A mass m = 13 kg is pulled along a horizontal floor with NO friction for a dista

Question

A mass m = 13 kg is pulled along a horizontal floor with NO friction for a distance d =8 m. Then the mass is pulled up an incline that makes an angle = 36° with the horizontal and has a coefficient of kinetic friction k = 0.35. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of = 36° (thus on the incline it is parallel to the surface) and has a tension T =50 N.

What is the work done by friction after the block has traveled a distance x = 3 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 = 3 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

Explanation / Answer

Here,

mass of block , m = 13 Kg

theta = 36 degree

uk = 0.35

T = 50 N

work done by friction = - u *m * g * d * cos(theta)

work done by friction = - 0.35 * 13 * 9.8 * 3 * cos(36)

work done by friction = - 108.22 J

the work done by friction after the block travelled 3 m is - 108.22 J

----------------------------

work dome by gravity = - m * g * d * sin(theta)

work dome by gravity = - 13 * 9.8 * 3 * sin(36)

work dome by gravity = - 224.6 J

the work dome by gravity is - 224.6 J

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Here ,

let the distance travelled up the incline is d

Using work energy theorum

50 * cos(36) * 8 + d * (50) - (0.35 * cos(36) + sin(36) ) * 13 * 9.8 * d = 0

solvibg for d

d = 5.31 m

the distance travelled up the incline is 5.31 m

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as the blocks stop moving on the incline

the incline the net work done on the block is:

negative

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