How to Determine Lost Energy and Analyze Inelastic Collisions Using Hooke's Law?

[mikemult]

Homework Statement

Homework Equations

I am unsure how to find the value for b) and c). If anyone could tell me how to find these values it would be appreciated.

The Attempt at a Solution

To find a) I simply found the slope of the positively slopped line and used Hooke's law equation (E_e =0.5kx² ). There does not seem to be any permanent deformation in the spring so is there energy lost? My guess is it would be lost to other causes but that still doesn't help me answer b). I am unable to calculate the lost energy to prove that the collision is inelastic (my guess).

 

[BigJDubs]

The total energy of the system, according to Hooke's law, is 0.5kx2. Part a) is asking for the change in energy of the spring when the distance the spring is stretched is x/2. So the answer to part a) is 0.5k(x/2)2. For b) I am not sure how to calculate the lost energy. Is this just the difference between the total energy (0.5kx2) and the energy after the distance is halved (0.5k(x/2)2)? For c) I am not sure how to calculate the speed of the block when it is released.

 

[thomate1]

To find the values for b) and c), you will need to use the equations for energy conservation and elastic potential energy. In this case, the lost energy can be calculated by finding the difference between the initial and final elastic potential energies. This will help determine if the collision is inelastic. Additionally, you can also use the equation for kinetic energy to find the final velocity of the object after the collision. This will give you a better understanding of the overall energy transfer during the collision. It is important to consider all forms of energy (elastic potential, kinetic, and any other forms) in order to accurately analyze the situation. Additionally, it may be helpful to plot the data points on a graph and use the area under the curve to calculate the energy. I would also suggest reviewing the units used in the calculations to ensure they are consistent. I hope this helps.