A big toy school bus rear-ends a small toy school bus initially at rest. The bigger bus is several times heavier than the smaller one. Which of the following statements are true if the collision is totally inelastic?

1. The big bus exerts the same amount of force on the small bus as vice versa.

2. The two buses continue together at the same speed.

3. Mechanical energy is conserved.

4. Momentum is conserved.

5. The big bus will go backwards.

I put:

1. True
2. False
3. False
4. True
5. False

...but apparently one or more of the answers is incorrect. Please help?

To determine the correct answers, let's first understand what happens in a totally inelastic collision.

In a totally inelastic collision, the two objects stick together and move as one mass after the collision. This means they have the same final velocity. During the collision, kinetic energy is not conserved, and some energy is transformed into other forms, such as heat or deformation.

Now let's analyze each statement individually:

1. The big bus exerts the same amount of force on the small bus as vice versa.
True. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. So, the force exerted by the big bus on the small bus is equal to the force exerted by the small bus on the big bus.

2. The two buses continue together at the same speed.
True. In a totally inelastic collision, the two objects stick together and move as one mass after the collision. Thus, they continue moving at the same speed.

3. Mechanical energy is conserved.
False. In a totally inelastic collision, some of the initial mechanical energy is lost as it transforms into other forms, such as heat or deformation. Therefore, mechanical energy is not conserved.

4. Momentum is conserved.
True. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, as long as no external forces act. Since no external forces are mentioned, momentum would be conserved in this case.

5. The big bus will go backwards.
False. In a totally inelastic collision, the two objects stick together and move as one mass after the collision. Since the smaller bus was initially at rest, the bigger bus would carry the smaller bus forward after the collision, not backward.

Based on this analysis, the incorrect answer is statement 3, which claims that mechanical energy is conserved.

Your answers are mostly correct, but there is one statement that needs to be corrected. Let's go through each statement to determine the correct answer.

1. The big bus exerts the same amount of force on the small bus as vice versa.
- True. According to Newton's third law of motion, the forces between the two buses are equal and opposite in direction.

2. The two buses continue together at the same speed.
- False. In a totally inelastic collision, the two objects stick together and move as one object after the collision. Their final speed will depend on their masses.

3. Mechanical energy is conserved.
- False. In a totally inelastic collision, some kinetic energy of the system is lost due to deformation or other forms of energy dissipation.

4. Momentum is conserved.
- True. In any collision, momentum is always conserved. Before the collision, the total momentum of the two buses is zero since the smaller bus is initially at rest. After the collision, their combined momentum will also be zero.

5. The big bus will go backward.
- False. In a rear-end collision, the bigger bus, being several times heavier than the smaller one, will experience a smaller change in velocity compared to the smaller bus. Therefore, the bigger bus will continue moving forward but at a slower speed or come to a stop.

So, the correct answers are:

1. True
2. False
3. False
4. True
5. False