Exercise 10.29 A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up

Question

Exercise 10.29

A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 6.00 mabove the base of the hill. We can model this ball as a thin-walled hollow sphere.

Part A

At what rate was it rotating at the base of the hill?

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Part B

How much rotational kinetic energy did it then have?

Exercise 10.29

A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 6.00 mabove the base of the hill. We can model this ball as a thin-walled hollow sphere.

Part A

At what rate was it rotating at the base of the hill?

SubmitMy AnswersGive Up

Part B

How much rotational kinetic energy did it then have?

Explanation / Answer

K.E. initially = 0.5*I*w2+ 0.5*m*v^2

v= w*R

I = 2/3 mR^2

potential energy final = mgH

= 0.426 *9.81 * 6

R= 11.3 cm

0.5*2/3*m*V^2 +0.5* mv^2 = 0.426 *9.81 * 6

0.5*2/3*V^2 +0.5* v^2 = 9.81 * 6

8.40428462155 m/s =V

w=

8.40428462155 / (11.3/100) =74.3742001907 rad/s

rotational K.E. = 0.5*  2/3 *0.426 (11.3/100)^2 * 74.3742001907^2

=10.029744 J

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