Question

Suppose the two cars had rubber bumpers in the front and back – similar to the bumper cars children (of all ages!) ride at amusement parks. Also, suppose that the cars are sturdy enough that the metal they are made of does not bend during the collision. In this case, the cars would undergo a perfectly elastic collision. Assume just like in the first collision question that the SUV (initially moving to the right) collides into the stationary smart car.

After the collision, the smart car will obviously move to the right. What about the SUV? (Hint: What do you think would happen if the SUV was much larger than the smart car, e.g., has a mass that is 50 times larger?)

The SUV will move to the right.

After the collision, which car do you think moves faster? Why?

The smart car because it has less mass.

Since this is a collision, momentum is conserved. Write down the momentum conservation equation for this situation. Mass of smart car = 1000 kg, mass of SUV = 4000 kg, initial speed of SUV = 15 m/s.

4v1 + v2 = 60

Is this equation sufficient to find the speeds of the two cars after the collision? Why or why not?

No because it includes two variables and we still need to find the speed after the collision.

What other quantity is conserved during a perfectly elastic collision? Write down the equation for that conservation.

1/2m1u1²+1/2m2u2² = 1/2m1v1²+1/2m2v2²

If you have not done so already, simplify the two equations (e.g., by dividing by 1000) and rewrite them here. If you have simplified them, just rewrite them here.

4v1+v2 = 60

4v1²+v2² = 900

A. Using these two equations it is possible to solve for both final speeds. However, the algebra is somewhat challenging because one of the equations has the final speeds of the two cars both squared. The book provides the general solutions to these equations in which you can plug in the initial speeds and the masses of the cars and obtain the final speeds. That won’t be necessary here. Instead, suppose someone measures the final speed of the SUV to be 9.0 m/s. What is the final speed of the smart car? You should get the same number if you use either equation, so make sure you use both.

Using the momentum equation                                                       Using the conservation of KE equation

  

B. Suppose that this collision also took 0.1 seconds. What is the magnitude of the net force acting on either car during the collision? How does this force compare to the perfectly inelastic collision? What is the acceleration acting on the smart car? On the SUV?

C. Generally how do elastic collisions compare to perfectly inelastic collisions? Discuss the forces being exerted on the cars, the accelerations and the kinetic energies.

Answer 1