Is the Book Right? Examining Conservation of Momentum

In summary, the conversation discusses the proposed solution for a physics problem involving a student stopping a moving carriage and a ticket collector jumping off. The correct momentum balance equation is provided, and the mistake of not using brackets and having the ticket collector on both sides is pointed out and corrected.
  • #1
phantomvommand
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Homework Statement
This is a problem from 200 Puzzling Physics Problems.
A student and ticket collector of mass m are in a stationary railway carriage of mass M. The collector realises the student has no ticket, so the student runs towards the end of the carriage, and the collector chases after him with speed v relative to the carriage. The student stops at the end of the carriage and jumps out. Find the velocity of the carriage when the collector stops at the open end of the carriage and watches the student escape.
Relevant Equations
Conservation of Momentum
My proposed solution:

When the student stops at the end, suppose the carriage is moving at speed u.
0 = (M+2m)u - m(v - u)
==> u = mv/ M+3m

After jumping out, the total momentum of the Carriage + collector system is 0 - mu = -m^2v/ M+3m.

By conservation of momentum for the Carriage + collector system, at the time when the collector stops at the open end:

-m^2v/ M+3m = 0 + (M+m)V, where V is the final velocity of the carriage + collector.

V = -m^2v/ (M+3m)(M+m)

The book (200 Puzzling Phys Problems) writes that the speed of the carriage when the student has reached the end and stopped (but not yet jumped) is u = mv/M+2m.

I suppose this is from the Conserve momentum equation: (M+2m)u = mv. Doesn't this forget the fact that v is a relative velocity?

Is the book right, and why am I wrong?

Thank you!
 
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  • #2
phantomvommand said:
When the student stops at the end, suppose the carriage is moving at speed u.
0 = (M+2m)u - m(v - u)
==> u = mv/ M+3m
1) your lack of using brackets will cause errors -- if not now, then later
2) Your momentum balance should not have the ticket collector on both sides, but: ticket collector on one side and carriage + student on the other.

##\ ##
 
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  • #3
BvU said:
1) your lack of using brackets will cause errors -- if not now, then later
2) Your momentum balance should not have the ticket collector on both sides, but: ticket collector on one side and carriage + student on the other.

##\ ##
I see my mistake now, thank you very much!
 
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Related to Is the Book Right? Examining Conservation of Momentum

1. What is conservation of momentum?

Conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time. This means that the total momentum before a collision or interaction is the same as the total momentum after the collision or interaction.

2. Why is it important to examine conservation of momentum?

Examining conservation of momentum allows us to better understand the behavior of objects in motion and how they interact with each other. It also plays a crucial role in many real-world applications, such as in the design of vehicles and understanding the movement of celestial bodies.

3. How is conservation of momentum related to Newton's laws of motion?

Conservation of momentum is a direct consequence of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In other words, the momentum of an object will change only if it experiences a net external force.

4. What factors can affect conservation of momentum?

Conservation of momentum is affected by the mass and velocity of the objects involved in a collision or interaction. Other factors such as external forces, friction, and air resistance can also play a role in the conservation of momentum.

5. How is conservation of momentum used in real-life situations?

Conservation of momentum is used in a variety of real-life situations, such as in car crashes, sports, and rocket propulsion. It is also crucial in understanding the movement of particles in the microscopic world, as well as in large-scale events like the motion of planets and stars.

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