Problem 15.48 Two blocks, of masses m1 and m2, are placed on a horizontal surfac
ID: 1468700 • Letter: P
Question
Problem 15.48
Two blocks, of masses m1 and m2, are placed on a horizontal surface and attached to opposite ends of a spring as in (Figure 1) . The blocks are then pushed toward each other to compress the spring. The spring constant for the spring is k. Ignore friction and the mass of the spring.
PART A) Describe the motion of the center of mass of the system when the blocks are released.
a. The center of mass of the system will move to the left.
b. The center of mass of the system will move to the right.
c. The center of mass of the system will not move.
PART B) Derive an expression for the angular frequency ? of the motion.
Express your answer in terms of k, m1 and m2.
? =?
PART C) What is ? in the limit m2?m1?
Express your answer in terms of k, m1 and m2.
? = ?
PART D) What is ? when m1=m2?
Express your answer in terms of k and m1.
? = ?
cm m2Explanation / Answer
Since there is no external force centre of mass remains at rest
Vcm = 0 as dXcm = 0 and hence acm = 0
B : Wuth respect to COM
we can replace two masses into reduced mass system
u = m1m2/(m1+m2)
W = sqrt(K/m)
W = sqrt(K(m1+m2)/m1m2
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C:
uf m2 << m1
W = Sqrt(k/m1)
m1+m2 = m2
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D: if m1 = m2
W = sqrt(2k/m1)