Question

A billiard ball with a mass of m and a radius of r is rolling down...

A billiard ball with a mass of m and a radius of r is rolling down without friction along an inclined plane with a slope of Θ at h height from the floor.

(1) Find an inertial moment for the center of a billiard ball. Here the mass distribution of billiard balls is assumed to be uniform.

(2) What is the speed of a billiard ball when it reaches the floor?

((1)If you can't solve the question yourself, use inertia moment I=2/5*mr^2.)

Homework Answers

Answer #1

Solution :

Part (a) Solution :

Inertial moment for the center of a billiard ball : I = (2/5) m r2

.

Part (b) Solution :

Let the speed of the billiard ball when it reaches the floor is : v.

Then, Total kinetic energy of the billiard ball at the bottom of the inclined plane will be : KEtotal = KErot + KEtran

∴ KEtotal = (1/2) I ω2 + (1/2) m v2

∴ KEtotal = (1/2) {(2/5) m r2} (v/r)2 + (1/2) m v2

∴ KEtotal = (1/5) mv2 + (1/2) m v2

∴ KEtotal = (7/10) m v2

.

Now, According to the conservation of energy : KEf = PEi

∴ (7/10) m v2 = m g h

∴ (7/10) v2 = g h

∴ v2 = (10/7) g h

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 hollow cylinder (hoop) of mass M and radius R starts rolling without slipping (with negligible...
A hollow cylinder (hoop) of mass M and radius R starts rolling without slipping (with negligible initial speed) from the top of an inclined plane with angle theta. The cylinder is initially at a height h from the bottom of the inclined plane. The coefficient of friction is u. The moment of inertia of the hoop for the rolling motion described is I= mR^2. a) What is the magnitude of the net force and net torque acting on the hoop?...
7. We found that if a cue ball, rolling without slipping at speed v0, strikes an...
7. We found that if a cue ball, rolling without slipping at speed v0, strikes an identical, stationary billiard ball head-on, eventually both balls will roll without slipping. The balls are uniform solid spheres, each of mass m, radius r, and moment of inertia I =2/5 m r^2 about its center. The final speed of the target ball is 5/7 *v0 ; that of the cue ball is 2/7 v0. Calculate the total fraction of the initial kenetic energy of...
URGENT!! a) A ball of radius ? and mass ? is rolling without slipping on the...
URGENT!! a) A ball of radius ? and mass ? is rolling without slipping on the surface of a ring of radius ?. At a given instant, the ring is rotating with angular speed Ω counterclockwise as shown in the figure and the ball is rolling without slipping. What is the speed of the center of mass of the ball at that instant if it has clockwise angular speed of ω? b)A yo-yo of mass ? has a spool of...
A bowling ball (solid sphere, moment of inertia is (2/5)MR2) of mass M and radius R...
A bowling ball (solid sphere, moment of inertia is (2/5)MR2) of mass M and radius R rolls down a hill without slipping for a distance of L along the hill with slope of angle θ, starting from rest. At that point, the hill becomes frictionless.The ball continues down the hill for another segment of length 2L (thus the total distance travelled on the hill is 3L). The hill levels out into a horizontal area, where the coefficient of friction is...
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?
A bowling ball (mass = 6.2 kg, radius = 0.11 m) and a billiard ball (mass...
A bowling ball (mass = 6.2 kg, radius = 0.11 m) and a billiard ball (mass = 0.37 kg, radius = 0.028 m) may each be treated as uniform spheres. What is the magnitude of the maximum gravitational force that each can exert on the other?
Billiard ball A is half the mass as billiard ball B. Ball A is moving to...
Billiard ball A is half the mass as billiard ball B. Ball A is moving to the left at 5 m/s while ball B is moving to the right at 2 m/s. Find the final velocities of the two balls assuming they hit in the center, and do not deflect off at an angle.
A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm is rolling up...
A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm is rolling up a ramp that rises at 30.0° above the horizontal. Speed of the ball at the base of the ramp is 8.20 m/s. Moment of inertia of 2 hollow sphere is given by I=(2/3)m r . (a) What is the angular velocity of the ball at the base of the ramp? (b) Determine how far up the ramp does it roll before it starts to...
A uniform, solid disk of mass M=4 kg and radius R=2 m, starts from rest at...
A uniform, solid disk of mass M=4 kg and radius R=2 m, starts from rest at a height of h=10.00 m and rolls down a 30 degree slope as shown in the figure. a) Derive the moment of inertia of the disk. b) What is the linear speed of the ball when it leaves the incline? Assume the ball rolls without slipping.
A ball of mass M and radius R rolls smoothly from rest down a ramp and...
A ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.47 m. The initial height of the ball is h = 0.35 m. At the loop bottom, the magnitude of the normal force on the ball is 2.0 Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT