Question

Santa doesn't want to push a 25.0 kg wooden box across a wooden floor with a uk of 0.20 at

a constant speed of 1.0 m/s. So he asks the same guy in a blue polo shirt to move the box for

him. How much force does the "helpful guy" have to exert on the box?

Answer 1

49 N

Step-by-step explanation:

In order to move the box at constant speed, the acceleration of the box must be zero (a=0): this means, according to Newton's second law,

F = ma

that the net force acting on the box, F, must be zero as well.

Here there are two forces acting on the box in the horizontal direction while it is moving:

- The force of push applied by the guy, F

- The frictional force,
`F_f`

For an object moving on a flat surface, the frictional force is given by

`F_f = \mu_k mg`

where

`\mu_k` is the coefficient of friction

m is the mass of the box

g is the acceleration of gravity

So the equation of the forces becomes

`F-\mu_k mg = 0`

And substituting:

`\mu_k = 0.20\\m = 25.0 kg\\g = 9.8 m/s^2`

We find the force that must be applied by the guy:

`F=\mu_k mg = (0.20)(25.0)(9.8)=49 N`