Elastic collision physics homework problem

[eric.c]

Hey guys I am completely stuck and have no idea where to start. Help?

Homework Statement

Car A and Car B collide in an elastic collision. Use the data in the table shown to calculate the maximum compression of the car bumpers. The spring constant of the car bumper is 60 000 N/m. Assume that the cars bumpers are of equal length.



Car A
2 500 kg
75 km/h

Car B
3 200kg
-58km/h

 

[Ush]

1. what are your relevant equations for elastic collisions.

 

[eric.c]

it is

E = 0.5 kx^2

 

[Ush]

it is

E = 0.5 kx^2

that's the equation for energy in a spring.
what are the equations for conservation of momentum: elastic collisions.

 

[rwisz]

Hello, it looks like you have a problem involving elastic collisions between two cars. To start, we need to understand what an elastic collision is. An elastic collision is a collision where the total kinetic energy of the system is conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. In other words, the cars will bounce off each other without any energy being lost.

To solve this problem, we can use the equations for conservation of momentum and conservation of kinetic energy. We know that the total momentum before the collision is equal to the total momentum after the collision. We can also use the fact that the kinetic energy is equal to 1/2 times the mass times the velocity squared. Using these equations, we can solve for the unknown variables, which in this case is the maximum compression of the car bumpers.

First, we need to convert the given velocities from km/h to m/s. This can be done by multiplying the velocities by 1000/3600. So, for Car A, the velocity is 75 km/h * (1000/3600) = 20.83 m/s. For Car B, the velocity is -58 km/h * (1000/3600) = -16.11 m/s. The negative sign for Car B indicates that it is moving in the opposite direction of Car A.

Now, using the conservation of momentum equation, we can set up the following equation: m1v1 + m2v2 = m1v1' + m2v2'. Since the cars are of equal length, we can assume that the maximum compression of the bumpers is equal to the change in velocity of both cars. So, v1' = v2' = Δv. Plugging in the values, we get (2500 kg)(20.83 m/s) + (3200 kg)(-16.11 m/s) = (2500 kg + 3200 kg)Δv. Solving for Δv, we get Δv = 1.49 m/s.

Now, using the conservation of kinetic energy equation, we can set up the following equation: 1/2m1v1^2 + 1/2m2v2^2 = 1/2m1(v1')^2 + 1/2m2(v2')^2. Plugging in the values,