Explanation Given: The mass of the collar is 0.25 kg . Initially the collar is at rest at A . The unstretched length of the spring is 100 mm . The stiffness of the spring is k = 150 N/m . Draw the free body diagram of collaras shown in Figure (1). Write the formula for kinetic energy ( T ) . T = 1 2 m v 2 (I) Here, m is the mass and v is the velocity. Refer Figure (1). Write the formula for elastic potential energy ( V e ) . V e = 1 2 k s 2 (II) Here, k is the stiffness of the spring and s is the displacement. Write the formula for gravitational potential energy ( V g ) . V g = m g h (III) Here, m is the mass, g acceleration due to gravity and h is the displacement. Write the formula total potential energy ( V ) . V = V g + V e (IV) Here, V g is gravitational potential energy and V e is elastic potential energy. Write the formula for conservation of energy. T A + V A = T B + V B (V) Here, T A , T B are the initial and final kinetic energy and V A , V B are the initial and final potential energy. Conclusion: At position A : Refer Figure (1). Calculate the extension length of the spring. s A = 200 mm + 400 mm − 100 mm = 500 mm × 1 m 1000 mm = 0.5 m Here, 100 mm is the unstretched length of the spring. When the collar is rest, the kinetic energy of the collar is zero. T A = 0 Calculate the elastic potential energy ( V e ) of the collar. Substitute 150 N/m for k and 0.5 m for s in Equation (II) V e = 1 2 ( 150 N/m ) ( 0.5 m ) 2 = 18 .75 J Refer Figure (1). Calculate the gravitational potential energyof the collar. Substitute 0.25 kg for m , 9.81 m/s 2 for g and ( 200 + 400 ) mm for h in Equation (III). V g = 0.25 kg ( 9.81 m/s 2 ) ( 200 + 400 ) mm × 1 m 1000 mm = 0.25 ( 9.81 ) ( 0.6 ) = 1

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 14.5, Problem 7RP

To determine

The speed of the collar at position B .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 6RP

Chapter 14.5, Problem 8RP

Students have asked these similar questions

Block A has a mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B, having a mass mB, is pressed against A so that the spring deforms a distance d, determine the distance both blocks slide on the smooth surface before they begin to separate. What is their velocity at this instant?

The van is traveling at 20 km/h when the coupling of the trailer at A fails. If the trailer has a mass of 300 kg and coasts 50 m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop.

The collar has a mass of 2 kg and is attached to the light spring, which has a stiffness of 30 N∕m and an unstretched length of 1.5 m. The collar is released from rest at A and slides up the smooth rod under the action of the constant 50-N force. Calculate the velocity v of the collar as it passes position B. Use point A as datum (starting point).

Chapter 14 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 14.3 - Determine the work of the force when it displaces...Ch. 14.3 - Determine the kinetic energy of the 10-kg block.Ch. 14.3 - Prob. 1FP Ch. 14.3 - If the motor exerts a constant force of 300 N on...Ch. 14.3 - If the motor exerts a force of F = (600 + 2s2) N...Ch. 14.3 - The 1.8-Mg dragster is traveling at 125 m/s when...Ch. 14.3 - When s = 0.5 m, the spring is unstretched and the...Ch. 14.3 - The 5-lb collar is pulled by a cord that passes...Ch. 14.3 - The 20-kg crate is subjected to a force having a...Ch. 14.3 - Prob. 2P

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.

The speed of the collar at position B .

Solution Summary: The author explains how to determine the speed of the collar at position B.

Videos

The speed of the collar at position B .

Want to see the full answer?

Chapter 14 Solutions