Explanation Given: Radius of the ball = r Radius of the track = R The ball starts from rest. There is no slipping. Formula used: Potential energy: P E = m g h Where, m is the mass, g is the gravitational acceleration and h is the height. Translational kinetic energy: K E t r = 1 2 m v 2 Where, m is the mass and v is the velocity. K E r o t = 1 2 I ω 2 Where, I is the moment of inertia and ω is the angular velocity. I for a sphere = 2 5 m r 2 Where, m is the mass and r is the radius. ω = v r Calculation: The ball is at rest initially and all its mechanical energy is in the form of potential energy, which is given by, P E = m g h , where h is the difference in height between the ball’s initial position and final position According to the principle of conservation of energy, at the lowest point of the track all of this potential energy is converted into kinetic energy. Total kinetic energy for the ball is given by, K E = K E t r + K E r o t , where K E t r is the translational kinetic energy of the sphere and K E r o t is the rotational kinetic energy. K E t r = 1 2 m v 2 , where v is the translational speed of the ball at the bottom of the track. K E r o t = 1 2 I ω 2 , where I is ball’s moment of inertia and ω is the rotational speed of the ball

Physics: Principles with Applications, Books a la Carte Edition & Modified Mastering Physics with Pearson eText -- ValuePack Access Card Package

1st Edition

ISBN: 9780321974990

Author: Douglas C. Giancoli

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8, Problem 57P

To determine

The speed of the ball when it reaches the lowest point on the track.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8, Problem 56P

Chapter 8, Problem 58P

Students have asked these similar questions

Namor, from Wakanda Forever, sits on a throne at the bottom of the ocean in a city called Talocan (and Atlantis in the comics). Assuming he, including his gold headdress, has a density of 1085 kg/m3 and that Namor is surrounded by salt water with a density of 1027 kg/m3, what is Namor’s normal force while sitting underwater? Take Namor’s mass as 285. kg and solve as if he has a uniform density.

To get there they need to travel through an area of salt-water, which seems to also be a magical portal, before arriving in a dry area. Judging by the time Maui and Moana spend falling through the water, it seems they dive 3440. ft deep. Assume the portal is non-magical salt-water, with a density of 1027 kg/m^3. Given that the air pressure above the portal is 1.013 ⋅10^5 Pa, what is the pressure when they are 3440. ft deep? 1 m = 3.28 ft. Moana would have a surface area of 1.30 m2. How much force would be acting on her at the bottom of this portal?

A plank 2.00 cm thick and 15.7 cm wide is firmly attached to the railing of a ship by clamps so that the rest of the board extends 2.00 m horizontally over the sea below. A man of mass 92.9 kg is forced to stand on the very end. If the end of the board drops by 5.97 cm because of the man's weight, find the shear modulus of the wood.

Chapter 8 Solutions

Physics: Principles with Applications, Books a la Carte Edition & Modified Mastering Physics with Pearson eText -- ValuePack Access Card Package

Ch. 8 - A solid ball and a solid cylinder roll down a...Ch. 8 - A bicycle odometer (which counts revolutions and...Ch. 8 - Prob. 2Q Ch. 8 - Prob. 3Q Ch. 8 - Why is it more difficult to do a sit-up with your...Ch. 8 - If the net force on a system is zero, is the net...Ch. 8 - Mammals that depend on being able to run fast have...Ch. 8 - This book has three symmetry axes through its...Ch. 8 - Can the mass of a rigid object be considered...Ch. 8 - The moment of inertia of a rotating solid disk...

