A mass of 9.8 kg is moving in the positive x direction at 16.6 m/s and collides in a perfectly elastic, head on collision with a mass of 12.7 kg at rest. The same mass of 9.8 kg in the positive direction at 16.6 m/s also collides with the mass of 12.7 kg at rest in an inelastic collision. If both collisions occur over a time of 0.13 seconds, what is the difference between the magnitdue of the average force on the 9.8 kg mass in the elastic collision, and magnitude of the the average force on the 9.8 kg mass in the inelastic collision? That is, how much greater is magnitude of the the average force in the elastic collsion compared to the inelastic collision? Answer in Newtons.
To solve this problem, we need to calculate the magnitudes of the average force exerted on the 9.8 kg mass in both elastic and inelastic collisions.
Let's start with the elastic collision:
In an elastic collision, both momentum and kinetic energy are conserved.
The momentum before the collision is given by:
Momentum = mass * velocity
For the mass of 9.8 kg moving in the positive x-direction at 16.6 m/s:
Initial momentum = 9.8 kg * 16.6 m/s
Since the second mass is at rest (initial velocity = 0), its initial momentum is zero.
During the collision, momentum is conserved, so the total momentum after the collision is equal to the initial momentum.
Now let's consider the inelastic collision:
In an inelastic collision, momentum is conserved, but kinetic energy is not conserved.
Again, the initial momentum is the same as in the elastic collision.
To find the magnitude of the average force, we need to calculate the change in momentum and divide it by the time of the collision.
In both cases (elastic and inelastic collisions), the momentum change is equal to the initial momentum because momentum is conserved.
Now we have all the necessary information to find the magnitudes of the average force:
For the elastic collision:
Average force = (Final momentum - Initial momentum) / time
The final momentum is the same as the initial momentum because momentum is conserved.
For the inelastic collision:
Average force = (Final momentum - Initial momentum) / time
Again, the final momentum is the same as the initial momentum because momentum is conserved.
To calculate the difference in average forces between the two cases, simply subtract the magnitude of the average force in the inelastic collision from the magnitude of the average force in the elastic collision.
Finally, convert the answer to Newtons to represent the units of force.
I hope this explanation helps you to solve the problem!