Question

A sphere is released from the top of a rough inclined plane. The friction is sufficient so that the sphere rolls without slipping. Mass of the sphere is M and radius is R. The height of the center of the sphere from ground is h. Find the speed of the center of the sphere as it reaches the bottom of the sphere.

Answer #1

A sphere of mass M, radius r, and rotational inertia I is
released from rest at the top of an inclined plane of height h as
shown above. (diagram not shown)
If the plane has friction so that the sphere rolls without
slipping, what is the speed vcm of the center of mass at the bottom
of the incline?

A sphere is released from rest at the top of an inclined plane.
What is the speed of the sphere at a distance 6.0 m below its
starting point. Assume that the sphere rolls without slipping.

A hollow sphere (mass M, radius R) starts from rest at the top
of a hill of height H. It rolls down the hill without slipping.
Find an expression for the speed of the ball's center of mass once
it reaches the bottom of the hill.

3) A solid cylinder with mass 4kg and radius r=0.5 m rolls
without slipping from a height of 10 meters on an inclined plane
with length 20 meters. a) Find the friction force so that it rolls
without slipping b) Calculate the minimum coefficient of rolling
friction mu c) Calculate its speed as it arrives at the bottom of
the inclined plane

1. A solid sphere of mass 50 kg rolls without slipping. If the
center-of-mass of the sphere has a translational speed of 4.0 m/s,
the total kinetic energy of the sphere is
2.
A solid sphere (I = 0.4MR2) of
radius 0.0600 m and mass 0.500 kg rolls without slipping down an
inclined plane of height 1.60 m . At the bottom of the plane, the
linear velocity of the center of mass of the sphere is
approximately
_______ m/s.

A hollow, thin-walled sphere of
radius R = 12.0 cm rolls down an inclined plane from a height of
23.0 cm. How fast will its center of gravity be moving when it
reaches the bottom?
Ans: 1.64 m/s

A solid sphere of radius r and mass m is released from a rest on
a track. At a height h above a horizontal surface. The sphere rolls
without slipping with its motion continuing around a loop of radius
R<<r
A) If R=0.3h, what is the speed of the sphere when it reaches
the top of the loop? Your response must be expressed in terms of
some or all of the quantities given above and physical and
numerical constants
B)...

A solid sphere with a radius 0.25 m and mass 240 g rolls without
slipping down an incline, starting from rest from a height 1.0
m.
a. What is the speed of the sphere when it reaches the bottom of
the incline?
b. From what height must a solid disk with the same mass and
radius be released from rest to have the same velocity at the
bottom? It also rolls without slipping.

A sphere is released from a height h from a smooth inclined
plane.
a. Calculate how fast the sphere reaches the base of the
inclined plane.
b. If a block were to be released simultaneously from that same
height, which would first reach the base of the plane, the block or
the sphere? Explain your answer.

1. a 3.00 kg bucket is released from rest. It is secured by a
rope held by a 0.600 m radius, 5.00 kg pulley. Treat the pulley as
a solid cylinder for this problem. Find the speed of the pulley
after the bucket has fallen 2.00 m.
2. a 22.00 kg sign hangs from the end of a 3.00 m long
horizontal beam. What is the tension in the cable? The beam has a
mass of 4.00 kg?
3. A...

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