A mass m = 14 kg is pulled along a horizontal floor with NO friction for a dista

Question

A mass m = 14 kg is pulled along a horizontal floor with NO friction for a distance d =8.9 m. Then the mass is pulled up an incline that makes an angle = 28° with the horizontal and has a coefficient of kinetic friction k = 0.42. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of = 28° (thus on the incline it is parallel to the surface) and has a tension T =66 N.

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

2) What is the speed of the block right before it begins to travel up the incline? m/s

3) What is the work done by friction after the block has traveled a distance x = 5.1 m up the incline? (Where x is measured along the incline.) J

4) What is the work done by gravity after the block has traveled a distance x = 5.1 m up the incline? (Where x is measured along the incline.) J

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

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

positive

negative

zero

Explanation / Answer

1) Work done = F.d = Fdcos@

   W = 66 x 8.9 x cos28 = 518.64 J

2) using work energy theorem.

work done by tension = change in KE

518.64 = 14v^2 /2 - 0

v = 8.61 m/s

3) f= uk N and N = mgcos28

f = uk mg cos28

work done = (uk mg cos28) x 5.1 x cos180

        = 0.42 x 14 x 9.81 x cos28 x 5.1 x cos180 = - 259.75 J

4) work done = mg d cos(90 +28)

= - 14 x 9.81 x 5.1 x sin28 = - 328.83 J

5) work done by gravity + work done by friction + work done by tension = change in KE

- (14 x 9.81 x d x sin28) - (0.42 x 14 x 9.81 x cos28) + (66 x d) = 518.64

49.41d = 518.64

d = 10.50 m

6) negative

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.