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

Question

The air-track carts in the figure are sliding to the right at 1.0m/s. The spring between them has a spring constant of 100 N/m and is compressed 4.1 cm. The carts slide past a flame that burns through the string holding them together.

Figure: http://session.masteringphysics.com/problemAsset/1070485/3/10.CP74.jpg

Part A) What is the speed of 100-g cart?

Part B) What is the direction of the motion of 100-g cart?
- TO THE LEFT
- TO THE RIGHT

Part C) What is the speed of 300-g cart?

Part D) What is the direction of the motion of 300-g cart?

Explanation / Answer

From the law of conservation of energy 1/2(0.1kg)v1^2 +1/2(0.3kkg)v2^2=1/2(100N/M)(0.041 m)^2 --------- (1) and From conservation of momentum (0.1kg)v1= (0.3kg)v2 v1 = 3v2 1/3 v1 = v2 Substitute this value in equation (1) 1/2(0.1kg)v1^2 + 1/2(0.3kg)(1/3v1)^2 = 1/2(100N/M)(0.041)^2 (0.1kg)v1^2 + (0.3kg)(1/3v1)^2 = (100N/M)(0.041)^2 v1 ˜1.122831 m/s Adjust this for the refrence frame moving at 1m/s so: v1 =1.122831 m/s-1.0 m/s = 0.122831 m/s v2 = 0.374277 m/s + 1.0 m/s = 1.374277 m/s Cart 1 is moving slowly to the left while the heavier Cart 2 is moving quickly to the right.

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