Train car A is at rest when it is hit by train car B. The two cars, which have the same mass, are stuck together and move off after the collision. How does the final velocity of train cars A and B after the collision compare to the initial velocity of train car B before the collision?
The final velocity is double train car B’s initial velocity.
The final velocity is the same as train car B’s initial velocity.
The final velocity is half of train car B’s initial velocity.
The final velocity is zero since train car B will stop.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after a collision.
Momentum (p) is calculated by multiplying an object's mass (m) by its velocity (v): p = m * v.
In this case, since train car A is at rest, its initial momentum is zero (p_initial_A = 0). Train car B has an initial velocity (v_initial_B).
After the collision, the two cars stick together and move off as one unit. Let's denote the final velocity of the combined cars as v_final_AB.
To find the final velocity, we can use the equation for conservation of momentum:
Total initial momentum = Total final momentum
(m_B * v_initial_B) + (m_A * 0) = (m_A + m_B) * v_final_AB
Since mass of train car A and train car B are the same (m_A = m_B), we can simplify the equation:
m_B * v_initial_B = 2m_B * v_final_AB
Dividing both sides of the equation by m_B, we get:
v_initial_B = 2 * v_final_AB
Therefore, the final velocity of train cars A and B after the collision is half of train car B's initial velocity. So, the correct answer is: The final velocity is half of train car B's initial velocity.
The final velocity is the same as train car B’s initial velocity.
The final velocity is the same as train car B’s initial velocity.
WRONG ITS The final velocity is half of train car B’s initial velocity.
Apologies for the mistake. Indeed, the correct answer is that the final velocity is half of train car B's initial velocity. Thank you for pointing that out.
An astronaut on a space walk floats a little too far away from the space station. Without air to push against, he cannot paddle back. However, the astronaut is holding a hammer. Explain how the astronaut could use the hammer to move and why this will get him back to the space station.
The astronaut can use the principle of conservation of momentum to move and get back to the space station.
If the astronaut throws the hammer away from the space station with some force, according to Newton's third law of motion, an equal and opposite force will act on the astronaut. As a result, the astronaut will start moving in the opposite direction, towards the space station.
This phenomenon is based on the principle of conservation of momentum. Initially, the momentum of the astronaut and the hammer is zero because they are both at rest. When the astronaut throws the hammer, the hammer gains momentum in one direction. To ensure the total momentum remains zero, the astronaut gains an equal and opposite momentum in the opposite direction.
Once the astronaut starts moving back towards the space station, they can simply catch the hammer or retrieve it somehow to stop themselves from moving away further. By repeating this process of throwing the hammer and retrieving it, the astronaut can continue to change their momentum and move closer to the space station until they reach it.
It is important to note that in space, there is no significant air resistance or friction to slow down the motion, so the astronaut's movements can continue using this method until they reach the desired destination.
The astronaut can throw the hammer in a direction away from the space station. While he is holding the hammer, the total momentum of the astronaut and hammer is 0 kg • m/s. According to the law of conservation of momentum, the total momentum after he throws the hammer must still be 0 kg • m/s. In order for momentum to be conserved, the astronaut will have to move in the opposite direction of the hammer, which will be toward the space station.
What did you include in your response? Check all that apply.
The astronaut should throw the hammer away from the space station.
The total momentum before and after the astronaut throws the hammer is 0 kg • m/s.
To satisfy the law of conservation of momentum, the astronaut will move in the opposite direction of the hammer.
Based on the response given above, the following statements were included:
- The astronaut should throw the hammer away from the space station.
- The total momentum before and after the astronaut throws the hammer is 0 kg • m/s.
- To satisfy the law of conservation of momentum, the astronaut will move in the opposite direction of the hammer.