points HRW6 12.P A uniform sphere rolls down an incline 4.-13 007 My Notes Ask Y

Question

points HRW6 12.P A uniform sphere rolls down an incline 4.-13 007 My Notes Ask Your Teach (a) What must be the incline angle if the linear acceleration of the center of the sphere is to have a magnitude of 0.30g? (b)If a frictionless block were to slide down the incline at that angle, would its acceleration magnitude be more, less than, or equal to 0.30g? The acceleration magnitude would be less than 0.30g O The acceleration magnitude would be equal to 0.30g The acceleration magnitude would be more than 0.30g Why? This answer has not been graded yet

Explanation / Answer

a)

For object rolling down incline,
a = g sin /(1+I/MR^2)

I sphere = 2/5 MR^2

a = g sin /(1+(2/5 MR^2)/MR^2)
a = g sin /(1+2/5)= g sin /1.40
0.30 = sin /1.4

sin = 0.42

= 24.83 º

(b) MORE THEN 0.30g

On a frictionless surface, the block does not experience any torque.
Therefore, the block does not have any angular acceleration but the linear
acceleration which can be calculated using the same equation of motion as that used for the sphere,
mg*sin0 = ma
in absence of friction fk = 0 and the above equation reduces to
mg*sin0 = ma
a = gsin0
subsitute 24.83deg for 0
a = gsin*(24.83) = 0.41g

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