A 1.5 kg box moves back and forth on a horizontal frictionless surface between t

Question

A 1.5 kg box moves back and forth on a horizontal frictionless surface between two different springs, as shown in the accompanying figure. The box is initially pressed against the stronger spring, compressing it 4.9 cm , and then is released from rest. (Figure 1)

Part A

By how much will the box compress the weaker spring?

Express your answer in centimeters to two significant figures.

Part B

What is the maximum speed the box will reach?

Express your answer in meters per second to two significant figures.

Explanation / Answer

Here,

a)

0.5 * k1 * x1^2 = 0.5 * k2 *x2^2

x2 = x1 * (k1/k2)^1/2 = 4.9 * (32/16)^1/2 = 6.9297 cm

b)

0.5 *m*vmax^2 = 0.5 * k1 * x1^2

vmax = x1 *( k1 /m)^1/2 = 4.9 * 10^-2 * (3200 / 1.5)^1/2 = 2.2632 m/s

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