Sunday, December 31, 2006

Applying Newton's Laws to terminal velocity

Think about the freee fall parachutist example:

At first, the only force acting on her is her weight. She has no air resistance at first because her initial speed is zero.

Hence she has a resultant force downwards. Newton's Second Law states that rate of change of momentum is proportional to reultant force, so she accelerates.

As her velocity increases in magnitude, her weight remains constant but her air resistance increases. This means that her resultant force is still downwards but decreases in size. She still accelerates, but she does not gain as much speed each time.

Eventually, the air resistance is the same size as the weight. Resultant force is zero. Newton's First law says that objects continue with uniform motion (straight line, constant speed to you) unless an external resultant force acts. No resultant force thus means constant speed.

When she opens her parachute, her weight remains the same but the air resistance increases greatly. This gives her a resultant force upwards. The second part of Newton's Second Law states that the change in momentum takes place in the direction of the resultant force. If you have momentum downwards but the change is upwards, you must slow down.

As she slows down, her air resistance decreases, but her weight stays the same. Hence her resultant force upwards decreases. She continues to slow down but not by as much each time.

Eventually, she has slowed so much that the size of the air resistance is the same as her weight. Once again she goes at constant speed by Newton's First Law. However, this time it is a smaller terminal velocity so she does not get hurt when she hits the ground.