Predict Whether Collision will be Elastic or Inelastic

[dimensionless]

Homework Statement

A mass sits on the end of a spring and is at equilibrium.

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|/\/\/\/\/|_m_|________________()' o_____o '_________________

A car is costing gracefully towards the mass. The car has a semi-rigid rubber tire mounted on its front. The mass of the mass and mass of the car are approximately equal mass. When the car collides with the mass will the collision be elastic or inelastic?

Homework Equations

There are basic equations for collision problems. In elastic collisions

m1*v1_i + m2*v2_i = m1*v1_final + m2*v2_final

In inelastic collisions

m1*v1_i + m2*v2_i = (m1+m2)*v_f

In both types of problems kinetic energy in conserved and

m1*v1_i^2 + m2*v2_i^2 = m1*v1_final^2 + m2*v2_final^2

The Attempt at a Solution

The problem is to determine what type of collision is at hand. As far as attempting a solution, I can't really go any farther than this.

 

[chaoseverlasting]

The collision can't be elastic as due to the spring force, linear momentum along the x-axis is not conserved and that's a condition for elastic collisions.

 

[m2003]

Based on the given information, it is difficult to definitively predict whether the collision will be elastic or inelastic. Both types of collisions can occur in this situation, depending on various factors such as the speed and angle of approach, the stiffness of the spring, and the materials involved.

In an elastic collision, the objects would bounce off each other with no loss of kinetic energy. This would require the spring to be very stiff and the car to approach the mass at a low speed.

In an inelastic collision, the objects would stick together and some kinetic energy would be lost, potentially due to the deformation of the spring or the rubber tire. This would be more likely if the car is approaching the mass at a higher speed and the spring and tire are less rigid.

Therefore, to make a more accurate prediction, additional information about the specific circumstances of the collision would be needed.