Answer to Question #150210 in Physics for Andu

Question

The body with mass m = 1.2kg is pulled with the horizontal force F = 20 N on a rough horizontal surface and during 3 s makes the way 6 m starting from the resting position. Calculate the force and coefficient of sliding friction.

Answer 1

The net force, acting on the body is $\bold F + \bold N + \bold F_f + m\bold g$, and is equal to $m \bold a$, by second Newton's law. In projections:

$oy$: $N = mg$,

$ox$: $ma = F - F_f$.

Kinetic friction is $F_f = \mu N$, and using $oy$ equation, $F_f = \mu m g$. Substituting into $ox$ equation, obtain $ma = F - \mu mg$, or $a = \frac{F}{m} - \mu g$.

Displacement of the block in time $t$ is $s = \frac{a t^2}{2}$, from where $a = \frac{2 s}{t^2} = \frac{F}{m} - \mu g$.

From the last equation, coefficient of friction is $\mu = \frac{1}{g}\left[\frac{F}{m} - \frac{2 s}{t^2}\right] \approx 1.56$, and $F_f = \mu m g = 18.4 N$.