# Conservation of Linear Momentum (man on a moving railcar)

• Vertiviper
In summary, when the man runs along the flatcar in the negative x direction, the flatcar's velocity increases by 14.4 m/s.
Vertiviper

## Homework Statement

A man (weighing 915 N) stands on a long railroad flatcar (weighing 2005 N) as it rolls at 17.0 m/s in the positive direction of an x axis, with negligible friction. Then the man runs along the flatcar in the negative x direction at 46.00 m/s relative to the flatcar. What is the resulting increase in the speed of the flatcar?

Pi=Pf

## The Attempt at a Solution

Pi=m1v1+m2v2
Pi= 5065.49

Pf=m1(-46.0m/s+ 17m/s) + m2 (Vi+17m/s)
V=18.26 -incorrect

The answer is supposed to be 14.4 m/s.

-46.00 m/s relative to the flatcar final speed, so check Pf=m1(-46.0m/s+ 17m/s) + m2 (Vi+17m/s).

Last edited:
Vertiviper said:

## Homework Statement

A man (weighing 915 N) stands on a long railroad flatcar (weighing 2005 N) as it rolls at 17.0 m/s in the positive direction of an x axis, with negligible friction. Then the man runs along the flatcar in the negative x direction at 46.00 m/s relative to the flatcar. What is the resulting increase in the speed of the flatcar?

Pi=Pf

## The Attempt at a Solution

Pi=m1v1+m2v2
Pi= 5065.49
This is incorrect. Initially, the man was standing on the rail car so both had the same velocity, 17 m/s. The total momentum was (915)(17)+ (2005)(17)= 49640 Nm/s.

Pf=m1(-46.0m/s+ 17m/s) + m2 (Vi+17m/s)
V=18.26 -incorrect

Consider the man and the flat car as your system. No external force acts on it in the horizontal direction, conserving the momentum.
Let M and m represent the mass of flatcar and man resp. Let 'v' be the final velocity of flatcar w.r.t GROUND.
Initial momentum = (M+m) x 17
Final momentum= Mv + m(v-46) [Taking the direction of 'v' along positive x-axis]

Solving this you will get v=31.4m/s
You can find increase in velocity from this.

## 1. What is the principle of conservation of linear momentum?

The principle of conservation of linear momentum states that the total momentum of a closed system remains constant, unless acted upon by an external force. This means that in a system where there are no external forces, the total momentum before an event is equal to the total momentum after the event.

## 2. How does this principle apply to a man standing on a moving railcar?

In the case of a man standing on a moving railcar, the man and the railcar form a closed system. This means that the total momentum of the man and the railcar before and after any event (such as the man jumping) must remain constant. This can be observed through the man's movement relative to the railcar and the ground.

## 3. What happens to the man's momentum when he jumps off the moving railcar?

When the man jumps off the moving railcar, his momentum changes. This is because he is now exerting a force on the railcar in the opposite direction of its motion, causing it to slow down. However, according to the principle of conservation of linear momentum, the man's change in momentum is equal and opposite to the change in momentum of the railcar, resulting in a constant total momentum for the system.

## 4. Does the mass of the man or the railcar affect the conservation of linear momentum?

According to the principle of conservation of linear momentum, the mass of an object does not affect the conservation of momentum. This means that even if the man and the railcar have different masses, their total momentum will still remain constant as long as there are no external forces acting on the system.

## 5. How is the principle of conservation of linear momentum used in real-life situations?

The principle of conservation of linear momentum has many real-life applications, such as in sports, transportation, and even space travel. For example, in a game of billiards, the total momentum of the balls before and after a collision remains constant. In transportation, the momentum of a moving vehicle must be conserved to ensure safe and efficient movement. In space travel, rockets use the principle of conservation of momentum to propel themselves forward by expelling gas in the opposite direction.

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