(a) Explanation Given information: The length of the chain is l . The mass of the chain is m . The rate of speed is Δ y Δ t = v . Calculation: Consider the mass per unit length of chain as m l = ρ . Assume the reaction from the floor is equal to the weight of the chain in contact with the floor. Calculate the reaction at the floor ( R ) as shown below. R = ρ g ( l − y ) = ρ l g ( 1 − y l ) Substitute m for ρ l . R = m g ( 1 − y l ) Sketch the Free Body Diagram of the chain as shown in Figure 1. Refer to Figure 1. Apply the impulse and momentum principle as shown below. ρ y v + P ( Δ t ) + R ( Δ t ) − ρ g L ( Δ t ) = ρ ( y + Δ y ) v P ( Δ t ) = (b) To determine The reaction of the floor.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 14.3, Problem 14.86P

(a)

To determine

The magnitude of force P applied at A.

(b)

To determine

The reaction of the floor.

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Chapter 14.3, Problem 14.85P

Chapter 14.3, Problem 14.87P

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The magnitude of force P applied at A .

Solution Summary: The author calculates the mass per unit length of the chain as ml=rho .