The air-track carts in the figure are sliding to the right at 1.0 m/s. The sprin

Question

The air-track carts in the figure are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 140 N/m and is compressed 4.2 cm. The carts slide past a flame that burns through the string holding them together.

1. What is the speed of the 100-g cart?

2. What is the speed of the 300-g cart?

The air-track carts in the figure are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 140 N/m and is compressed 4.2 cm. The carts slide past a flame that burns through the string holding them together. What is the speed of the 100-g cart? What is the speed of the 300-g cart?

Explanation / Answer

m1 = 100 g = 0.1 kg

m2 = 300 g = 0.3 kg

K = 140 N/m

d = 0.042 m

V1' = sqrt [ K d^2 / m1 ((m1 / m2)+1)]

V1' = sqrt (140 * 0.042^2 / [0.1((0.1/0.3)+1)]

= 1.36 m/s

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V2' = sqrt [K d^2 / m2((m2/m1)+1)]

V2' = sqrt (140*0.042^2 / [0.3((0.3/0.1)+1)]

= 0.45 m/s

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1) V1 = 1 - 1.36

= -0.36 m/s (left)

-------------------------------------

2)V2 = 1 + 0.45

=1.45 m/s (right)

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