Question

An ice skater at rest catches a bag of sand moving to the north with a speed of 5.4 m/s. This causes both the skater and the bag to move to the north at a speed of 1.5 m/s. If the skater's mass is 63 kg, what is the mass of the bag of sand?

Answer 1

Using the conservation of momentum for an inelastic collision, we calculate the mass of the bag of sand to be approximately 24.23 kg.

Step-by-step explanation:

The problem you've described is a classic example of the conservation of momentum in a one-dimensional inelastic collision, where two objects stick together after a collision. In such cases, the total momentum before the collision must equal the total momentum after the collision, assuming no external forces are acting on the system.

To find the mass of the bag of sand, we will use the momentum conservation formula:

• Total momentum before the collision = Total momentum after the collision
• m_sand * v_sand_before + m_skater * v_skater_before = (m_sand + m_skater) * v_after

Given that the skater's mass (m_skater) is 63 kg, the initial speed of the skater (v_skater_before) is 0 m/s since the skater is at rest. The speed of the bag of sand before the collision (v_sand_before) is 5.4 m/s, and the final speed of both (v_after) is 1.5 m/s. Using the formula, we find:

m_sand * 5.4 m/s + 63 kg * 0 m/s = (m_sand + 63 kg) * 1.5 m/s

Solving for m_sand (mass of the bag of sand), we get:

5.4 m/s * m_sand = 1.5 m/s * m_sand + 94.5 kg*m/s

5.4 m/s * m_sand - 1.5 m/s * m_sand = 94.5 kg*m/s

3.9 m/s * m_sand = 94.5 kg*m/s

m_sand = 94.5 kg*m/s / 3.9 m/s

m_sand = 24.23 kg

So, the mass of the bag of sand is approximately 24.23 kg.