A uniform solid sphere rolls down in an incline (a) what must be the incline angle if the linear acceleration of the center of the sphere is tohave a magnitude of the 0.10g? (b) If the frictionless block were to slide down the incline at that angle, would its acceleration magnitude be more than, less than, or equal to 0.10g? why?

Short Answer

Expert verified

a)8.0°

b)Magnitude of the acceleration is greater

Step by step solution

01

Listing the given quantities

The linear acceleration of the center of the sphere is 0.10g

02

Understanding the concept of torque

The force that may cause an item to revolve along an axis is measured as torque. Here, we have to calculate torque by using position vector and the force.

03

Calculation of theangle of inclination

(a) We substitute

I=25MR2-0.10g=-gsinθ1+[25MR2]/MR2=-gsinθ[75]

θ=sin-1(0.14)=8.0°

If the magnitude of the associated torque is zero Nm.thenangle between the directions of r and is8.0°

04

Step 4:explanation

(b)

It would accelerate more quickly. This can be seen in terms of either forces or energy. Since there would be no static friction on the uphill side, the only force responsible for the downhill acceleration would be gravity.In terms of the energy the potential energy is12mv2 (without it being ‘shared’ with another terms) resulting in a greater speed.

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