A 177-g air-track glider moving at 0.35 m/s collides with a 133-g glider initially at rest. The collision is perfectly inelastic. The final speed of the combined glider is

Question

A 177-g air-track glider moving at 0.35 m/s collides with a 133-g glider initially at rest. The collision is perfectly inelastic.  The final speed of the combined glider is

BlackTom AI · Accepted Answer

The problem involves a perfectly inelastic collision where two gliders stick together after colliding, so momentum is conserved.
First, compute the initial momentum: p_initial = m1*v1 + m2*v2. Here m1 = 0.177 kg, v1 = 0.35 m/s, m2 = 0.133 kg, v2 = 0 m/s. So p_initial = 0.177×0.35 + 0.133×0 = 0.06195 kg·m/s.
Next, determine the combined mass after the collision: m_total = m1 + m2 = 0.177 + 0.133 = 0.310 kg.
Because momentum is conserved, p_initial = p_final = m_total * v_final. Therefore, v_final = p_initial / m_total = 0.06195 / 0.310 ≈ 0.19984 m/s, which rounds to 0.200 m/s.
Now evaluate each answer option:
- 0.350 m/s: This would require the final momentum to equal 0.310 kg × 0.350 m/s = 0.1085 kg·m/s, which does not match the initial momentum of 0.06195 kg·m/s; thus this is incorrect.
- 1.130 m/s: This would imply a final momentum of 0.310 kg × 1.130 m/s ≈ 0.3503 kg·m/s, far from the initial momentum, so incorrect.
- 0.200 m/s: This matches the momentum balance exactly (0.310 kg × 0.200 m/s ≈ 0.0620 kg·m/s, essentially equal to 0.06195 kg·m/s), so this is correct.
- 0.263 m/s: This would yield 0.310 kg × 0.263 m/s ≈ 0.0815 kg·m/s, which does not equal the initial momentum; thus incorrect.

SPHY001 Practice Quiz - Unit 08 | LA048

A 177-g air-track glider moving at 0.35 m/s collides with a 133-g glider initially at rest. The collision is perfectly inelastic. The final speed of the combined glider is

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