A hollow, spherical shell with mass 1.50 kg rolls without slipping down a slope angled at 40.0 degrees.(adsbygoogle = window.adsbygoogle || []).push({});

a) Find the acceleration.

b) Find the friction force.

c) Find the minimum coefficient of friction needed to prevent slipping.

** When the sphere rolls, the rate of rotation and the linear velocity of the center are related. If the center is moving with speed v, and the contact point is not moving, the angular velocity, w (really the Greek letter omega), is v/R. The kinetic energy is the sum of translational energy of the center of mass and the rotational energy

KE = (1/2)mv^2 + (1/2)Iw^2

You can substitute for w and you will have the kinetic enegry expressed in terms of constants (m, I, R) and v^2. Then you can use the expression for I of a spherical shell to replace I and R in terms of m. You know that as the sphere rolls down the plane, it loses potentail energy and gains an equal amount of kinetic energy. You should be able to find a relationship between the distance rolled and v^2 that involves a trig function of the tilt angle. Then you can use the formula for the change in v^2

(v_f)^2 - (v_i)^2 = 2as

to find the aceleration. From the acceleration, you can find the net force causing the acceleration, which is the component of gravity parallel to the plane minus the friction.

I try this method but still get the wrong answers. Am I using the wrong values or wrong equations? What do I do?

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# Homework Help: Rolling energy

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