# Homework 10/19/99

## Chapter 4:

Q4.  When you start out you must push hard enough (i.e., exert enough force) to counterbalance the frictional force and to cause the acceleration: F = friction + ma.   After you come up to speed you are no longer accelerating and you only need to exert enough force to counter balance the frictional force.

Q5.  When one non-zero force acts on an object it most accelerate since F = ma.   It can have zero velocity for an instant since it may be starting from a state of rest.

Q10.  Consider three cases:

• When you are not pulling on the thread, the tension in the lower thread is zero.   The tension in the upper thread must then equal the weight of the stone.   [Since the stone is not accelerating, sum of the vertical forces must be zero which means the upward force exerted by the tension in the upper thread must exactly balance the downward weight force.]  If the stone weighs enough, the tension is the upper thread could be large enough for the thread to break.
• When you slowly pull on the lower thread you stretch both threads and increase the tension in both threads.  Since you do it very slowly, the acceleration is essentially zero.  The tension in the lower thread equals the force you are exerting.   The tension in the upper thread must equal the weight of the stone plus the tension in the lower thread.  [Since the stone does not accelerate, the sum of the upward forces acting on the stone (the tension in the upper thread) must equal the sum of the downward forces acting on the stone ( the tension in the lower thread plus the weight of the stone).]  Since the tension in the upper thread is always higher, the upper thread will break first.