#85012 QUIZ 4

 1. A block at rest slides from the top of a 3-m incline with an inclination of 20˚ to the horizontal. The block gains a speed of 2.5m/s at the base of the incline. What is the coefficient of kinetic friction between the block and the incline?

Solution. We draw the free-body diagram for the block, and choose the coordinate system as shown. We find the acceleration of the block from                v2 = v02 + 2axx;               (2.5m/s)2 = 0 + 2ax(3m),  which gives ax = 1.04m/s2.                      We write SF = ma for the block.                x-component: mgsinq - Ffr = max;                y-component: FN - mgcosq = 0. We have Ffr = mkFN = mkmg. From x-equation we have ax = (sinq  - mkcosq)g.                (1.04m/s2) = (sin20° - mkcosq)(9.80m/s2), which gives mk = 0.25.

2.A horizontal force of 250N force is exerted on a 5.0-kg ball as it is rotated uniformly in a horizontal circle of radius 1.00m. Calculate the speed of the ball.

Solution.

We find the speed from

                 F = mv²/R;

                 250N = (5.0kg)v²/(1.00m), which gives v = 7.07m/s.