Im stuck on both of these problems. Can someone explain them? A heavy spherical

Question

Im stuck on both of these problems. Can someone explain them?

A heavy spherical ball with mass m = 4.4 kg and radius 11 cm is ready to roll down a track, without slipping, onto an expanse of grass, as shown in the figure below. The friction force of the grass on the rolling ball is 7 N. If the ball reaches the bottom of the track and starts rolling, without slipping, across the grass with a speed of 3 m/s, how far will the ball roll before coming to rest (closest answer in meters)? The moment of inertia of a sphere is (2/5)mR^2. 0 m 1 m 2 m 3 m 4 m 5 m 6 m 7 m 8 m In the previous problem the ball rolls down the track without slipping and without frictional losses, arriving at the bottom with speed 3 m/s. What Ls the height h of the track (closest answer in meters)? 0.05 m 0.25 m 0.45 m 0.65 m 0.85 m

Explanation / Answer

first problem

initial velocity=3 m/s

angular speed=velocity/radius=3/0.11=300/11 radian/sec

initial kinetic energy=0.5mv62+0.5*I*w^2=27.72 J

let it move x m

initial kinetic energy=tranlation kinetic energy+translational kinetic energy=work done by friction

27.72=7x

x=3.96 m

so answer is 4 m

second question

final kinetic energy=initial potential energy

kinetic energy=rotational kinetic energy+translation kinetic energy=7.92+19.8=27.72 J

27.72=mgH

27.72=4.4*9.8*H

H=0.65 m

correct answer is 0.65 m

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