b) What our setup looked like:
We used two of these tracks side by side during our experiment. The cart had a spring attached to the back of it.
c) What we were given:
Cart A had a spring constant that was 84 N/m.
Cart B had a spring constant that was 112 N/m.
Both carts had equal masses of .552 Kg
How we solved how far to compress the springs:
The elastic energy in the spring is equal to the kinetic energy when the cart is moving. (assuming no friction)
Eel = Ek
Because of this, we can say that both carts originally hold the same amount of elastic energy.
To find the elastic energy of cart A, we decided to compress the spring .06m.
Eel = (1/2)(k)(x^2)
Eel = 1/2(84)(.06^2)
Eel = .1512
Since we know that the elastic energy of cart A will equal that of cart B, we can use the elastic energy formula to determine how far we should compress the spring.
Eel = (1/2)(k)(x^2)
.1512 = (1/2)(112)(x^2)
x = .051m
In order for the carts to have the same amount of kinetic energy, which would give them the same velocity, we would need to compress cart A's spring .06m and cart B's .051m.
To test this hypothesis, we set both carts on tracks next to each other with our predicted compressions. We released both carts at the same time and used a motion sensor to determine the velocities. The velocity of both carts was .78m/s, giving us a 0% error.
