(a) Explanation Given information: The mass of the cylinder A is m = 4 kg . The radius of the cylinder A is r = 150 mm . The angular velocity in the cylinder A is ω 0 = 50 rad/s . The number of revolution executed to attain constant velocity by cylinder A is θ A = 3 rev . The number of revolution executed to attain constant velocity by cylinder B is θ B = 1 rev . Calculation: Consider the acceleration due to gravity is g = 9.81 m/s 2 . Find the mass moment of inertia ( I ¯ ) of the cylinder using the equation. I ¯ = 1 2 m r 2 Substitute 4 kg for m and 150 mm for r . I ¯ = 1 2 × 4 × ( 150 mm × 1 m 1,000 mm ) 2 = 0.045 kg ⋅ m 2 Cylinder A : Show the free-body diagram of the cylinder A as in Figure 1. Resolve the vertical component of forces to find the normal forces. ∑ F y = 0 N − W = 0 N = m g Substitute 4 kg for m and 9.81 m/s 2 for g . N = 4 × 9.81 = 39.24 N Find the frictional force F using the relation. F = μ k N Here, the coefficient of kinetic friction is μ k . Substitute 39.24 N for N . F = 39.24 μ k Find the moment at cylinder A by taking moment about point A . ∑ M A = 0 M A = F r Substitute 39.24 μ k for F and 150 mm for r . M A = 39.24 μ k × 150 mm × 1 m 1,000 mm = 5.886 μ k N ⋅ m Initial stage (before contact with cylinder B ); Find the total kinetic energy ( T 1 ) using the relation. T 1 = 1 2 I ¯ ω 0 2 Substitute 0.045 kg ⋅ m 2 for I ¯ and 50 rad/s for ω 0 . T 1 = 1 2 × 0.045 × 50 2 = 56.25 N ⋅ m Final stage (After contact with cylinder B ): Find the final total kinetic energy ( T 2 ) using the relation. T 2 = 1 2 I ¯ ω A 2 Substitute 0.045 kg ⋅ m 2 for I ¯ . T 2 = 1 2 × 0.045 × ω A 2 = 0.0225 ω A 2 Find the work done ( U 1 → 2 ) for cylinder A to be in contact with cylinder B as follows; U 1 → 2 = − M A θ A Substitute 5.886 μ k N ⋅ m for M A and 3 rev for θ A . U 1 → 2 = − 5.886 μ k × 3 rev × 2 π rad 1 rev = − 110.9485 μ k N ⋅ m Write the equation of work and energy for the system using the equation. T 1 + U 1 → 2 = T 2 Substitute 56.25 N ⋅ m for T 1 , − 110.9485 μ k N ⋅ m for U 1 → 2 , and 0.0225 ω A 2 for T 2 56 (b) To determine Find the coefficient of kinetic friction μ k .

12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 17.1, Problem 17.8P

(a)

To determine

Find the final angular velocity of each cylinder.

(b)

To determine

Find the coefficient of kinetic friction μk.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.1, Problem 17.7P

Chapter 17.1, Problem 17.9P

Students have asked these similar questions

Disk A has a mass mA = 4 kg, a radius rA = 300 mm, and an initial angular velocity ω0 = 300 rpm clockwise. Disk B has a mass mB = 1.6 kg, a radius rB = 180 mm, and is at rest when it is brought into contact with disk A. Knowing that µk = 0.35 between the disks and neglecting bearing friction, determine (a) the angular acceleration of each disk, (b) the reaction at the support C.

Please answer nos. 2, 4, & 5.

Disk A has a mass of 6 kg and an initial angular velocity of 360 rpm clockwise; disk B has a mass of 3 kg and is initially at rest. The disks are brought together by applying a horizontal force of magnitude 20 N to the axle of disk A. Knowing that µk = 0.15 between the disks and neglecting bearing friction, determine (a) the angular acceleration of each disk, (b) the final angular velocity of each disk.

Chapter 17 Solutions

VECTOR MECH. FOR EGR: STATS & DYNAM (LL

Ch. 17.1 - A round object of mass m and radius r is released...Ch. 17.1 - Prob. 17.2CQ Ch. 17.1 - Prob. 17.3CQ Ch. 17.1 - Prob. 17.4CQ Ch. 17.1 - Slender bar A is rigidly connected to a massless...Ch. 17.1 - A 200-kg flywheel is at rest when a constant 300...Ch. 17.1 - The rotor of an electric motor has an angular...Ch. 17.1 - Prob. 17.3P Ch. 17.1 - Two disks of the same material are attached to a...Ch. 17.1 - The flywheel of a punching machine has a weight of...

Knowledge Booster

Learn more about

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

Find the final angular velocity of each cylinder.

Solution Summary: The author calculates the final angular velocity of each cylinder using the equation.

Concept explainers

Videos

Find the final angular velocity of each cylinder.

Find the coefficient of kinetic friction μk.

Want to see the full answer?

Chapter 17 Solutions