Question

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

Answer #1

A hollow cylinder (hoop) of mass M and radius R starts rolling
without slipping (with negligible initial speed) from the top of an
inclined plane with angle theta. The cylinder is initially at a
height h from the bottom of the inclined plane. The coefficient of
friction is u. The moment of inertia of the hoop for the rolling
motion described is I= mR^2.
a) What is the magnitude of the net force and net torque acting
on the hoop?...

A cylinder of mass and radius R rolls without slipping down an
incline plane starting from ??rest at a height d above the ground.
The plane is angled 30 degrees from the horizontal. Ignoring air
resistance, find the speed and the
acceleration of the cylinder at the
bottom of the plane.
a.Use the methods of conservation of energy to solve
this problem.
b. Use the methods of torques to check your answer.
c. Look ? at your answer to this...

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 uniform disc of mass M=2.0 kg and radius R=0.45 m rolls
without slipping down an inclined plane of length L=40 m and slope
of 30°. The disk starts from rest at the top of the incline. Find
the angular velocity at the bottom of the incline.

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 thin cylinder starts from rest and rolls without slipping on
theloop-the loop with radius R. Find the minimum starting height of
the marblefrom which it will remain on the track through the loop.
Assume the cylinder radius is small compared to R.

A solid sphere with mass M=4.2kg and radius R=0.25m rolls across
the floor without slipping. If the sphere has a totoal kinetic
energy of K=6.5J what is the angular speed?

A solid 0.5750-kg ball rolls without slipping down a track
toward a loop-the-loop of radius R = 0.6550 m. What minimum
translational speed vmin must the ball have when it is a height H =
1.026 m above the bottom of the loop, in order to complete the loop
without falling off the track?

A solid 0.595-kg ball rolls without slipping down a track toward
a loop-the-loop of radius R = 0.7350 m. What minimum translational
speed vmin must the ball have when it is a height H = 1.091 m above
the bottom of the loop, in order to complete the loop without
falling off the track?

A uniform cylinder of mass M and radius R rolls without slipping
down a slope of angle theeta to the horizontal. The cylinder is
connected to a spring constant K while the other end of the spring
is connected to a rigid support at P. The cylinder is released when
the spring is unstrectched. The maximum displacement of cylinder is
?

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