A man (weighing 915 N) stands on a long railroad flatcar (weighing 2720 N) as it rolls at 18.5 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 55.00 m/s relative to the flatcar. What is the resulting increase in the speed of the flatcar?
This is a conservation of momentum problem, but I think you have made an error in the runner's speed. No one can run 55 m/s. The world's fastest human, Olympic champion Usain bolt, runs 11 m/s at most.
The problem has 55m/s... the instructor changed numbers in the original problem and I guess he wanted to change that number to 55. I thought it was strange too at first. So for conservation of momentum, would i use mhvh=mcvc where h is for human and c is for car?
To find the resulting increase in the speed of the flatcar, we need to use the principle of conservation of momentum.
Momentum is defined as the product of mass and velocity. In this case, we are dealing with a system of two objects: the man and the flatcar. The total momentum of the system before and after the man starts running will remain constant if there are no external forces acting on the system.
Let's break down the problem step by step:
1. Determine the initial momentum of the system before the man starts running.
The momentum of an object is given by the equation: momentum = mass × velocity.
The initial momentum of the flatcar can be calculated as follows:
Momentum of the flatcar = mass of the flatcar × velocity of the flatcar
Given that the mass of the flatcar is 2720 N and its velocity is 18.5 m/s, we get:
Momentum of the flatcar = 2720 kg × 18.5 m/s
2. Calculate the initial momentum of the man.
Similar to the flatcar, the momentum of the man can be calculated as:
Momentum of the man = mass of the man × velocity of the man
Given that the mass of the man is 915 N and his velocity is initially 0 m/s (since he is standing still), we have:
Momentum of the man = 915 kg × 0 m/s
3. Calculate the final momentum of the system after the man starts running.
The final momentum of the system is the sum of the momentum of the flatcar and the man.
Momentum of the system = Momentum of the flatcar + Momentum of the man
Since momentum is a vector quantity and the man is running in the opposite direction to the motion of the flatcar (negative x direction), we need to consider the negative sign for the man's momentum. This means that the final momentum of the system will be the momentum of the flatcar minus the momentum of the man.
Momentum of the system = Momentum of the flatcar - Momentum of the man
4. Calculate the resulting increase in the speed of the flatcar.
The resulting increase in the speed of the flatcar can be obtained by dividing the total momentum of the system by the mass of the flatcar.
Resulting increase in speed = (Momentum of the system) / (mass of the flatcar)
By substituting the respective values, we should be able to solve for the resulting increase in the speed of the flatcar.