A box with an initial speed of #3 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #4/5 # and an incline of #( pi )/6 #. How far along the ramp will the box go?
The box will move 0.38 m along the ramp.
A change in gravitational potential energy:
Before we can continue, we need to be aware of a couple of complications
We must express
Also, we must note that the normal force on an incline is not equal to mg, but to
With all that looked after, our equation becomes
Notice that we can divide every term by the mass m, (including the right side of the equation).
Also, you should check the equation for signs. The kinetic energy term will be negative - the box slows down. The potentail enrgy and frictional heat terms are both positive. Both of these energy forms increases.