A mass m = 12 kg is pulled along a horizontal floor with NO friction for a dista

Question

A mass m = 12 kg is pulled along a horizontal floor with NO friction for a distance d =6.1 m. Then the mass is pulled up an incline that makes an angle = 37° with the horizontal and has a coefficient of kinetic friction k = 0.41. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of = 37° (thus on the incline it is parallel to the surface) and has a tension T =47 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 = 1.8 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 = 1.8 m up the incline? (Where x is measured along the incline.)

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 :

a) positive b) negative or c ) zero?

Explanation / Answer

Horizontal tension: T=Fcos(37)=47cos(37) = 37.5 N
work=T*distance = 37.5*6.1 = 229 J

2. k=.5*mv^2, where k equals the number found above.
v = 6.18 m/s

3. Force by friction=uN
= umgcos(37) = 0.41 × 94 = 38.5 N
w=Fd = 38.5*1.8 = 69 J and its negative

4. use dsin37 to find verticle distance, than plug in w=m*g*dsin37 = 12*9.8*1.8sin(37) = 127.4 J

5. 0.5*mv^2 = mgh*sin(37)
v = 6.18 m/s
h = 3.23 m

6. Net work = 0

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