The air-track carts in the figure ( Figure 1 ) are sliding to the right at 1.0 m

Question

The air-track carts in the figure(Figure 1) are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 140N/m  and is compressed 4.3cm . The carts slide past a flame that burns through the string holding them together.

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

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

The air-track carts in the figure(Figure 1) are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 140N/m and is compressed 4.3cm . The carts slide past a flame that burns through the string holding them together. What is the speed of 100-g cart? What is the speed of 300-g cart?

Explanation / Answer

Intial energy = 0.5mv^2 = 0.5*100*1/1000 = 0.05

Spring gives 0.5*kx^2 energy = 0.5*140*4.3/100 = 3.01

Spring gives energy to the left side, so energy used to get velovity = 3.01-0.05 = 2.96

so 2.96 = 0.5mv^2

so v = 7.69 m/s

final velocity of 100 gms = 7.69 m/s to the left

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