Two spheres of equal mass M and equal radius R roll down an inclined plane as...
Two spheres of equal mass M and equal radius R roll down an inclined plane as shown in the figure. One sphere is solid and the other is a hollow spherical shell. The plane makes an angle ? with respect to the horizontal. The spheres are released simultaneously from rest at the top of the inclined plane and they each roll down the incline without slipping.
The total distance each sphere rolls down the ramp (the hypotenuse) is d. There is a coefficient of kinetic friction ?k between each sphere and the plane if they were sliding rather than rolling.
Use the following values:
M = 2.35 kg
R= 5.2 cm
d = 24.0 cm
? = 24.0o
?k = 0.440
a) How long does it take the solid ball to reach the bottom of the inclined plane?
b) If angle of the incline, ?, is adjusted to be 25.4o so that the (linear, not angular) acceleration of the solid ball down the incline is 3.00 m/s2 . What would the magnitude of the frictional force on the ball as it moves down the plane?
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Two uniform spheres of identical mass and radius are placed on
inclined planes at the same height h and inclination angle θ. One
plane is rough and causes one sphere to roll down the plane; the
other is frictionless, and so the sphere on it slides down the
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bottom of the incline: .
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