Question

A mass m = 13 kg is pulled along a horizontal floor with NO friction for a distance d =7.4 m. Then the mass is pulled up an incline that makes an angle θ = 32° with the horizontal and has a coefficient of kinetic friction μ_k = 0.31. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ = 32° (thus on the incline it is parallel to the surface) and has a tension T =59 N.

What is the work done by tension before the block goes up the incline? (On the horizontal surface.)

What is the speed of the block right before it begins to travel up the incline?

What is the work done by friction after the block has traveled a distance x = 4.1 m up the incline? (Where x is measured along the incline.)

What is the work done by gravity after the block has traveled a distance x = 4.1 m up the incline? (Where x is measured along the incline.)

How far up the incline does the block travel before coming to rest? (Measured along the incline.)

On the incline the net work done on the block is:

positive

negative

zero

Answer 1

(1)

The work done by the force is this times the distance moved:

W = F s cos32º = ( 59 N ) ( 7.4 m ) cos32º = 370 J

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(2)

Change in kinetic enregy is equal to work done

Equation for  kinetic energy of the block W = ½ . m . V²

Solve for V

V =√ 2 W / m = √  2 ( 370 J ) / 13 kg = 7.5 m/s

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(3)

The friction force on the block is F = µ . Fn

  F = µ mgx cos32 = ( 0.31 ) ( 13 kg ) ( 9.8 ) ( 4.1 )cos32 =  137. 3 N

In two significant digits, F = 140 N

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(4)

Work done by gravity:

W = mgx sin32 = ( 13 kg ) ( 9.8 ) ( 4.1 ) sin 32 =  276.7 N

In two significant digits, W = 280 N