(2) A soccer ball can be modeled as a thin spherical shell. Its mass M = 450 g a

ID: 2240263 • Letter: #

Question

(2) A soccer ball can be modeled as a thin spherical shell. Its mass M = 450 g and radius R = 25.0 cm. It

rolls across the ground and then rolls up a hill without slipping, reaching a maximum height of 4.0 m

above the base of the hill before rolling back down.

(b) Using energy arguments, determine the speed v of the ball at the base of the hill.

(d) If the hill has a slope of 53 degrees, what is the smallest value of ? that allows the rolling without

slipping condition?

Here

mgh = 0.5*m*v^2 + 0.5*I*w^2

gh = 0.5*v^2 + 0.5*(2/3)v^2gh = 0.8333v^2

v = sqrt(9.8*4/0.8333)

= 6.8587 m/sec

v^2 - u^2 = 2as

Therfore

-6.8587^2 + 0^2 = 2*a*4

a = - 5.88 m/sec^2

Alpha = a/r

= - 5.88/0.25

= - 23.52 rad/sec^2

rF = I*alpha

r*umgCos(hteta) = (2/3)*m*r^2*alpha

0.25*u*9.8*Cos(53 degree) = (2/3)*0.25^2*23.52

u = 0.66

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