Question

34. Two students, Tom and Jerry devise a plan to determine the coefficient of friction between socks and freshly waxed floors at the school. Tom (60kg) pulls Jerry (75kg) with a force of 185N to get him to start sliding across the floor.a) What is the magnitude of the force that Jerry exerts on Tom? b) What is the normal force of Jerry from the surface? c) What is the coefficient of static friction between the socks and the waxed floor?

Answer 1

a.

By Newton's third law we know that every action has an equal but opposite reaction, in this situation this means that if Tom pulls Jerry with a force of 185 N, then Jerry pulls Tom with equal force but in opposite direction.

Therefore the magnitude of the force that Jerry exerts on Tom is 185 N.

b.

The normal force is defined as the force that any surface exerts on an object. In this case the normal force exerted on Jerry has to be equal to its weight, this is consequence of Newton's third law: If Jerry exerts its weight on the surface then the surface exerts a force with the same magnitude but in opposite direction; and by definition this is the normal force. Hence we have:

`\begin{gathered} N=W \\ N=mg \\ N=(75)(9.8) \\ N=735 \end{gathered}`

Therefore the normal force exerted on Jerry is 735 N

c.

The force of static friction fullfils the following relation:

`f_s\leq\mu_sN`

and it is equal when the force applied to the object is enough for the object to start moving.

In this case we know that the force applied is enough for Jerry to start sliding across the floor, this means that in this case we have that:

`f_s=\mu_sN`

Since Jerry is starting to slide this means that the force of friction is equal to the force applied, then we have:

`\begin{gathered} 185=735\mu_s \\ \mu_s=(185)/(735) \\ \mu_s=0.252 \end{gathered}`

Therefore, the coeeficient of static friction is 0.252 (rounded to three decimal plances)