Question

With what acceleration will a horizontal force of 20 N move a 5 kg object along a horizontal floor if the coefficient of friction between the floor and the object is 0.18?

Answer 1

Projections of net forces, acting on the object are:

$ox:$ $F_x = F - F_f$, where $F = 20 N$ is given horizontal force and $F_f = \mu N$ is static friction, $N$ is normal force.

$oy:$ $F_y = N - m g$

Since $a_y = 0$, from the second equation, $N = m g$, hence from the first equation: $m a_x = F_x = F - F_f = F - \mu N = F - \mu m g$, from where $a_x = \frac{F}{m} - \mu g \approx 2.23 \frac{m}{s^2}$.