A man (weighing 915 N) stands on a long railroad flatcar (weighing 2805 N) as it rolls at 18.0 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 40.00 m/s relative to the flatcar. What is the resulting increase in the speed of the flatcar?
Use conservation of momentum. I will be happy to critique your thinking.
Ok, so I use mv = m1v1 + m2v2??? And I would get m1 and m2 by dividing the weights by 9.8 m/s^2? Please explain.
Yes, you're on the right track! To solve this problem, you can indeed use the principle of conservation of momentum, which states that the total momentum before an interaction is equal to the total momentum after the interaction, assuming that no external forces are acting.
In this case, the momentum of the system is given by the sum of the momentum of the man and the momentum of the flatcar. The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v), so you can use the equation:
p = m1v1 + m2v2
Where m1 and m2 are the masses of the man and the flatcar, and v1 and v2 are their respective velocities.
To find the masses (m1 and m2), you correctly divide their weights by the acceleration due to gravity (9.8 m/s^2):
m1 = weight1 / 9.8
m2 = weight2 / 9.8
Therefore, plugging in the given values:
m1 = 915 N / 9.8 m/s^2 = 93.37 kg
m2 = 2805 N / 9.8 m/s^2 = 286.22 kg
Now that you have the masses, you can substitute them into the conservation of momentum equation:
mv = m1v1 + m2v2
Initially, the man is stationary relative to the flatcar, so the momentum is zero:
0 = (93.37 kg)(0 m/s) + (286.22 kg)(18.0 m/s)
The man then runs in the negative x direction at 40.0 m/s relative to the flatcar, so the final momentum can be calculated as:
pf = (93.37 kg)(-40.0 m/s) + (286.22 kg)(18.0 m/s)
You can now calculate the resulting increase in the speed of the flatcar by subtracting the initial momentum from the final momentum:
Change in momentum = pf - pi
Where pi is the initial momentum (which is zero in this case). The resulting increase in the speed of the flatcar can then be determined by dividing the change in momentum by the mass of the flatcar and solving for velocity:
Change in velocity = (Change in momentum) / (mass of the flatcar)
Plug in the calculated values and solve to obtain the answer.