Two carts of masses 5.0 kilograms and 1.0 kilogram are pushed apart by a compressed spring. If the 5.0-kilogram cart moves westward at 2.0 meters per second, then the 1.0-kilogram cart moves eastward at what speed?A 0.4 m/sB 2.0 m/sC 5.0 m/sD 10.0 m/s
Question
Two carts of masses 5.0 kilograms and 1.0 kilogram are pushed apart by a compressed spring. If the 5.0-kilogram cart moves westward at 2.0 meters per second, then the 1.0-kilogram cart moves eastward at what speed?A 0.4 m/sB 2.0 m/sC 5.0 m/sD 10.0 m/s
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the carts are pushed apart is zero (since they are initially at rest), and the total momentum after they are pushed apart must also be zero (since no external forces are acting on the system).
The momentum of an object is given by the product of its mass and its velocity. So, the momentum of the 5.0 kg cart after it is pushed apart is 5.0 kg * 2.0 m/s = 10.0 kg*m/s westward.
Since the total momentum must be zero, the momentum of the 1.0 kg cart must be 10.0 kg*m/s eastward to balance out the momentum of the 5.0 kg cart.
The velocity of the 1.0 kg cart is then given by its momentum divided by its mass, or 10.0 kg*m/s / 1.0 kg = 10.0 m/s.
So, the 1.0 kg cart moves eastward at a speed of 10.0 m/s. The correct answer is D.
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