Question
Problem 7.30 Part A A 1.44-kg block is held in place against the spring by a 33-N horizontal external force (see the figure). The external force is removed, and the black is projected with a velocity v1 12 ms 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 fricdion over this section is 0.31. The velocity of the block is v 3 1.4 m/s at C. The block moves on to D, where it stops. The initial compression of the spring is closest to v O 7.6 cm O 6.3 cm. O 8.8 cm O 3.8 cm. 05.0 cm. Submit My Answers Give Up oblemiD-471004948 hmentPr masteringphysics.com/myct/itemView?assignmentProblemID-47100494&e; https://session.masteringphysics.com/myct/itemView?assign
Explanation / Answer
let x is the compresiion of the spring,
Apply Hook's law
F = k*x
33 = K*x ---(1)
Apply Energy conservation
0.5*m*v1^2 = 0.5*k*x^2
0.5*m*v1^2 = 0.5*(k*x)^2/k
m*v1^2 = (k*x)^2/k
k = (k*x)^2/(m*v1^2)
= (33)^2/(1.44*1.2^2)
= 525.2 N/m
now from equation 1
x = F/k
= 33/525.2
= 0.063 m
= 6.3 cm
so, option 2 is the correct answer.