A 1.04-kg block is held in place against the spring by a 76-N horizontal externa
ID: 1376459 • Letter: A
Question
A 1.04-kg block is held in place against the spring by a 76-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity V2= 2.1 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.23. The velocity of the block is v3 = 1.4 m/s at C. The block moves on to D, where it stops. The initial compression of the spring is closest to:Explanation / Answer
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A 0.12 kg block is held in place againstthe spring by a 35 N horizontal external force. The external forceis removed, and the block is projected with a velocityv1= 1.2 m/s upon separation from thespring. The block descends a ramp and has a velocityv2= 1.4 m/s at the bottom. The trackis frictionless between points A and B. The track is frictionlessbetween points A and B. The block enters a rough section at B,extending to E. The coefficient of kinetic friction is 0.26. Thevelocity of the block is v3=1.4 at C. The block moves on to D, where it stops. In Figure 7.4,the initial compression of the spring, in cm, is closestto:
a. 0.26
b. 0.99
c. 0.67
d. 0.18
e. 0.49
answers
First, the initial compression of the spring is from force "F"which is 35N. This must equal:
F = kx
Now consider the block leaving the spring: conservation of energy.
Energy stored in the spring: (1/2) kx2
KE of block leaving the spring: (1/2) mv2 where v = 1.2 m/s
set these equal: (1/2) kx2 = (1/2) mv2 or kx2 = mv2
Notice these two equations: F =kx and kx2 = mv2 have twounknowns, k and x
Solve the first one for k: k =F/x and pop it into the secondone:
(F/x) x2 = m v2 and solve for x.
All the stuff about the friction and such is a nice story, butits not needed to answer the question.
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