Question

A solid sphere of uniform density starts from rest and rolls
without slipping a distance of **d = 4.4 m** down a
**θ = 22°**incline. The sphere has a
mass **M = 4.3 kg** and a radius **R
= 0.28 m**.

1)Of the total kinetic energy of the sphere, what fraction is translational?

**KE**
_{tran}/**KE**_{total} =

2)What is the translational kinetic energy of the sphere when it reaches the bottom of the incline?

**KE** _{tran} =

3)What is the translational speed of the sphere as it reaches the bottom of the ramp?

**v** =

4)Now let's change the problem a little.

Suppose now that there is **no frictional force**
between the sphere and the incline. Now, what is the translational
kinetic energy of the sphere at the bottom of the incline?

**KE** _{tran} =

Answer #1

A solid metal ball starts from rest and rolls without slipping a
distance of d = 4.2 m down a θ = 38° ramp. The ball has uniform
density, a mass M = 4.7 kg and a radius R = 0.33 m.
What is the magnitude of the frictional force on the sphere?

A solid metal ball starts from rest and rolls without slipping a
distance of d = 4.2 m down a θ = 38° ramp. The ball has uniform
density, a mass M = 4.7 kg and a radius R = 0.33 m.
What is the magnitude of the frictional force on the sphere?

A sphere of radius r0 = 23.0 cm and mass m = 1.20kg starts from
rest and rolls without slipping down a 35.0 ∘ incline that is 13.0
m long.
A. Calculate its translational speed when it reaches the
bottom.
B. Calculate its rotational speed when it reaches the
bottom.
C. What is the ratio of translational to rotational kinetic
energy at the bottom?

A sphere of radius r=34.5 cm and mass m= 1.80kg starts from rest
and rolls without slipping down a 30.0 degree incline that is 10.0
m long. calculate the translational and rotational speed when it
reaches the bottom.

A
2.9 kg solid sphere (radius = 0.15 m) is released from rest at the
top of a ramp and allowed to roll without slipping. The ramp is
0.85 m high and 5.2 m long.
1. When the sphere reaches the bottom of the ramp, what are
its total kinetic energy,
2. When the sphere reaches the bottom of the ramp, what is its
rotational kinetic energy?
3. When the sphere reaches the bottom of the ramp, what is its...

A uniform, solid sphere of radius 3.00 cm and mass 2.00 kg
starts with a purely translational speed of 1.25 m/s at the top of
an inclined plane. The surface of the incline is 1.00 m long, and
is tilted at an angle of 25.0 ∘ with respect to the horizontal.
Assuming the sphere rolls without slipping down the incline,
calculate the sphere's final translational speed v 2 at the bottom
of the ramp.

A uniform, solid sphere of radius 4.50 cm and mass 2.25 kg
starts with a purely translational speed of 1.25 m/s at the top of
an inclined plane. The surface of the incline is 2.75 m long, and
is tilted at an angle of 22.0∘ with respect to the horizontal.
Assuming the sphere rolls without slipping down the incline,
calculate the sphere's final translational speed ?2 at the bottom
of the ramp.
?2=__________ m/s

A uniform, solid sphere of radius 3.50 cm and mass 1.25 kg
starts with a purely translational speed of 2.50 m/s at the top of
an inclined plane. The surface of the incline is 1.50 m long, and
is tilted at an angle of 28.0∘ with respect to the horizontal.
Assuming the sphere rolls without slipping down the incline,
calculate the sphere's final translational speed ?2 at the bottom
of the ramp. ?2= m/s

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 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.

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