Physics: Energy and momentum study guide 2

when the speed is a maximum and the displacement is 0

KE

when the speed is a 0 and the displacement is at a maximum

PE

A weightlifter brings a 400-N barbell upward from his shoulders to a point 50 cm higher at a steady speed. During this process, what is the total work done on the barbell?

0 joules

A weightlifter exerts an upward force on a 1000-N barbell and holds it at a height of 1 meter for 2 seconds. Approximately how much power does the weightlifter exert on the barbell during this time?

0 watts

When do I have a minimum velocity?

Also, when I am at equilibrium

In a pendulum, the law establishes that, when the ball is at its highest point, all the energy is potential energy and there is zero kinetic energy.

At the ball's lowest point, all the energy in the ball is kinetic and there is zero potential energy. The total energy of the ball is the sum of the potential energy and kinetic energy.

Where is my velocity at zero?

At the maximum and minimum velocity

When do I have a maximum velocity?

I have a maximum velocity when my position is at equilibrium.

According to the work-energy theorem the total work on an object is equal to the change in that object's kinetic energy.

Since the barbell is moving at a constant speed its kinetic energy does not change during that process and the total work on it must be zero. In other words, the work done by the weightlifter (+200 J) and the work done by gravity (-200 J) cancel each other out, causing no change in the barbell's kinetic energy.

When you push on the block and compress the spring, the potential energy in the spring increases because the spring does negative work on the block. By definition, the change in potential energy is equal to the negative work done by the force: Delta U equals negative W.

Since the work done by the spring force is negative because the force points in the opposite direction of the displacement, this makes the potential energy increase: Positive delta U equals negative negative W. Whenever the spring is compressed or stretched, it will store non-zero potential energy. The potential energy stored in the spring is a function of the deformation of the spring, x, and increases more and more as the spring is compressed.

200 J is the amount of work done by the weightlifter, but it is not the total work done on the barbell. -200 J is the amount of work done by Earth's gravity, but it is not the total work done on the barbell.

Since the work done by the weightlifter and Earth's gravity have opposite signs they cannot be added to get a total of 400 J or -400 J.

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction to compress the spring and then release the block, what happens to the energy in the system immediately after the block is released?

The elastic potential energy in the spring decreases while the kinetic energy of the block increases.

The spring has zero potential energy when the block is at x = 0, where the spring is neither stretched nor compressed.

The elastic potential energy stored in a spring is a function of the deformation in the spring, x, or how much it has been stretched or compressed from equilibrium: ½kx2. At equilibrium, x = 0, so the elastic potential energy is zero.

When the spring is stretched or compressed to its maximum value, the elastic potential energy stored in the spring is at maximum.

The elastic potential energy then decreases as the spring relaxes back to its equilibrium position.

A block slides along a rough surface and comes to a stop. What can you conclude about the frictional force exerted on the block?

The frictional force does negative work on the block and decreases its kinetic energy.

Since there are no non-conservative forces doing work on the system, the mechanical energy of the system is conserved. This means that the elastic potential energy that is stored in the system when the spring is compressed will convert into kinetic energy of the block as the spring decompresses.

The gravitational potential energy of the block does not change during this horizontal motion because the block does not experience a change in height at all. The only types of mechanical energy that change during this motion are kinetic energy and elastic potential energy.

The work done by the force is equal to the area under the force versus position function. Work is defined as F sub x times delta x, or the x-component of the force multiplied by the displacement in the x-direction when the force is constant. If the force is varying then one needs to consider infinitesimal segments where the force is approximately constant and add them together. This sum of small rectangular areas is equivalent to the area under the curve when calculating the area under the force versus position graph.

The slope of the force versus position graph would have units of N/m, which are not Joules, the units for work, so the slope cannot be the method to determine the work done by the force. The maximum value of the force has units of N, not J, so it cannot be equal to the work done by the force. Multiplying the maximum value of the force and the object's position, 10 N x 8 m, does result in the correct units for work, N*m, or J, but it would result in twice as much work from 0 to 8 m and it would not include the work for the last part of the motion (from 8 m to 12 m).

Where along the x-axis does the block have to be for the spring to have zero potential energy?

The spring has zero potential energy when the block is at x = 0, where the spring is neither stretched nor compressed.

Power is the rate at which work is done, or W divided by delta t. Since the barbell is not moving, the weightlifter is not doing work on the barbell.

Therefore, if the work done is zero, then the power is also zero.

the frictional force acting on the block points in the opposite direction to the displacement of the block, so by definition the work is negative. A

according to the work-energy theorem, the work done is equal to the change in kinetic energy. A negative change in kinetic energy means that the kinetic energy decreases.