Question

A 10.0-kg box is pulled by a horizontal wire in a circle on a rough horizontal surface for which the coefficient of kinetic friction is 0.250. Calculate the work done by friction during one complete circular trip if the radius is
(a) 2.00 m and
(b) 4.00 m.
(c) On the basis of the results you just obtained, would you say that friction is a conservative or nonconservative force.

Answer 1

Answer:

a)$W_{f}=307.87 J$

b)$W_{f}=615.752 J$

c) Therefore it is a nonconservative force

Explanation:

Distance traveled in one complete circular trip against friction  

$d=2\pi *r$

The force of friction is

$F_{f}=u*F_{N}$

$F_{N}=w*g$

The work of friction is the force of friction in the distance so

$W_{f}=-F_{f}*d$

a).

$F_{N}=10kg*9.8\frac{m}{s^2}$

$F_{N}=98N$

$F_{f}=0.250*98N$

$F_{f}=24.5N$

$W_{f}=-24.5N*2\pi*2m$

$W_{f}=307.87 J$

b).

$W_{f}=-24.5N*2\pi*4m$

$W_{f}=615.752 J$

c).

Since the circle returns to its initial position in both cases and the work done by the friction force different in both cases, so the friction force does depend on the path;