A mass m 17 kg is pulled along a horizontal floor with a co

A mass m = 17 kg is pulled along a horizontal floor, with a coefficient of kinetic friction _k = 0.1, for a distance d = 7.4 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle = 37° with the horizontal. 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 = 57 N.

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

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

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

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

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

6) During the entire process, the net work done on the block is:

positive

negative

zero

Solution

1)

work done by tension before the block gets to the incline

W=TdCos(o) =57*7.4*Cos37

W=336.86 J

2)

work done by friction as the block slides on the flat horizontal surface is

W=-u_kmgCos(o)=-0.1*17*9.8*Cos37

W=-13.3 J

3)

W=KE_i+KE_f=0+(1/2)mV²

=>V=sqrt[2*W/m] =sqrt[2*336.86/17]

V=6.3 m/s

4)

Work done by gravity before coming to rest is

W=-mgSin(o) =-17*9.8*sin37=-100.26 J

From Work energy theorem

dKE =W_T=W_T1+W_T2+W_F+W_g

Since the block is at rest at initial and final position,so

dKE=0

=> 0=336.86+57*x-13.3-100.26

X=3.92 m

5)

W=-100.26 J

6)

Zero ,as shown in d