A worker pushes horizontally on a 32 kg crate with a force of magnitude 108 N .

Question

A worker pushes horizontally on a 32 kg crate with a force of magnitude 108 N . The coefficient of static friction between the crate and the floor is 0.37.
(a) What is the frictional force on the crate from the floor?


N

(b) What is the maximum magnitude fs, max of the static frictional force under the circumstances?


N
(c) Does the crate move?
yes
no
cannot tell from the information given



(d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull that will allow the first worker's 108 N push to move the crate?


N

(e) If, instead, the second worker pulls horizontally to help out, what is the least pull that will get the crate moving?


N

Explanation / Answer

(a) The frictional force on the crate from the floor = mg = 0.37 X 32 X 9.8

= 116.032 N

But as the applied force is 108N , the frictional force is also 108N.

(b) The maximum magnitude fs, max of the static frictional force under the circumstances

= mg = 0.37 X 32 X 9.8

= 116.032 N

(c) No

(d) The second worker pulls up. Let the force applied by him be F.

Now (mg - F) = 108

This gives F = 21.7N

(e)

The least horizontal force = mg - 108 = 116.032 N - 108N = 8.032 N

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