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.
- When you rapidly jerk on the lower thread, the lower thread stretches rapidly and the
tension rapidly increases. This rapidly increasing force is applied to the stone
which accelerates (tension in upper thread - tension in lower thread = mass of stone x
acceleration of stone). The tension in the upper thread only increases as the upper
thread stretches and it can only stretch due to the motion of the stone. The motion
of the stone takes time due to the stone's finite mass and therefore the increase in the
tension in the upper thread lags behind that in the lower thread. If the tension
increases fast enough in the lower thread and if the stone is massive enough, the tension
in the lower thread will exceed the breaking point before the upper thread and the lower
thread will break.
Q13. When you car is struck from the rear, the forward motion of the seat exerts
a force on your body which causes it to accelerate forward. Unless your head is in
contact with a headrest attached to the seat, this force is not transmitted to your head.
Your body accelerated forward as you head tends to remain at rest. Your head
rotates as your neck pulls your head forward. This twisting and sudden jerk (i.e.,
force) exerted by your neck to accelerate your head forward and prevent it from becoming
detached from your neck is called "whiplash."
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