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A block is pushed up an inclined plane by a horizontal force f as shown in Figur

ID: 1421076 • Letter: A

Question

A block is pushed up an inclined plane by a horizontal force f as shown in Figure 7.P11. Attached to the upper end of the incline is a spring with stiffness constant k = 320. N/m. The horizontal force continues to act as the block moves an additional 0.500 m along the incline. Assume the following magnitudes for the forces acting on the block as it moves the 0.500 m after contacting the spring: P = 300. N, N = 260. N, W = 100. N, and F_fric = 70.0 N. Calculate the work done on the block by each of the following forces for the 0.500-m distance: (a) the push force P, (b) the normal force N, (c) the weight force W, (d) the frictional force F_fric, (e) the spring, (f) What is the net work done on the block over the 0.500-m distance? (g) If the block had a speed of 1.00 m/s when it first contacted the spring, what is its speed after traveling the 0.500 m as described above?

Explanation / Answer

Work done = F.d = |F||d|cos@

where @ is the angle between force F and displacement d.


a) d = 0.5m along incline upward

P = 300 N horizontal

@ = 36.87 deg


W = 0.5 x 300 x cos36.87 =120 J

b) normal force is perpendicular to the inclien.

@ = 90 deg

W = 260 x 0.5 x cos90 = 0

c) W = 100 N

@ = 90 + 36.87 = 126.87 deg


Wrok done = 100 x 0.5 x cos126.87 = - 30 J

d) @ = 180 deg

Work done = 70 x 0.5 x cos180 = -35 J

e) work done by spring = - potential energy stored

   = -kx^2 /2 = - 320 x 0.5^2 / 2


= - 40 J


f) Total work done = -40 -35 -30 + 0 + 120 = 15 J

g) using work energy theorem,

total work done   = change in KE


15 = 10 ( vf^2 - 1^2) /2

vf^2 -1 = 3

vf   = 2 m/s

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