Question

A 1.0-kg ring with an inner radius of 0.060 m and an outer radius of 0.080...

A 1.0-kg ring with an inner radius of 0.060 m and an outer radius of 0.080 m is sent rolling without slipping up a ramp that makes an angle of 30? with the horizontal. The initial speed of the ring is 3.8 m/s

How far along the ramp does it travel before it comes to a stop?

Homework Answers

Answer #1

The system is like annular disc. Moment of inertia of this system is I = ½ * M(r12 + r22)

r1 = outer radius r2 = inner radius , M mass , velocity = 3.8 m/s

I = ½ * 1 * (0.0802 + 0.0602) kg m2

I = 0.005 kg m2

Total Kinetic Energy is KE

KE = ½mv² + ½I?² v = r1 ?

= ½mv² + ½I(v/r1

=  ½ * 1 * 3.8 * 3.8 +  ½ * 0.005 * (3.8 / 0.08)2

= 7.22 +5.64

= 12.86 J

All it converts to Potential energy

PE = m g h

12.86 = m g h

h = 12.86 / m g

= 1.312 m

How far along the ramp does it travel before it comes to a stop?

Since it is a ramp

d = 1.312 / sin 30

d = 2.624 m

It is 2.624 m along the ramp it travel before it comes to a stop.

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 sphere (mass 8.8 kg, radius 54.8 cm) is rolling without slipping along a horizontal...
A hollow sphere (mass 8.8 kg, radius 54.8 cm) is rolling without slipping along a horizontal surface, so its center of mass is moving at speed vo. It now comes to an incline that makes an angle 56o with the horizontal, and it rolls without slipping up the incline until it comes to a complete stop. Find a, the magnitude of the linear acceleration of the ball as it travels up the incline, in m/s2.
QUESTION 4 A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls...
QUESTION 4 A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If the cylinder has a mass of 10 kg, what is its moment of inertia? a. 1.30 kg m^2 b. 3.00 kg m^2 c. 1.25 kg m^2 d. 1.20 kg m^2 QUESTION 5 A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. What is the rotational (angular) speed of...
1 a- A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls...
1 a- A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If the cylinder has a mass of 10 kg, what is its linear kinetic energy? Optional Answers: 1. 80 J 2. 41.6 J 3. 121.6 J 4. 0 J b- A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If the cylinder has a mass of 10 kg, what...
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 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 hollow sphere is given by I=(2/3)m r2. (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 roll downward....
A 5.00-kg 5.00-kg block is sent up a ramp inclined at an angle ?= 25.0 ∘...
A 5.00-kg 5.00-kg block is sent up a ramp inclined at an angle ?= 25.0 ∘ θ=25.0∘ from the horizontal. It is given an initial velocity ? 0 =15.0 m/s v0=15.0 m/s up the ramp. Between the block and the ramp, the coefficient of kinetic friction is ? k =0.50 μk=0.50 and the coefficient of static friction is ? s =0.60. μs=0.60. What distance ? D along the ramp's surface does the block travel before it comes to a stop?
A hoop (cylindrical shell) is rolling without slipping along a horizontal surface with a forward (translational)...
A hoop (cylindrical shell) is rolling without slipping along a horizontal surface with a forward (translational) speed of 6.51 m/s when it starts up a ramp (still rolling without slipping) that makes an angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.48 m up as measured along the surface of the ramp? a) 5.29 m/s b) 6.50 m/s c) 5.97 m/s d) 3.91 m/s e) 2.70 m/s
A 5.00-kg5.00-kg block is sent up a ramp inclined at an angle ?=28.0∘θ=28.0∘ from the horizontal....
A 5.00-kg5.00-kg block is sent up a ramp inclined at an angle ?=28.0∘θ=28.0∘ from the horizontal. It is given an initial velocity ?0=15.0 m/sv0=15.0 m/s up the ramp. Between the block and the ramp, the coefficient of kinetic friction is ?k=0.50μk=0.50 and the coefficient of static friction is ?s=0.60.μs=0.60. What distance ?D along the ramp's surface does the block travel before it comes to a stop?
A uniform solid disk is rolling without slipping along a horizontal surface with a linear speed...
A uniform solid disk is rolling without slipping along a horizontal surface with a linear speed of 3.60 m/s when it starts going up a ramp that makes an angle of 31.0o with the horizontal. What is the speed of the disk after it has rolled 1.75 m up the ramp (the 1.75 m is the distance along the ramp)? Make sure you show any appropriate diagrams and all of your work. SHOW ALL WORK
A spherical bowling ball with mass m = 4.2 kg and radius R = 0.1 m...
A spherical bowling ball with mass m = 4.2 kg and radius R = 0.1 m is thrown down the lane with an initial speed of v = 8.1 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.28. Once the ball begins to roll without slipping it moves with a constant velocity down the lane. 3) How long does it take the bowling ball to begin rolling without slipping? 4) How far...