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Chapter 10: Q. 56 (page 259)

A 2.6kgblock is attached to a horizontal rope that exerts a variable force Fx=20-5xN, where x is in m. The coefficient of kinetic friction between the block and the floor is 0.25.Initially the block is at rest at x=0m. What is the block’s speed when it has been pulled to x=4.0m?

Short Answer

Expert verified

The speed of the block when it is pulled tox=4.0mis3.34m/s.

Step by step solution

01

Given information

The weight of the block m=2.6kg

Force exerted by the block to a horizontal rope Fx=20-5xN

The coefficient of kinetic friction between the block and the floor =0.25

02

Explanation

The work done on the mass acted upon by a variable force Fxin moving from x1tox2,W=∫x1x2F(x)dx

Work done on the block is given by

W=∫04F(x)dxW=∫04(20-5x)dxW=20∫04dx-5∫04xdxW=20[x]x=04-5x22x=04W=80-5162W=40J

Now,

localid="1649412556558" 12mv2+μmgx2-x1=W12mv2=W-μmgx2-x1v2=2W-μmgx2-x1mv2=240J-0.252.6kg9.81m/s24m-0m2.6kgv=240-0.252.6kg9.81m/s24m2.6kgv=3.34m/s

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