A solid ball of mass 1.0kg and radius 10 cm rolls with a forward speed of 10 m/s

Question

A solid ball of mass 1.0kg and radius 10 cm rolls with a forward speed of 10 m/s when it comes to a hill. There is enough friction on the hill to keep the ball from slipping as it rolls up. Consider the ball a sphere with a Moment of Inertia = 2/5MR2.

a. How high vertically up the hill can the ball roll before coming to rest.

b. How high vertically could the ball go if the hill were totally frictionless.

c. Based on your answers from parts A and B above, which trial did the ball roll higher? Explain your rationale why that is correct.

Explanation / Answer

(a)

when there is enough friction on the hill,

ball's total initial KE,

KEi = (1/2)*m*v^2 + (1/2)*l*w^2

KEi = 0.5*m*v^2 + 0.5*(2/5*m*r^2)*(v / r)^2

KEi = 0.70*m*v^2

apply conservation of energy,

KEi + PEi = KEf + PEf

0.70*m*v^2 = m*g*h

h = 0.70*100 / 9.8

h = 7.1 m

(b)

when hill is totally frictionless,

apply conservation of energy,

KEi + PEi = KEf + PEf

(1/2)*m*v^2 = m*g*h

h = 100 / 2*9.8

h = 5.1 m

(c)

The Ball goes higher with friction than without friction.

Because  with friction, all the initial kinetic energy (translational and rotational) goes into potential energy.

Without friction, only the translational kinetic energy goes into potential energy.

answer

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