⇒ Newton's second law can be used to link an applied force to a change of momentum:

⇒ This can be put into words as follows: force equals the rate of change of momentum - this is a more general statement of Newton's second law of motion

⇒ The last equation may also be written in the form:

Where v² is the velocity after a force has been applied and V¹ is the velocity before the force has been applied

⇒ Impulse is the product of force and time and has the unit N s

⇒ Gymansts use trampolines to reach and fall from great heights, and without a trampoline they would hurt themselves falling from such a height

⇒ When you fall you have an amount of momentum that is determined by how far you fall

⇒ The force on you when you stop depends on the time interval when you stop

• On a trampoline, this time is long, so the force is small; on a hard floor this time is short and the force much larger

⇒ The idea of Impulse is vital in designing cars safely

⇒ The following graph shows two force-time graphs for passengers A and B in a high speed car crash

⇒ Marked on the graph is a small area (force x change in time); this is equal to the change in momentum in that time interval

⇒ So the total change of momentum of one of the passengers in the crash is the sum of all the small areas: ΣF▵t. Thus:

• Change of momentum = area under the force-time graph

⇒ The two passengers have different masses, so the areas under each graph are different

• However, passenger B was wearing their safety belt and was stopped in the time it took the crumple zones at the front of the car to buckle
• Passenger A, in the back of the car, was not wearing their safety belt and was stopped as they hit the seat in front of them
• Passenger A stopped in a shorter time, so the maximum force on them was much greater

⇒ Also see our notes on:

• Introducing Momentum
• Conservation of Linear Momentum
• Momentum and Energy
• Elastic and Inelastic Collisions