- #1
bodensee9
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Hello:
Can someone help with the following?
A ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.48m. The initial height of the ball is h = 0.36m. At the loop bottom, the magnitude of the normal force on the ball is 2.00 Mg. The ball consists of an outer spherical shell (of certain uniform density) that is glued to a central sphere(of different uniform density). The rotational inertia of the ball can be expressed in terms of the general form bMR^2, but b is not 0.4 as it is for a ball of uniform density. Find the b for this ball.
I thought to use conservation of energy? So this gives me:
M*g*0.36 = 1/2*I*w^2 + 1/2*M*v^2, where I is the rotational inertia and w is the angular velocity and v is the linear velocity.
But then I'm not sure what to do after like (for example, how do I get rid of the v's)? And is it true that the ball is not accelerating at the loop bottom with respect to the ground (since it is at the bottom) so that the normal force = force from gravity? But then what good is that since it only gives me M?
Thanks!
Homework Statement
Hello:
Can someone help with the following?
A ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.48m. The initial height of the ball is h = 0.36m. At the loop bottom, the magnitude of the normal force on the ball is 2.00 Mg. The ball consists of an outer spherical shell (of certain uniform density) that is glued to a central sphere(of different uniform density). The rotational inertia of the ball can be expressed in terms of the general form bMR^2, but b is not 0.4 as it is for a ball of uniform density. Find the b for this ball.
I thought to use conservation of energy? So this gives me:
M*g*0.36 = 1/2*I*w^2 + 1/2*M*v^2, where I is the rotational inertia and w is the angular velocity and v is the linear velocity.
But then I'm not sure what to do after like (for example, how do I get rid of the v's)? And is it true that the ball is not accelerating at the loop bottom with respect to the ground (since it is at the bottom) so that the normal force = force from gravity? But then what good is that since it only gives me M?
Thanks!