Question

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?**

Answer #1

As we know that the linear kinetic energy is defined by K_linear
= (1/2)mv^2, where

m = mass of the body in motion

v = velocity of the body in motion

Rotational kinetic energy is defined by K_rotational = 1/2Iω^2,
where

I = mass moment of inertia of the body in motion

ω = rotational velocity of the body in motion

For solid sphere, I=2/5mr^2

where r = the radius of the sphere

Put this in the above –

We get, K_rotational = 1/2(2/5mR^2)ω^2 = 1/5m(R^2)(ω^2) = (1/5)mv^2 [since v = Rω]

So, total kinetic energy, KE = (1/2)mv^2 + (1/5)mv^2 = 0.7*
mv^2

Now given that total kinetic energy = 6.5 J

So, 0.7* mv^2 = 6.5

=> 0.7*4.2*v^2 = 6.5

=> v = 1.49 m/s

Now, v = R* ω

=> ω = v/R = 1.49/0.25 = 5.96 rad/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 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...

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

A solid, uniform sphere of mass 2.0 kg and radius 1.7m rolls
without slipping down an inclined plane of height 7.0m . What is
the angular velocity of the sphere at the bottom of the inclined
plane? a) 5.8 rad/s b) 11.0 rad/s c) 7.0 rad/s d) 9.9 rad/s

A sphere of mass M = 5kg and radius R = 0.1m rolls withour
slipping with velocity V = 8.4 m/s toward an incline defined by
angle θ = 10 degrees.
1. Calculate the kinetic energy of the sphere right bfore it
goes up the incline
2. Calculate the height the mass gets up the ramp.
3. Consider a box with the same mass and velocity instead
sliding without friction toward the incline. How does this objects
KE before the...

A 320-N sphere 0.20 m in radius rolls without slipping 6.0 m
down a ramp that is inclined at 34° with the horizontal. What is
the angular speed of the sphere at the bottom of the slope if it
starts from rest?

A large sphere rolls without slipping across a horizontal
surface as shown. The sphere has a constant translational speed of
10. m/s, a mass of 7.3 kg (16 lb bowling ball), and a radius of
0.20 m. The moment of inertia of the sphere about its center is I =
(2/5)mr2. The sphere approaches a 25° incline of height
3.0 m and rolls up the ramp without slipping.
(a) Calculate the total energy, E, of the sphere as it rolls...

A 350-N sphere 0.20 m in radius rolls without slipping 6.0 m
down a ramp that is inclined at 25° with the horizontal. What is
the angular speed of the sphere at the bottom of the slope if it
starts from rest? rad/s

A 340-N sphere 0.20 m in radius rolls without slipping 6.0 m
down a ramp that is inclined at 34° with the horizontal. What is
the angular speed of the sphere at the bottom of the slope if it
starts from rest?
in rad/s

Suppose a solid sphere of mass 450 g and radius 5.00 cm rolls
without slipping down an inclined plane starting from rest. The
inclined plane is 7.00 m long and makes an angel of 20.0 o from the
horizontal. The linear velocity of the sphere at the bottom of the
incline is _______ m/s. please show work

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 54 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago