7. [25] A box of bananas weighing 40.0 N rests on a horizontal surface. The coef
ID: 2031547 • Letter: 7
Question
7. [25] A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40 and the coefficient of kinetic friction is 0.20. (a) If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on the box? (b) What is the magnitude of the friction force if a monkey applies a horizontal force of 6.0 N to the box and the box is initially at rest? (c) What minimum horizontal force must the monkey apply to start the box in motion? (d) What minimum horizontal force must the monkey apply to keep the box moving at constant velocity once it has been started? (e) If the monkey applies a horizontal force of 18.0 N, what is the magnitude of the friction force? () If the monkey applies a horizontal force of 18.0 N, what is the box's acceleration?Explanation / Answer
a) Static friction is the relevant type for an object at rest, and would oppose a horizontal force. With no applied force
in the horizontal there’s no friction force either.
b) The maximum possible static friction force this box-surface interface could produce is fS,max =µSN =(0.40) (40.0)=
16 N.
The applied 6.0 N is below that maximum, so static friction will negate it with an opposing force of 6.0 N.
c) The monkey would need to apply more than 16 N
d) In order that it move at a constant velocity, the net force on the box should be zero. The monkey will need to balance the friction force by carefully applying a force of equal magnitude and opposite direction. A moving box is in the realm of kinetic friction, so we use the kinetic friction coefficient to calculate the necessary applied force:
Fapplied
= | fK| = µKN = (0.20) (40.0) = 8.0 N.
e) 18.0 N is more than either the static or kinetic friction are capable of opposing, so in this case the box will always experience a net horizontal force and hence accelerate. At any time when the box’s velocity is nonzero, the friction
force will be 8.0 N as in part (d).One could argue that even an accelerating object can have zero velocity for an instant, and in such an instant the maximum static friction force, 16 N, would exist instead. However it’s unlikely that our empirical formulae for
friction forces are so reliable as to pertain to such an extreme case.
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