Newton's Laws and Momentum

• Momentum is a physical quantity that a moving object has

• The momentum of an object depends on its mass (m) and velocity (v)

• Momentum is a VECTOR quantity - therefore has magnitude and direction

• Momentum is always conserved

• Hence, total momentum before a collision = total momentum after a collision

Elastic Collision

• Momentum is always conserved

• Kinetic energy is conserved

• No energy is dissapated to the surroundings

Inelastic Collision

• Momentum is always conserved

• Kinetic energy is not conserved

• Energy is dissapated to the surroundings eg. heat, sound

Newton's Second Law says - the force is equal to the rate of change of momentum

• F = (mv-mu)/t .... rearrange to get Ft = mv-mu

• Impulse = average force x time

• Therefore, the force of an impact can be reduced by increasing the time of the impact

• This is why cars have crumple zones

An object will continue in a state of rest of of uniform motion unless acted upon by a resultant force.

• If forces are not balanced eg. there is a resultant force, then the overall resultant force will cause the object to accelerate

• Acceleration of an object can mean a change in direction or speed, or both

The rate of change of momentum of an object is directly proportional to the resultant force on the object and in the same direction.

• If mass is constant then F=ma applies

• The more force you have on a mass, the more the mass accelerates

• For a given force, the more mass you have, the smaller the acceleration

• F=ma cannot be used when the mass of an object is changing

• In this situation Newton's Second Law still applies but you must use Force=change in momentum/time

If object A exerts a force on object B, then object B exerts an equal and opposite force of the same type of object A.

• The forces represent the same interaction but from different perspectives

• Newton's Third Law is a consequence of the conservation of momentum

• A resultant force acting upon an object means a change in mass or acceleration

• Hence this means a change in momentum

• Momentum is always conserved, so the forces must be equal so that the overall change in momentum is zero