Question

A 15.0 kg sled is pushed at 5 m/s up an icy slope that has an incline angle of 10 degrees. If the coefficient of kinetic friction is 0.050, how far up the slope will the sled travel before stopping? (The answer is 5.73 m, but I need to see all the steps to understand how to arrive at this answer.)

Answer 1

This question will be easily solved by applying Energy Conservation.

i.e. One form of energy gets converted to other form. Therefore, total energy of a system at an instant always remains constant.

Here the sled got pushed with an initial velocity (u) = 5 m/s , that means it acquired kinetic energy (K.E) from that push. As it moves up the icy slope, some part of this kinetic energy gets converted into it's potential energy (P.E) and the rest part gets consumed in overcoming the frictional force (F) that is trying to stop the motion of the sled.

where, m is the mass of the sled and u is it's initial speed

where, m is the mass, g is acceleration due to gravity (9.8 m/s^{​​​​​​2}​​​) and h is the vertical height of the object from ground

where ( is the coefficient of friction and N is the normal reaction force on sled exerted by the slope and it's given by mg cosθ, and θ is the incline angle)

Now the sled will gradually come to stop (let's say after traveling a distance S). At that instant all of it's kinetic energy has spent (converted into potential energy + lost in overcoming friction).

Now you can see from the diagram that :-

Using it in eqn.(1)

Putting the values :-