When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 1.95 m/s. The mass stops a distance S2 = 2.15 m along the level part of the slide. The distance S1 = 1.10 m and the angle theta = 37.1 degrees. Calculate the coefficient of kinetic friction for the mass on the surface.

Question

anonymous · Answer

Find the deceleration from friction:
V2^2 = V1^2 - 2ad

Then add up force of friction and the component of mg along the plane and set it equal to ma.

anonymous · Answer

i dont understand.. can you show me the steps?

anonymous · Answer

After you find the deceleration from the equation given, add up the forces and set it equal to ma:
Frictional force: $$F_{f} = \mu_{k}mg\cos{\theta}$$
The component of mg in the direction of the plane = mgSin(theta)

Draw a picture of all these forces, including the Normal force which gives the equation for friction.

anonymous · Answer

Can you figure it out from here?

anonymous · Answer

Sorry, the first equation should be:
V2^2 = V1^2 + 2ad
That will give you a negative acceleration.
Then look at the direction of the frictional force and the component of mg along the incline to determine if they should be positive or negative.