How would you do this problem?

Question

A 2-kg block sits on an incline where the top part of the incline has a coefficient of friction of kinetic friction of 0.70. The bottom section of the plane has kinetic friction of 0.95. THe angle of inclination is 40 degrees. The block is released and travels 10 m along the initial part of the incline and then enters the lower section. Calculate how far the block travels along the second section before it is brought to a stop.

I only want to know how to do it, because i don't know how to set it up. Please help me figure this out.

Answer 1

I agree with nitrojunkie that you need to resolve the force of gravity into components that are perpendicular to the inclined plane and parallel to it.

The force parallel to the plane (i.e., down the ramp) tends to accelerate the block. The force perpendicular to the plane results in a force between the block and the plane. This force times the coefficient of friction equals the force that resists the force accelerating the block.

So you calculate the NET force accelerating the block down the first part of the plane, and determine the rate of acceleration, a. Then use the formula s = a t^2/2 to determine the time (t) that it takes to travel 10 m. Finally, multiply t by a to find the velocity at the end of the 10 m.

Similarly, you can calculate the net force DEcelerating the block in the second part of the plane. Given its velocity at the end of the first part, you can determine how many seconds it will take for the velocity to reach 0.

You can then use the standard formula to calculate the distance traveled during this time (given the initial velocity in this section and the rate of deceleration). Or you can just say that the AVERAGE velocity in this section is half of the velocity at the beginning of the section. So this average velocity, multiplied by the time before the block stops, equals the distance traveled in the second section.

Hope that gives you what you need.

Answer 2

Hints.... Friction deals only with the perpendicular component of force. So you're going to need to break gravitational forces up into components parallel and perpendicular to the incline. Then you're going to need potential and kinetic energies for the block. It might be usefull to consider the work-energy theorem too (work=force*distance).