# 9709. Mechanics 1. Work & Energy

Work done is calculated as the force applied to an object multiplied by the distance over which it is applied (Work Done = Fs).

Clearly if the force is acting at an angle to the direction of motion, we multiply the force by the cosine of the angle.

Note that we talk about work done by or against specific forces and in a specific direction. Work done is, however, a scalar quantity measured in Newton metres, typically called Joules. If a particle doesn’t move, then work done is zero.

Worked Examples

• A book, initially at rest, is raised by a force averaging 40N to a height 5m above the ground (where it is again at rest). How much work is done by the force?
• A book of mass 5kg is pushed up a slope inclined at 30º to the horizontal by a force of 30N at an angle 10º to the slope. The frictional force acting on the book is 2N. The book moves 3m up the slope.
• Find the work done
• against friction;
• against gravity;
• by the push force;
• by the normal reaction.
• Find the total work done on the book by all four forces.

Exercise

Kinetic Energy

In this section we are only interested in mechanical energy (i.e. not heat, light, chemical energy etc.)

Kinetic energy is the energy a body possesses because of its motion. $KE = \frac{1}{2}mv^2$

Kinetic energy is measured in Joules.

Worked Examples

• Find the kinetic energy of a body of mass 3kg moving at 5ms-1.
• A ball of mass 50g hits the ground with speed 10ms-1 and rebounds with speed 6ms-1. Find the loss in kinetic energy that occurs in the bounce.

Exercise

Gravitational Potential Energy

As well as kinetic energy (“KE“), the other mechanical energy we will consider here is gravitational potential energy (“PE“), which is the energy that a body has stored and could release if it fell under gravity, PE = mgh

Worked Example

• Find the increase in potential energy when a box of mass 1kg is raised to a height of 3m.
• A skier slows down a smooth ski slope 400m long which is at an angle of 30º to the horizontal.
• Find the speed of the skier when she reaches the bottom of the slope.
• At the foot of the slope the ground becomes horizontal and is made rough in order to help her stop. The coefficient of friction between her skis and the ground is 1/4.
• Find how far the skier travels before coming to rest;
• In what way is your model unrealistic?
• Evelyn, whose mass is 40kg, takes part in an assault course. The obstacle shown below is a river at the bottom of a ravine 8m wide, which she must cross by swinging on a rope 5m long secured to a branch of a tree immediately above the centre of the ravine. Find out how fast she is travelling at the lowest point of her crossing if:
• She starts from rest;
• She launches herself at a speed of 1ms-1.

Exercise and General Exercises