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solve 3 and 4 using the energy and work 3. A block is given an initial speed of

ID: 2039393 • Letter: S

Question

solve 3 and 4 using the energy and work

3. A block is given an initial speed of 5 m/ s up a 30° incline. The coefficient far up the incline of friction between the block and plane u 0.25. How does the block travel before coming to rest? 4rskg block is pulled along a rough horizontal surface by a force of 20 N directed at a 30° angle above the horizontal. The coefficient of friction between the block and surface is u 0.25. If the block starts from rest, how far along the floor must it be pulled so that the final speed is 4 m/s?

Explanation / Answer

Given

3.

initial speed is 5 m/s

the angle of inclinationis 30 degrees

the coefficient of friction is mue = 0.25

from work energy theorem

the work done = change in k.e

0.5*m*(v2^-v1^2) = F_f*s

0.5*m*(v2^-v1^2) = mue*m*g cos theta*s+ mg s sin theta

s = 0.5(v1^2)/(mue*g cos theta+g sin theta)

s = 0.5*5^2 /(0.25*9.8 cos30+9.8 sin 30) m

s = 1.78018 m

the block can travel before coming to rest is 1.78018 m along the incline

4.

given

m = 5 kg , F = 20 N directed 30 degrees above the horizontal

the coefficient of friction is mue = 0.25

the final speed is 4 m/s , initial speed is 0 m/s

the net force force acting on the block is

net force F = Fcos theta - mue(mg - F sin theta)  

work done = change in kinetic energy  

W = F*S = 0.5*m*v^2

W = (Fcos theta - mue(mg - F sin theta))s

W = (20 cos30 - 0.25(5*9.8 - 20 sin30))s

then change in kinetic energy is k.e = 0.5*5*4^2 J = 40 J

equating these , (20 cos30 - 0.25(5*9.8 - 20 sin30))s = 40 J

solving for s

s = 5.2837 m

the block can move to s = 5.2837 m