Question

A solid sphere ( of mass 2.50 kg and radius 10.0 cm) starts rolling without slipping on an inclined plane (angle of inclination 30 deg). Find the speed of its center of mass when it has traveled down 2.00 m along with the inclination.

Groups of choices:

a. 3.13 m/s

b. 4.43 m/s

c. 3.74 m/s

d. 6.26 m/s

Answer #1

**Given Solid sphere of mass m = 2.5 kg, radius R=10.0
cm**

**on an 30 degrees inclined plane,rolling without
slipping
traveled a distance of 2 m along the incline**

**from the data we can calculate the height of the incline
h,**

**sin 30 = h/2 ==> h = 2 sin 30 =2*0.5 = 1
m**

**assuming that there is no friction then by conservation
of energy**

**initially the total energy is gravitational potential
energy and later kinetic energy
here the sphere will have both rotational kinetic energy and
translational kinetic energy
so**

**mgh = 0.5*I*W^2 +0.5*m*v^2
mgh = 0.5*(2/5)*m*R^2*W^2 + 0.5*m*v^2**

**mgh = 0.5*(2/5)*m*R^2*V^2/R^2+0.5*m*v^2**

**gh = 0.5*(2/5)*V^2+0.5*v^2**

**gh = 0.5*v^2(2/5 +1)**

**v^2 = 2gh/(2/5 +1)
v = sqrt(2gh/(2/5 +1))**

**V = sqrt(2gh/(2/5 +1))**

**substituting the values**

**V = sqrt((2*9.8*1)/(2/5+1)) m/s**

**V = 3.74 m/s**

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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 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.

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.
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linear velocity of the center of mass of the sphere is
approximately
_______ m/s.

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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
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?2=__________ m/s

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.A
uniform sphere of mass m radius r starts rolling down without
slipping from the top of another larger sphere of radius R. Find
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(b) How much time elapses (in s) while the sphere moves up the
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