The figure shows two train cars that move toward each other, collide, and couple together.

How much thermal energy is created in this collision?

Figure caption: Before and after diagrams show forces involved in a collision between two train cars.

Question

The figure shows two train cars that move toward each other, collide, and couple together.

How much thermal energy is created in this collision?

Figure caption: Before and after diagrams show forces involved in a collision between two train cars.

BlackTom AI · Accepted Answer

Energy converted to thermal energy equals the loss of mechanical kinetic energy: ΔEth = Kinitial − Kfinal (because momentum is conserved but the collision is inelastic).

Relevant knowledge points:
- Conservation of momentum determines the final velocity of the coupled cars (here the problem gives the final speed).
- Kinetic energy is 1/2 m v^2 and is scalar (use squared speeds).
- Thermal energy produced = total initial kinetic energy − total final kinetic energy.

Step-by-step calculation:
1) Write given quantities:
- m1 = 2.0×10^4 kg, v1i = +1.5 m/s
- m2 = 4.0×10^4 kg, v2i = −1.1 m/s
- Combined mass m = m1 + m2 = 6.0×10^4 kg
- Given final speed vf = −0.25 m/s (direction irrelevant for kinetic energy)

2) Compute initial kinetic energies:
- K1 = 1/2 m1 v1i^2 = 0.5 × (2.0×10^4 kg) × (1.5 m/s)^2
  = 1.0×10^4 × 2.25 = 22,500 J
- K2 = 1/2 m2 v2i^2 = 0.5 × (4.0×10^4 kg) × (1.1 m/s)^2
  = 2.0×10^4 × 1.21 = 24,200 J
- Total initial K = K1 + K2 = 22,500 J + 24,200 J = 46,700 J

3) Compute final kinetic energy of the coupled cars:
- Kfinal = 1/2 (m1 + m2) vf^2 = 0.5 × (6.0×10^4 kg) × (0.25 m/s)^2
  = 3.0×10^4 × 0.0625 = 1,875 J

4) Thermal energy generated:
- ΔEth = Kinitial − Kfinal = 46,700 J − 1,875 J = 44,825 J

Why the correct answer is correct:
This collision is inelastic (cars couple), so kinetic energy is not conserved; the lost kinetic energy appears as thermal (and deformation) energy. Subtracting final from initial kinetic energy gives 44,825 J released as thermal energy.

Why other options are incorrect:
- 1,875 J is the final kinetic energy, not the lost (thermal) energy.
- 46,700 J is the total initial kinetic energy, not the energy converted.
- 24,200 J and 22,500 J are the individual initial kinetic energies of one car each, not the thermal energy.

Final confirmation: the thermal energy created is 44,825 J, matching the provided correct answer.

The figure shows two train cars that move toward each other, collide, and couple together. How much thermal energy is created in this collision? Figure caption: Before and after diagrams show forces involved in a collision between two train cars.单项选择题

类似问题

A 1-kg box is sliding horizontally along a frictionless surface with a speed of 3 m/s. It collides with and sticks to a 2-kg box that is initially at rest. What is the speed of the boxes after the collision?

A truck of mass 2500 kg and a car of mass 1000 kg collide at an intersection as shown on the diagram below. What is the possible path of the vehicles if they lock together at impact?

An impact resulting in the total loss of velocity would be called a perfectly Answer Question 13[input] impact. NOTE: The answer requires a single word and correct spelling. Double check the spelling.

A 5.0-gram bullet is shot vertically into a 1.2-kg block. The bullet penetrates the block and becomes embedded in the block, lifting the block upward by 6.0 cm (see the figure below). Assuming that air resistance is negligible, the initial speed of the bullet is closest to

In Example 11.3, when Bob jumps on the cart, what kind of collision is this?

In Example 11.3, when Bob jumps on the cart, what kind of collision is this?

A 150 gm bullet travelling at a speed of 500 m/s hits a block weighing 10 kg and gets embedded in it. The block was initially resting on a frictionless surface and starts moving due to this event. Determine the energy lost in the impact as a percentage of the bullet’s original kinetic energy.

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