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Chapter 10: Q. 52 (page 258)

Use work and energy to find an expression for the speed of the block in FIGURE P10.52 just before it hits the floor if

(a) the coefficient of kinetic friction for the block on the table is μkand

(b) the table is friction less

Short Answer

Expert verified

(a) The speed of the block just before it hits the floor when the table has coefficient of kinetic friction μk2ghm-μkMm+M

(b) The speed of the block just before it hits the floor when the table is frictionless is2mghm+M

Step by step solution

01

Given information (part a)

Given a mass pulley system. The table is either frictionless or has a coefficient of kinetic friction μk.

02

Explanation (part a)

From the conservation of energy, the loss of P.E. of the block with mass m is used up in the gain of K.E. of both the blocks and in doing work against friction.

Let m be the mass of the block and v be the speed of the block.

mgh=12(m+M)v2+μkMgh

12(m+M)v2=mgh-μkMgh

(m+M)v2=2ghm-μkM

v2=2ghm-μkMm+M

localid="1648546745696" v=2ghm-μkMm+M

03

Given information (part b)

Given a mass pulley system. The table is frictionless.

04

Explanation (part b)

Speed of the block:

v=2ghm-μkMm+M

For a frictionless table, μk=0.

ν=2mghm+M

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