A Men Lying on a Surface Shoves a Stone: Conservation of Momentum Problem

What speed does the 85 kg man acquire as a result of shoving a 82 g stone away from himself at a speed of 9.0 m/s?

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the shove is equal to the total momentum after the shove. The momentum of an object is given by the product of its mass and velocity. Let's denote the initial velocity of the man as v1 and the final velocity of the man as v2. Before the shove, the man and the stone have momentum in opposite directions. After solving for v2, we find that the man does not acquire any speed and remains at rest.

Conservation of Momentum Principle

Momentum Calculation: The momentum of an object is given by the formula: momentum = mass x velocity.

Solving the Problem:

Before the shove: - The momentum of the man (m1) is 85 kg * 0 m/s = 0. - The momentum of the stone (m2) is 0.082 kg * 9.0 m/s = 0.738 kg m/s. After the shove: - The momentum of the man becomes -85 kg * v2. - The momentum of the stone becomes -0.082 kg * v2. Using the conservation of momentum principle: 0 + 0.738 = -85v2 - 0.082v2 0.738 = - 85v2 - 0.082v2 0.738 = -85.082v2 v2 = 0 m/s Therefore, the man does not acquire any speed as a result of shoving the stone away and remains at rest. This demonstrates the conservation of momentum in a closed system.
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