Question

Q8

Two solid spheres of equal radius and equal mass start at rest at
the same height and move to the bottom of two different curved
ramps in two different ways.

In the first case (i), depicted in the left figure above, the ramp
has no friction so the sphere slides without rotating. In the
second case (ii), depicted in the right figure above, the sphere
rolls without slipping down the ramp.

In which case will the sphere have more translational kinetic
energy when it reaches the bottom of the ramp?

a) Case (i)

b) Case (ii)

c) The translational kinetic energy at the bottom will be the same
in both case (i) and case (ii).

d) More information is needed to determine which will have the
greatest translational kinetic energy at the bottom.

a) Explain how energy was transferred to/from or within your chosen
system for the two cases described in this problem. b) How did you
incorporate the fact that gravity was a conservative force?

Answer #1

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 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/KEtotal =
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...

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 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 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

A Brunswick bowling ball with mass M= 7kg and radius R=0.15m
rolls from rest down a ramp without slipping. The initial height of
the incline is H= 2m. The moment of inertia of the ball is
I=(2/5)MR2
What is the total kinetic energy of the bowling ball at the
bottom of the incline?
684J
342J
235J
137J
If the speed of the bowling ball at the bottom of the incline is
V=5m/s, what is the rotational speed ω at the...

A uniform, solid sphere of radius 5.75 cm 5.75 cm and mass 3.25
kg 3.25 kg starts with a purely translational speed of 1.25 m/s
1.25 m/s at the top of an inclined plane. The surface of the
incline is 2.25 m 2.25 m long, and is tilted at an angle of 29.0 ∘
29.0∘ with respect to the horizontal. Assuming the sphere rolls
without slipping down the incline, calculate the sphere's final
translational speed ? 2 v2 at the...

A sphere of radius r0 = 22.0 cm and mass m = 1.20kg starts from
rest and rolls without slipping down a 38.0 degree incline that is
11.0 mm 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?
D. Does your answer in part A depend on mass or radius of the
ball?
E....

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