Work, Energy and Power

By using the initial elastic potential energy of the compressed spring, calculate its spring constant.

spring constant = ______ $\text{N m}^{-1}$

Calculate the speed of the spring as it leaves the surface of the table.

speed = ______ $\text{m s}^{-1}$

Calculate, for this movement of the spring, the increase in height of the spring after leaving the surface of the table.

increase in height = ______ $\text{m}$

Calculate the average frictional force exerted by the rod on the spring as it rises.

average frictional force = ______ $\text{N}$

The rod is replaced by another rod that exerts negligible frictional force on the moving spring. The initial compression $x$ of the spring is now varied in order to vary the maximum increase in height $\Delta h$ of the spring after leaving the surface of the table. Assume that the spring obeys Hooke’s law for all compressions.

On Fig. 3.2, sketch a graph to show the variation with $x$ of $\Delta h$. Numerical values are not required.

Define power.

state the change in the kinetic energy

change in kinetic energy = ______ $\text{J}$

calculate the work done against the total resistive force.

work done = ______ $\text{J}$

the increase in vertical height $h$ of the car for its movement from A to B

$h$ = ______ $\text{m}$

angle $\theta$.

$\theta$ = ______ $^{\circ}$

The engine of the car in (b) produces an output power of $1.7 \times 10^4\ \text{W}$ to move the car along the slope.

Calculate the time taken for the car to move from A to B.

time = ______ $\text{s}$

State what is meant by work done.

Use Fig. 2.2 to determine:

1. the acceleration of the lift between time $t = 0$ and $t = 3.0\ \text{s}$

acceleration = ______ $\text{m s}^{-2}$

1. the work done by the motor to raise the lift between time $t = 3.0\ \text{s}$ and $t = 6.0\ \text{s}$.

work done = ______ $\text{J}$

The motor has an efficiency of $67\%$. The tension in the cable is $1.6 \times 10^{4}\ \text{N}$ at time $t = 2.5\ \text{s}$.

Determine the input power to the motor at this time.

input power = ______ $\text{W}$

State and explain whether the increase in gravitational potential energy of the lift from time $t = 0$ to $t = 7.0\ \text{s}$ is less than, the same as, or greater than the work done by the motor. A calculation is not required.

Define power.

Use your definition in (i) to show that power may also be expressed as the product of force and velocity.

Calculate the useful power from the engine to move the lorry up the road.

power = ______ $\text{kW}$

State two reasons why the rate of change of potential energy of the lorry is equal to the power calculated in (i).

1. ______

2. ______

Explain what is meant by gravitational potential energy and kinetic energy.

gravitational potential energy: ______

kinetic energy: ______

Calculate

1. the initial kinetic energy of the ball,

kinetic energy = ______ $\text{J}$

1. the maximum height $H$ of the ball,

$H$ = ______ $\text{m}$

1. the gravitational potential energy of the ball at height $H$.

potential energy = ______ $\text{J}$

1. Determine the kinetic energy of the ball at its maximum height.

kinetic energy = ______ $\text{J}$

1. Explain why the kinetic energy of the ball at maximum height is not zero.

Explain what is meant by work done.

State a word equation that links the work done by the force $F$ on B to the changes in potential and kinetic energy.

The boy on the board B moves with velocity $v$ down the slope. The variation with time $t$ of $v$ is shown in Fig. 3.2.

The total mass of B is $75\ \text{kg}$.
For B, from $t = 0$ to $t = 2.5\ \text{s}$,

1. show that the distance moved down the slope is $9.3\ \text{m}$,

2. calculate the gain in kinetic energy,

gain in kinetic energy = ______ $\text{J}$

1. calculate the loss in potential energy,

loss in potential energy = ______ $\text{J}$

1. calculate the resistive force $F$.

$F$ = ______ $\text{N}$

in the first $2.0\ \text{s}$,

change in kinetic energy = ______ $\text{J}$

in the next $25\ \text{s}$,

change in kinetic energy = ______ $\text{J}$

in the final $3.0\ \text{s}$.

change in kinetic energy = ______ $\text{J}$

the gain in potential energy,

energy gain = ______ $\text{J}$

the power required.

power = ______ $\text{W}$

An object falls vertically from rest through air. State and explain the energy conversions that occur as the object falls.

Calculate the initial kinetic energy of the ball.

$\text{kinetic energy}$ = ______ $\text{J}$

The ball reaches a height of $21\text{ m}$ above the point of release.

For the ball rising to this height, calculate

1. the loss of energy of the ball to air resistance,

$\text{energy loss}$ = ______ $\text{J}$

1. the average force due to the air resistance.

$\text{force}$ = ______ $\text{N}$