Question

A sled of mass 10.0 kilograms is pulled along flat snow-covered ground. The static friction coefficient is 0.335, and the kinetic friction coefficient is 0.126.a. What force is needed to start the sled moving?b. What force is needed to keep the sled moving at a constant velocity?

Answer 1

a.

The force needed to move an object has to be more than the maximum force of friction which is given by:

`f_s_{}=\mu_sN`

in this case the normal is the same as the weight then the maximum force of friction is:

`\begin{gathered} f_s=(0.335)(10)(9.8)_{} \\ f_s_{}=32.83 \end{gathered}`

Therefore the force needed to move the object is 32.83 N.

b.

Now that the object is moving we have two forces acting on it, the force applied (which we are going to denote by F) and the kinetic force of friction, then our equation of motion is:

`F_{}-f_k=ma`

since we want the sled moving at constant speed the acceleration has to be zero, then we have:

`\begin{gathered} F-f_k=0 \\ F=f_k \\ F=\mu_kN \\ F=(0.126)(10)(9.8) \\ F=12.35 \end{gathered}`

Therefore the force needed to keep the sled moving at constant speed is 12.35 N.