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 =8.4 m. Then the mass is pulled up an incline that makes an angle ? = 39 with the horizontal and has a coefficient of kinetic friction ?k = 0.38. 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 =59 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 = 2.7 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 = 2.7 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

A mass m = 13 kg is pulled along a horizontal floor with NO friction for a distance d =8.4 m. Then the mass is pulled up an incline that makes an angle ? = 39½ with the horizontal and has a coefficient of kinetic friction ?k = 0.38. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of ? = 39½ (thus on the incline it is parallel to the surface) and has a tension T =59 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 = 2.7 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 = 2.7 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 by tension before the block goes up the incline is,

           W = Fx = Td = 59*8.4 = 495.6 J

2. speed of the block right before it begins to travel up the incline is,

            v = [2W/m]1/2 = [2*495.6/13]1/2 = 8.73 m/s

3. work done by friction after the block has traveled a distance x = 2.7 m up the incline is,

          W = ukmgxcos39o = 0.38*13*9.8*2.7*cos39o = 101.58 J

4. What is the work done by gravity after the block has traveled a distance x = 2.7 m up the incline is,

W = mgxsin39o = 13*9.8*2.7*sin39o = 216.47 J

5. The acceleration of the block is,

        a = T/m - gsin39o -ukgcos39o

           = -4.522 m/s2

Hence, the required distance is,

       S = v2 - u2 /2a = 0- (8.73 m/s)/2*[-4.522 m/s2] = 8.425 m

6. Work done is not zero. Since it comes rest finally, so the net work done is negative.

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