Work done is the change in energy of a body, when a force acts on it. It is defined as the product of the force × distance.
Work will be the area under a force displacement graph. This is particularly true if the force is not constant. The units of work (Joules) must be the same as the units of energy, because work done is change in energy.
If a force acts at an angle to the direction of the displacement, then the work done is given by:
If the force acts at right angles to the direction of motion, then the work done is zero because cos 90° = 0.
A fundamental principle of nature is that energy is never lost… Energy cannot be created or destroyed, it can only change from one form to another.
Lets consider the energy transformation of a simple tennis ball of mass 0.1 kg, at a height of 3m…
At this height the gravitational potential energy is:
Ep = mgh = 0.1 ´ 9.8 ´ 3
Ep = 2.94 J
The Kinetic energy (EK = ½mv2) at this point = 0
The elastic potential energy of the tennis ball = 0, as the tennis ball has not yet been compressed.
Ep = 0.1 ´ 9.8 ´ 1.5
= 1.47 J
EK = 1.47 J
Es = 0 J Et = 2.94 J
Ep = 0.1 ´ 9.8 ´ 0
= 0 J
EK = 2.94 J
Es = 0 J Et = 2.94 J
Question
A 2 kg mass is thrown to a height of 20 m.
a) What is its potential energy at this height?
b) What is the kinetic energy at this height?
c) What is its kinetic energy as it hits the ground?
d) With what velocity will it hit the ground?
When two objects collide, the total energy of the system is always conserved.
However, the total energy of the two objects is not conserved, because when they make contact some of their energy is transferred to the surroundings.
As we know, energy cannot be created or destroyed. It can only be converted from
one form into another. During most energy transformations, some energy is degraded into less useful forms, heating the surroundings and causing noise.
The collision between the two billiard balls is an almost perfect elastic collision.
An elastic collision is one in which the total kinetic energy after the collision is the same as it was before the collision.
A perfectly elastic ‘collision’ can only take place if the interacting objects do not actually make contact with each other. A perfectly elastic interaction can take place when two electrons move towards each other in a vacuum.
The collision between the two cars is an inelastic collision.
Even though momentum is conserved, the total kinetic energy of the cars after the collision is considerably less than it was before the collision.
An inelastic collision is one in which momentum is conserved but kinetic energy is transferred into other forms.
A significant proportion of the initial kinetic energy of the system is transferred to the bodies of both cars, changing their shapes and heating them.
Question
A white car of mass 800 kg is driven along a slippery straight road with a speed of 20 m s−1. It collides with a stationary blue car of mass 700 kg. The blue car is pushed forwards with a speed of 12 m s−1.
a) What is the speed of the white car after the collision?
b) Show that the collision is not elastic.
Remember: In an elastic collision, EK before collision = EK after collision