Two trolleys are rolling toward each other and when they collide they stick to each other. Trolley A has a mass of 23.1 kg and Trolley B has a mass of 6.7 kg. Before the collision, Trolley A was moving East at 12.4 m s-1 and Trolley B was moving West at 13.8 m s-1. Both trolleys stick together after the collision so what is their final velocity?

Question

BlackTom AI · Accepted Answer

Conservation of momentum applies because the trolleys stick together in a completely inelastic collision (external horizontal forces are negligible during the collision), so total momentum before equals total momentum after.

1) Relevant concepts
- Momentum p = m v (vector). 
- For an isolated system, total momentum is conserved: m1 v1 + m2 v2 = (m1 + m2) v_final.
- Use a sign convention: take East as positive and West as negative.

2) Step-by-step reasoning and arithmetic
- Assign values with signs:
  - Trolley A: m1 = 23.1 kg, v1 = +12.4 m/s (East)
  - Trolley B: m2 = 6.7 kg, v2 = −13.8 m/s (West)
- Compute initial total momentum:
  - p1 = m1 v1 = 23.1 × 12.4 = 286.44 kg·m/s
  - p2 = m2 v2 = 6.7 × (−13.8) = −92.46 kg·m/s
  - p_total = p1 + p2 = 286.44 − 92.46 = 193.98 kg·m/s

3) Final velocity calculation (showing intermediate steps)
- Combined mass M = m1 + m2 = 23.1 + 6.7 = 29.8 kg
- v_final = p_total / M = 193.98 / 29.8
- Perform division: 193.98 ÷ 29.8 ≈ 6.51 m/s

4) Why this answer is correct
- The positive result (≈ +6.51 m/s) means the stuck trolleys move East. This follows directly from the net positive initial momentum (A’s eastward momentum exceeds B’s westward momentum).

5) Why the other multiple-choice options are incorrect
- b (12.71 m/s East): magnitude too large; does not satisfy momentum conservation for the given masses/velocities.
- c (6.51 m/s West): magnitude correct but direction wrong — sign of momentum is positive (East).
- d (12.71 m/s West): both magnitude and direction incorrect.

6) Conclusion
- The correct final velocity is 6.51 m/s East, which matches the provided answer.

类似问题

A 9.3 kg cart moving horizontally on a frictionless surface initially at 1.6 ms-1, has a 3.4 kg load dropped vertically in it, increasing the cart's total mass.The duration of the drop took 1.7 s.Based on the conservation of momentum, calculate the final velocity of the now combined cart and load.

A 5.5 kg cart moving horizontally on a frictionless surface initially at 4.2 ms-1, has a 2.9 kg load dropped vertically in it, increasing the cart's total mass.The duration of the drop took 1.2 s.Based on the conservation of momentum, calculate the final velocity of the now combined cart and load.

A 2.8 kg cart is moving horizontally at an initial speed of 6.6 m/s across a frictionless surface when a 8.6 kg load is dropped vertically onto it. The vertical speed of the load is 4.1 m/s just prior to impact. What is the final horizontal speed of the combined cart and load after the impact?

A child falls sideways off a sled while sledding on frictionless ice. What happens to the velocity of the sled?

Object A has a mass of 5.0 kg and is moving towards east with a speed of 5.0 m s−1 and object B of mass 12 kg is moving towards west with a speed of 2.0 m s−1. After their collision A reverses its direction and moves with a speed of 2.0 m s−1. The new velocity of B is

A 60-kg swimmer dives from a 150-kg raft with a horizontal speed of 1.5 m/s. The raft is initially at rest. What is the speed of the raft immediately after the diver jumps?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单