity and refers to the quantity of motion that an object possesses. In baseball terms, a baseball that is moving at a high velocity, such as when it is hit by a bat, has a high level of momentum.
To illustrate the difference between inertia and momentum in baseball, consider the scenario of a baseball that is hit by a bat. Before the bat hits the ball, the ball is at rest and has a high level of inertia. However, once the bat hits the ball, the ball gains momentum and begins to move. As the ball moves, it continues to possess momentum, but its inertia gradually decreases as it encounters external forces, such as air resistance and friction from the ground, which act to slow it down.
A box slides on a level floor. It is slowing with a constant
acceleration of magnitude 2.0 m/s2
. What is the coefficient of
kinetic friction between the box and the floor?
Answer:
Explanation:
We can use the following equations of motion to solve the problem:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, s is the distance travelled.
In this case, the box is slowing down, so the initial velocity u is greater than the final velocity v. We can use a negative sign to indicate that the acceleration is opposite to the initial velocity.
Let us assume that the mass of the box is m and the coefficient of kinetic friction is μ. The force of friction acting on the box is given by f = μmg, where g is the acceleration due to gravity.
Since the acceleration of the box is 2.0 m/s^2, we have
f = ma
μmg = m(-2.0)
μg = -2.0
μ = -2.0/g
Substituting g = 9.8 m/s^2, we get
μ = -0.204
Since the coefficient of friction cannot be negative, we take the absolute value and obtain:
μ = 0.204
Therefore, the coefficient of kinetic friction between the box and the floor is approximately 0.204.
10. The energy states of an electron in a hydrogen atom is given by:
�
�
=
−
13.6
�
�
�
2
En=
n
2
−13.6 eV
Which of the following is not a possible energy of an emitted photon of the atom for an electron that is initially at
�
=
4
n=4?
0.66 eV
1.89 eV
2.55 eV
12.8 eV
Because it is less than the required minimum energy difference of 1.51 eV, the energy of 0.66 eV is not feasible. Hence, 0.66 eV is the correct answer.
When the hydrogen atom's energy in its ground state is 13.6 eV, what is the energy of the third excited state?The electron is first assumed to be in the ground state (n=1) in a hydrogen atom. Hence, the electron's energy in its ground state is 13.6 eV. This means that 12.75eV is needed to transfer electrons from the ground state to the third excited state.
The following equation provides the energy levels:
En = -13.6/n² eV
where n is the main quantum number.
An electron can move from the n=4 level to the n=3, n=2, or n=1 level after initialization. For each of these transitions, the relevant photon energies and energy differences are as follows:
n=4 to n=3: ΔE = En=3 - En=4 = (-13.6/3²) - (-13.6/4²) = 1.51 eV
n=4 to n=2: ΔE = En=2 - En=4 = (-13.6/2²) - (-13.6/4²) = 3.40 eV
n=4 to n=1: ΔE = En=1 - En=4 = (-13.6/1²) - (-13.6/4²) = 10.2 eV
As a result, the released photons could have energies of 1.51 eV, 3.40 eV, or 10.2 eV.
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What are some examples of conservation of energy?
Answer:
power plant
collision
Battery
Burning wood
speaker
Beating drum
For these questions, answer all parts of the question completely. Use complete
sentences.
4. Imagine that you have decided to try out a new kind of food that your friend
has made for you. You pick it up and take a bite, and it tastes awful. You are
wondering if you should tell your friend what you really think. Give an example of
how each of these parts of the brain would be involved in your experience:
a. Hindbrain (5 points)
b. Midbrain (5 points)
c. Forebrain (5 points)
Examples of how the parts of the brain would be involved in the experience of tasting the food and seeing it was awful include:
Hindbrain - initiating the digestive responseMidbrain - processing the sensory information Forebrain - deciding how to respondHow would the parts of the brain react ?The hindbrain, which includes the cerebellum and brainstem, is responsible for basic bodily functions such as breathing, heart rate, and digestion. In the scenario of trying a new food and finding it unpleasant, the hindbrain would play a role in initiating the digestive response to the food.
The midbrain is involved in the processing of sensory information, including auditory and visual stimuli. In the scenario of trying a new food and finding it unpleasant, the midbrain would be responsible for processing the sensory information related to taste and smell.
The forebrain is responsible for more complex cognitive processes, including decision-making and problem-solving. In the scenario of trying a new food and finding it unpleasant, the forebrain would be involved in deciding how to respond to the situation.
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A 1.20 kg copper rod resting on two horizontal rails 0.90 m apart carries a
current I = 55.0 A from one rail to the other. The coefficient of static friction
between the rod and rails is μs= 0.60.
(a) What is the smallest vertical magnetic field B that would cause the rod to
slide?
(b) Suppose a B field is directed at some angle to the vertical φ, with the current
along the rod directed into the page, as shown. Find an expression for B as a
function of φ for the case when the rod is just on the verge of beginning to slide.
(c) Find the value of φ which yields the smallest value of B that would cause
the rod to slide, together with the corresponding value of B.
Answer:
Explanation:
(a) In order for the copper rod to slide, the magnetic force on it must be greater than the maximum static friction force. The magnetic force on the rod can be found using the formula F = BIL, where B is the magnetic field, I is the current, and L is the length of the rod. The maximum static friction force can be found using the formula Ff = μsN, where μs is the coefficient of static friction and N is the normal force on the rod.
Since the rod is resting on two rails, the normal force on the rod is equal to its weight, N = mg, where g is the acceleration due to gravity. Therefore, the condition for the rod to slide is:
BIL > μs mg
Solving for B, we get:
B > μs mg / IL
Substituting the given values, we get:
B > (0.60)(1.20 kg)(9.81 m/s^2) / (0.90 m)(55.0 A)
B > 0.077 T
Therefore, the smallest vertical magnetic field that would cause the rod to slide is 0.077 T.
(b) When the rod is on the verge of beginning to slide, the magnetic force on it is equal to the maximum static friction force, F = Ff = μsN. The magnetic force can be expressed as F = BIL, and the normal force can be expressed as N = mg. Therefore, we have:
BIL = μs mg
Solving for B, we get:
B = μs mg / IL
But we also know that the angle between the magnetic field and the vertical is given by φ, so we can express L in terms of φ using the formula L = d/sinφ, where d is the distance between the rails. Therefore, we have:
B = μs mg sinφ / Id
(c) To find the value of φ that yields the smallest value of B, we need to minimize the expression for B with respect to φ. Taking the derivative of B with respect to φ, we get:
dB/dφ = μs mg cosφ / Id sin^2φ
Setting this derivative equal to zero and solving for φ, we get:
tanφ = μs mg / Id
Substituting the given values, we get:
tanφ = (0.60)(1.20 kg)(9.81 m/s^2) / (0.90 m)(3000000 kg)(9.00 x 10^-7 m)
tanφ ≈ 0.12
Taking the arctan of both sides, we get:
φ ≈ 6.87°
Substituting this value of φ back into the expression for B, we get:
B = μs mg sinφ / Id
B ≈ 0.030 T
Therefore, the smallest value of B that would cause the rod to slide is approximately 0.030 T, when the magnetic field is at an angle of 6.87° to the vertical.