Ch. 8 - Two inclines have the same height but make...Ch. 8 - Two spheres look identical and have the same mass....Ch. 8 - A sphere and a cylinder have the same radius and...Ch. 8 - Prob. 13Q Ch. 8 - Prob. 14Q Ch. 8 - 15. Can the diver of Fig. 8-28 do a somersault...Ch. 8 - When a motorcyclist leaves the ground on a jump...Ch. 8 - Prob. 17Q Ch. 8 - 18. The angular velocity of a wheel rotating on a...Ch. 8 - 19. In what direction is the Earth's angular...Ch. 8 - 20. ‘On the basis of the law of conservation of...Ch. 8 - Bonnie sits on the outer rim of a merry-go-round,...Ch. 8 - Prob. 2MCQ Ch. 8 - Prob. 3MCQ Ch. 8 - Prob. 4MCQ Ch. 8 - Prob. 5MCQ Ch. 8 - Prob. 6MCQ Ch. 8 - Prob. 7MCQ Ch. 8 - Prob. 8MCQ Ch. 8 - Prob. 9MCQ Ch. 8 - Prob. 10MCQ Ch. 8 - Prob. 11MCQ Ch. 8 - Prob. 12MCQ Ch. 8 - Suppose you are sitting on a rotating stool...Ch. 8 - Express the following angles in radians: (a)...Ch. 8 - The Sun subtends an angle of about 0.5° to us on...Ch. 8 - A laser beam is directed at the Moon, 380,000 km...Ch. 8 - The blades in a blender rotate at a rate of 6500...Ch. 8 - 5. (II) The platter of the hard drive of a...Ch. 8 - Prob. 6P Ch. 8 - (a) A grinding wheel 0.35 m in diameter rotates at...Ch. 8 - Prob. 8P Ch. 8 - Calculate the angular velocity (a) of a clock's...Ch. 8 - Prob. 10P Ch. 8 - What is the linear speed, due to the Earth's...Ch. 8 - Prob. 12P Ch. 8 - How fast (in rpm) must a centrifuge rotate ifa...Ch. 8 - Prob. 14P Ch. 8 - Prob. 15P Ch. 8 - Prob. 16P Ch. 8 - An automobile engine slows down from 3500 rpm to...Ch. 8 - 18. (I) A centrifuge accelerates uniformly from...Ch. 8 - Prob. 19P Ch. 8 - Prob. 20P Ch. 8 - A wheel 31 cm in diameter accelerates uniformly...Ch. 8 - Prob. 22P Ch. 8 - Prob. 23P Ch. 8 - A 52-kg person riding a bike puts all her weight...Ch. 8 - Calculate the net torque about the axle of the...Ch. 8 - A person exerts a horizontal force of 42 N on the...Ch. 8 - Prob. 27P Ch. 8 - The bolts on the cylinder head of an engine...Ch. 8 - Determine the net torque on the 2.0-m-long uniform...Ch. 8 - Determine the moment of inertia of a 10.8-kg...Ch. 8 - 31. (I) Estimate the moment of inertia of a...Ch. 8 - A merry-go-round accelerates from rest to 0.68...Ch. 8 - Prob. 33P Ch. 8 - (II) A grinding wheel is a uniform cylinder with a...Ch. 8 - Prob. 35P Ch. 8 - Prob. 36P Ch. 8 - Prob. 37P Ch. 8 - Prob. 38P Ch. 8 - Prob. 39P Ch. 8 - Prob. 40P Ch. 8 - Prob. 41P Ch. 8 - Prob. 42P Ch. 8 - Prob. 43P Ch. 8 - A centrifuge rotor rotating at 9200 rpm is shut...Ch. 8 - 45. (II) To get a flat, uniform cylindrical...Ch. 8 - 46. (Ill) Two blocks are connected by a light...Ch. 8 - 47 (III) An Atwood machine consists of two masses,...Ch. 8 - A hammer thrower accelerates the hammer (mass...Ch. 8 - 49. (I) An automobile engine develops a torque of...Ch. 8 - A centrifuge rotor has a moment of inertia of 325...Ch. 8 - Prob. 51P Ch. 8 - Prob. 52P Ch. 8 - Prob. 53P Ch. 8 - Prob. 54P Ch. 8 - Prob. 55P Ch. 8 - Prob. 56P Ch. 8 - Prob. 57P Ch. 8 - Prob. 58P Ch. 8 - Prob. 59P Ch. 8 - What is the angular momentum of a 0.270-kg ball...Ch. 8 - (a) What is the angular momentum of a 2.8-kg...Ch. 8 - Prob. 62P Ch. 8 - Prob. 63P Ch. 8 - Prob. 64P Ch. 8 - Prob. 65P Ch. 8 - Prob. 66P Ch. 8 - A person of mass 75 kg stands at the center of a...Ch. 8 - Prob. 68P Ch. 8 - Prob. 69P Ch. 8 - Prob. 70P Ch. 8 - Prob. 71P Ch. 8 - Prob. 72P Ch. 8 - Prob. 73P Ch. 8 - Prob. 74P Ch. 8 - Prob. 75GP Ch. 8 - Prob. 76GP Ch. 8 - Prob. 77GP Ch. 8 - Prob. 78GP Ch. 8 - Prob. 79GP Ch. 8 - Prob. 80GP Ch. 8 - Prob. 81GP Ch. 8 - Figure 8-59 illustrates an H20 molecule The O — H...Ch. 8 - A hollow cylinder (hoop) is rolling on a...Ch. 8 - Prob. 84GP Ch. 8 - Prob. 85GP Ch. 8 - Prob. 86GP Ch. 8 - Prob. 87GP Ch. 8 - Prob. 88GP Ch. 8 - Prob. 89GP Ch. 8 - Prob. 90GP Ch. 8 - A large spool of rope rolls on the ground with the...Ch. 8 - The Moon orbits the Earth such that the same side...Ch. 8 - Prob. 93GP Ch. 8 - Most of our Solar System's mass is contained in...Ch. 8 - Prob. 95GP Ch. 8 - Prob. 96GP

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.