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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 渭kand

(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 渭k2ghm-渭kMm+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 渭k.

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+渭kMgh

12(m+M)v2=mgh-渭kMgh

(m+M)v2=2ghm-渭kM

v2=2ghm-渭kMm+M

localid="1648546745696" v=2ghm-渭kMm+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-渭kMm+M

For a frictionless table, 渭k=0.

谓=2mghm+M

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