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

Question

BlackTom AI · Accepted Answer

Take east as positive and apply conservation of linear momentum (total momentum before collision equals total momentum after collision).

1) Relevant knowledge points and concepts
- Momentum p = m v is conserved for the two-body system if no external horizontal forces act during the collision.
- Choose a sign convention: east = +, west = −.
- Use the equation: mA vA,i + mB vB,i = mA vA,f + mB vB,f and solve for vB,f.

2) Step-by-step reasoning
- Given: mA = 5.0 kg, vA,i = +5.0 m s−1 (east); mB = 12 kg, vB,i = −2.0 m s−1 (west).
- After collision: A reverses and moves with speed 2.0 m s−1 to the west, so vA,f = −2.0 m s−1.
- Unknown: vB,f.

3) Calculations (all intermediate steps)
Write momentum conservation:
5.0( +5.0 ) + 12( −2.0 ) = 5.0( −2.0 ) + 12 vB,f
Compute left side: 25.0 + (−24.0) = 1.0
Compute right side first term: 5.0(−2.0) = −10.0
So: 1.0 = −10.0 + 12 vB,f
Add 10.0 to both sides: 11.0 = 12 vB,f
Solve: vB,f = 11.0 / 12 = 0.916666... m s−1 ≈ 0.92 m s−1 (positive, i.e. east).

4) Why the correct answer is correct
The computed vB,f is about 0.9167 m s−1 directed east, which matches the choice rounded to 0.9 m s−1 east. This result follows directly from exact conservation of momentum using the given masses and velocities.

5) Why the other options are incorrect
- 2.0 m s−1 west: far from the computed +0.917 m s−1 (wrong sign and magnitude).
- 0.5 m s−1 west: wrong sign (should be east) and magnitude (0.917 ≠ 0.5).
- zero: would imply total momentum after collision is zero, but initial total momentum was +1.0 kg·m s−1, so B cannot be zero while A is −2.0 m s−1.

6) Conclusion
The final velocity of B is 0.9 m s−1 east (rounded), which confirms the provided correct answer.

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单项选择题

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?

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