(a) Explanation Given information: The weight of the block A ( W A ) is 0.75 lb . The weight of the block B ( W B ) is 0.5 lb . The distance between the block B and block C ( x ) is 0.15 in . or 0.0125 ft . Assume the acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Calculate the mass of block A ( m A ) using the relation: m A = W A g Substitute 0.75 lb for W A and 32.2 ft / s 2 for g . m A = 0.75 32.2 = 0.0233 lb ⋅ ft / s 2 Calculate the mass of block B ( m B ) using the relation: m B = W B g Substitute 0.5 lb for W B and 9.81 m / s 2 for g . m B = 0.5 32.2 = 0.015528 lb ⋅ ft / s 2 Calculate the force ( F ) using the formula: F = k x 2 Substitute 0.0125 ft for x . F = k 0.0125 2 = 6400 k Calculate the constant ( k ) by considering the vertical equilibrium condition: ∑ F = 0 − W A − W B + F = 0 Substitute 0.75 lb for W A , 0.5 lb for W B and 6400 k for F . − 0.75 − 0.5 + 6 , 400 k = 0 k = 195.3 × 10 − 6 lb ⋅ ft 2 Here, the initial kinetic energy ( T 1 ) is zero due to zero initial velocity. Calculate the final kinetic energy ( T 2 ) using the formula: T 2 = 1 2 m B v max 2 Substitute 0.015528 lb ⋅ ft / s 2 for m B . T 2 = 1 2 ( 0.015528 lb ⋅ ft / s 2 ) v max 2 = 7.7639 × 10 − 3 v max 2 lb ⋅ ft Calculate the work done ( U 1 − 2 ) G by the magnetic force and weight using the formula: ( U 1 − 2 ) = ∫ 0.0125 x ( F − W B ) d x Substitute k x 2 for F and 0 (b) To determine Find the maximum acceleration ( a B ) of B .

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Clutches, Brakes, Couplings, and Flywheels

The clutch is described as a machine element used to connect or disconnect two shafts together to transmit torque or power. The clutch works on the principles of friction. The clutch is commonly used in automobiles to transfer power from the driving shaf…

Videos

Question

Chapter 13.1, Problem 13.32P

(a)

To determine

Find the maximum velocity (vmax) of B.

(b)

To determine

Find the maximum acceleration (aB) of B.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.1, Problem 13.31P

Chapter 13.1, Problem 13.33P

Students have asked these similar questions

5. A 2-kg sphere is attached to a massless rigid rod attached to a fixed pivot point O. The rigid rod and mass rotate in the horizontal plane. A moment is applied to the rod of magnitude M = 0.5t² N. m, where t is in seconds. The length of the rod is 0.5 m. Determine the speed of the sphere after the moment is applied for 5 seconds. M(t)

PROBLEM 3.12 An object is launched at a speed of 20.0 m/s from the top of a tall tower. The height y of the object with respect to the base of the tower as a function of the timet elapsed from launch is y(t) = -4.90t² + 19.32t + 60, where y is in meters and t is in seconds. Determine: 13. the height H of the tower. 50 m c. 70 m d. 80 m а. b. 60 m 14. the launch angle. с. 75.35° d. 77.35° а. 71.35° b. 73.35° 15. the horizontal distance traveled by the object before it hits the ground. с. 32.28 m d. 34.28 m a. 28.28 m b. 30.28 m

A brass (nonmagnetic) block A and a steel magnet B are in static equilibrium in a brass tube under the magnetic repelling force of another steel magnet, C. The magnet B is located a distance x =d, from C. If block A is suddenly removed, and the acceleration of block B is: k a =-g+ where g andk are known constants. Determine: a. the velocity, v, as a function of the position x and the known parameters (g,k,d,), and b. the position, x, when the velocity is maximum in terms of the known parameters (g,k,d,). В

Chapter 13 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

Ch. 13.1 - Block A is traveling with a speed v0 on a smooth...Ch. 13.1 - A 400-kg satellite is placed in a circular orbit...Ch. 13.1 - A 0.5-lb stone is dropped down the bottomless pit...Ch. 13.1 - A baseball player hits a 5.1-oz baseball with an...Ch. 13.1 - A 500-kg communications satellite is in a circular...Ch. 13.1 - Prob. 13.5P Ch. 13.1 - In an ore-mixing operation, a bucket full of ore...Ch. 13.1 - Determine the maximum theoretical speed that may...Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - An athlete is holding 30 lb of weights at a height...

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 maximum velocity ( v max ) of B .

Solution Summary: The author calculates the mass of the block A (w_A) using the relation: