Question

A sphere is released from rest at the top of an inclined plane. What is the...

A sphere is released from rest at the top of an inclined plane. What is the speed of the sphere at a distance 6.0 m below its starting point. Assume that the sphere rolls without slipping.

Homework Answers

Answer #1

Initial Kinetic Energy will be 0 since it was started from rest. Let mass of sphere be "m" and of radius "r", its final speed be "v" anf let it be initially at a height "h" from the ground.

Then Using Conservation of Energy

Initial Total Energy= Final Total Energy

  

(Since it rolls without slipping thus will have rotational kinetic energy also denoted above as R.K.E)

using the known formulas for energy,

  ............................(1)

where I= Moment of inertia of solid sphere, I= 2mr2/5

and = angular velocity of sphere

then using above values in equation 1, we get

  

  

  

  (ANS)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A sphere is released from the top of a rough inclined plane. The friction is sufficient...
A sphere is released from the top of a rough inclined plane. The friction is sufficient so that the sphere rolls without slipping. Mass of the sphere is M and radius is R. The height of the center of the sphere from ground is h. Find the speed of the center of the sphere as it reaches the bottom of the sphere.
A sphere of mass M, radius r, and rotational inertia I is released from rest at...
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. (diagram not shown) If the plane has friction so that the sphere rolls without slipping, what is the speed vcm of the center of mass at the bottom of the incline?
An 6.90-cm-diameter, 360 g solid sphere is released from rest at the top of a 1.80-m-long,...
An 6.90-cm-diameter, 360 g solid sphere is released from rest at the top of a 1.80-m-long, 20.0 ∘ incline. It rolls, without slipping, to the bottom. What is the sphere's angular velocity at the bottom of the incline? What fraction of its kinetic energy is rotational?
An 8.20 cm-diameter, 390g solid sphere is released from rest at the top of a 2.00m...
An 8.20 cm-diameter, 390g solid sphere is released from rest at the top of a 2.00m long, 19.0 degree incline. It rolls, without slipping, to the bottom. 1) What is the sphere's angular velocity at the bottom of the incline? 2) What fraction of its kinetic energy is rotational?
An 8.50-cm-diameter, 360 g solid sphere is released from rest at the top of a 1.90-m-long,...
An 8.50-cm-diameter, 360 g solid sphere is released from rest at the top of a 1.90-m-long, 15.0 ∘ incline. It rolls, without slipping, to the bottom. Part A What is the sphere's angular velocity at the bottom of the incline? Part B What fraction of its kinetic energy is rotational?
A hoop is released from rest at the top of a plane inclined at 29° above...
A hoop is released from rest at the top of a plane inclined at 29° above horizontal. How long does it take the hoop to roll 12.5 m down the plane? 2.84s 4.66s 2.42s 2.26s 3.24s
A solid sphere of radius r and mass m is released from a rest on a...
A solid sphere of radius r and mass m is released from a rest on a track. At a height h above a horizontal surface. The sphere rolls without slipping with its motion continuing around a loop of radius R<<r A) If R=0.3h, what is the speed of the sphere when it reaches the top of the loop? Your response must be expressed in terms of some or all of the quantities given above and physical and numerical constants B)...
A 2.9 kg solid sphere (radius = 0.15 m) is released from rest at the top...
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 320-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that...
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 solid sphere is released from the top of a ramp that is at a height...
A solid sphere is released from the top of a ramp that is at a height h1 = 2.25 m. It rolls down the ramp without slipping. The bottom of the ramp is at a height of h2 = 1.7 m above the floor. The edge of the ramp is a short horizontal section from which the ball leaves to land on the floor. The diameter of the ball is 0.19 m. a) Through what horizontal distance d, in meters,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT