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Chapter 37: Kinetic Energy and the Work-Energy Theorem
Energy can be seen through an object's motion.
An object starts at rest and gains 2 J of energy.
Determine the speed of the object.
When calculating the net work done by all external forces, the gain or loss of energy W is seen as a change in the object's speed.
The object is moving at 10 m/s.
We are told that it is 10 m/s.
The object lost a lot of movement energy as it slowed down.
The work is done by friction.
We could calculate the force required to stop the object if we knew the distance.
Potential energy is energy stored within a system between particles that are bound by forces.
The conservative forces are related to potential energy.
There are many different types of potential energy.
We are only concerned with three for the purposes of the AP exam.
We are only concerned with the changes in potential energies.
The more energy is stored in the system, the better.
The relationship between the mass that is interacting with Earth and the planet's surface may be changed by changing its height.
The greater the potential energy stored in the system, the more springs are compressed or stretched away from their equilibrium point.
The PE elastic is 1/2 kx 2 and is stored in the stretched or compressed spring.
See the examples.
The closer two charges are held, the greater the potential energy.
The electrical potential energy is given by the equation.
See the examples.
The mechanical energy is conserved if conservative forces are present.
The final mechanical energy must be equal to the initial mechanical energy according to the law.
A rock falls in a vacuum.
We are dealing with potential energy due to gravity.
The direction of vf is downward.
At the beginning of the problem-solving, the mass m canceled out completely.
An arrow is shot from the roof of a building at an angle of 45 degrees.
A mass sliding along a floor at 3 m/s hits a spring and bounces back.
We are dealing with the potential energy of a spring.
When the spring is at maximum compression, the quotient is 0 m/s.
The work done by nonconservative forces must be accounted for when calculating the final energy levels.
During the fall, the air friction does -39 J of work.
Julia is trying to calculate the final speed of a dropped ball.
She thinks the ball dropped over a vertical distance of D y.
Julia knows the answer is wrong.
Explain what she should do to correct her mistake.
Julia's work has included gravity twice.
The work was determined by gravity.
She included potential energy in her term.
Work is a force over a distance and a transfer of energy.
The rate at which work is done is called power.
Net work done by all forces to an object is the same as the change in energy of that object.
The work done by conservative forces is path independent.
Internal conservative forces store potential energy within a system.
The total mechanical energy is conserved if there are only conservative forces.
In an isolated system, missing mechanical energy can be found in the form of internal energy.
The work could be going into any of these.
If all forces are treated as external forces, the net work is going into the energy of the object.
The mechanical energy can be described as potential energies if the only external forces are gravity and springs.
Students assume that all the joules of energy are to be found in KE and PE in a problem.
They will overlook the nonspring force in the problem that takes some energy out of KE and PE and puts it into IE.
A problem can be solved with either energy or kinematics.
The more powerful tool is energy.
If the acceleration is constant, you can double-check your answer.
A pendulum consisting of a mass m attached to a light string of length is displaced from its rest position, making an angle th with the vertical.
The conveyor belt machine has an engine.
A mass m is moving along the floor.
The mass encounters a part of the floor that has a coefficient of friction.
Two mass are dropped at the same time.
The maximum vertical displacement of the pendulum is 17 cm above its rest position.
The spring has been compressed by 0.04 m and a mass rests on top of it.
A box is pulled along a smooth floor by a force F.
A sphere is dropped through a column of liquid.
The sphere has a speed of 5 m/s when it has fallen a distance of 2.0 m.
A mass is attached to a massless spring by a light string that passes over a pulley.
When the mass is released, the spring has a force constant of 500 N/m.
A block is on an incline.
The mass is connected to a massless spring by means of a light string.
The force constant is 100 N/m.
The spring is un stretched after the block is released.
The block comes to rest at a distance of 16 cm.
A car is travelling up a steep incline at a speed of 25 MPH.
If you divide 1 N by 2, you get 1 kg m/s 2.
You can verify which expression has units of joules per second to get the answer.
gravity is the only conservative force that can do work if there is no friction.
The average force must be halved if the velocity is doubled and the power is constant.
The average speed of the belt must be halved.
The work is being taken from the beginning.
Since the motion is horizontal, N is equal to f.
The velocity changes will be the same regardless of the amount of mass.
The work needed to raise the mass a height is provided by this energy.
h is equal to 0.54 m.
The value decreases with angle.
The work decreases as well.
As long as the same mass is raised to the same height, the work done to run up the stairs remains the same.
If we assume that the starting energy for the system is zero, the loss of potential energy is balanced by a gain in elastic potential energy for the spring.
The mass displacement is the same as the spring's.
v is 1.7 m/s.
The work done by gravity down the incline is affected by the work done by friction.
The net work is applied to stretching the spring by an amount equal to the displacement of the mass.
The coefficient of friction is given a value of 0.036.
The motion of an object is relative to the frame of reference.
We can imagine a second frame moving with the object in which it appears to be at rest, if an object is moving relative to one frame.
The object has energy because of its relative motion.
In the second frame, the object appears to be at rest.
The force of gravity causes your arm muscles to strain.
You feel tired because this requires energy from your body.
We use our knowledge of inclined planes to determine how much force the car must exert in order to cancel out the downward force of gravity.
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