Question

A 3.90 kg block is acted upon by a horizontal force F(x) = 24.0 - 10.0x where the force is measured in Newtons if x is measured in meters. The coefficient of kinetic friction between the block and the flat surface is 0.190. The block is initially at x = 0 m.

F(x)

a) What distance must the block travel if the net work done on the block by F(x) and friction combined is to be exactly zero?_________________

b) At what point along the way does the net force on the block reach zero?________________________

Answer 1

given

F = 24 - 10x

a) let the distance be = d meter

condition given is Wfr = WF

work done by F = F dx

Ffr x d = $\int_{0}^{d}$ (24 - 10x) dx

$\mu$ N d = 24 d - 5d²

0.19 (3.9 g) d = 24 d - 5d²

d = 3.35 m

answer

b) the net force will reach zero when F = friction force

24- 10x = $\mu$ N = 0.19 ( 3.9) 9.81

24 - 10 x = 7.27

x = 1.67 m

answer