A mass m = 16 kg is pulled along a horizontal floor, with a coefficient of kinet

Question

A mass m = 16 kg is pulled along a horizontal floor, with a coefficient of kinetic friction k = 0.14, for a distance d = 8.4 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle = 39° with the horizontal. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of = 39° (thus on the incline it is parallel to the surface) and has a tension T = 57 N.

1) What is the work done by tension before the block gets to the incline?

2) What is the work done by friction as the block slides on the flat horizontal surface?

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

4) How far up the incline does the block travel before coming to rest?

5) What is the work done by gravity as it comes to rest?

Please show the steps

Explanation / Answer

1)

at the horizontal surface ,

normal force , N = 16 * 9.8 - 57 * sin(39)

N = 16 * 9.8 - 57 * sin(39)

N = 120.9 N

frictional force = 120.9 * 0.14

frictional force , f = 16.93 N

1)

work done by tension = T * cos(39) * d

work done by tension = 57 * cos(39) * 8.4

work done by tension = 372.1 J

the work done by tension is 372.1 J

2)

work done by frictional force = 16.93 * (-8.4)

work done by frictional force = -142.2 J

the work done by frictional force is -142.2 J

3)

at the bottom of incline
0.5 * 16 * v^2 = 372.1 - 142.2

v = 5.36 m/s

the speed of the block is 5.36 m/s

4)

Using conservation of energy

0.5 * 16 * 5.36^2 + 57 * d = 16 * 9.8 * sin(39) * d

solving for d

d = 5.51 m

the block travels 5.51 m up the incline

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