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A block of mass 37.6kg is moving at 37.6(m)/(s) when it collides with a stationary block of mass m². After the collision they move at 12.0(m)/(s). What is the mass of the block that had been stationary?

Answer :

Using the conservation of momentum principle, the mass of the stationary block is calculated as approximately 80.533 kg. This method compares the total momentum before and after collision, yielding the solution.

To solve this problem, we can use the principles of conservation of momentum.

According to the conservation of momentum:

The total momentum before the collision is equal to the total momentum after the collision.

The momentum (p) of an object is given by the product of its mass (m) and velocity (v).

Given:

Mass of the moving block (m1) = 37.6 kg

Velocity of the moving block before collision (v1) = 37.6 m/s

Velocity of the moving block after collision (v1') = 12.0 m/s

Mass of the stationary block (m2) = unknown (m)

Velocity of the stationary block before collision (v2) = 0 m/s (as it is stationary)

Velocity of the stationary block after collision (v2') = 12.0 m/s (as they move together after collision)

Using the conservation of momentum:

m1 × v1 + m2 × v2 = m1 × v1' + m2 × v2'

37.6 × 37.6 + m × 0 = 37.6 × 12.0 + m × 12.0

1417.6 + 0 = 451.2 + 12m

1417.6 = 451.2 + 12m

966.4 = 12m

m = 966.4 / 12

m = 80.533 kg

Therefore, the mass of the stationary block is approximately 80.533 kg.

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