these are the charts for the experiment what formula do I use for question one.

Question

these are the charts for the experiment what formula do I use for question one. And for question two how do I find the final momentum of the cart in the inelastic collisions is there a specific formula to find final momentum. please answer the questions this is due today and explain if you can your help is appreciated thank you.

Physics 1401 Department of Physics What is the total kinetic energy of the system during the inelastic collisions in your experiment? Was the kinetic energy conserved? 2) 3) What is the final momentum of the cart in the inelastic collision for the cart launcher settings of 2, 2.5, 3cm. Prove your results mathematically 4) Explain why energy is not conserved in both inelastic and perfectly inelastic collisions?

Explanation / Answer

First of all few pieces of information are missing in this question like the direction of collision not discussed so here, I am assuming both carts are moving in opposite direction and in question 2 they asked final momentum for 2,2.5,3 setting and here 2.5 setting data is not provided.

Question (1)

As the collision, here we are talking about is perfectly inelastic that means after the collision the final velocity is same for both carts i.e. there will be common final velocity.

As per data (Setting=2),

m1= 0.5302

m2= 0.5293

Avg Initial velocity of cart 1 (V1i)= 0.8933m/s

Avg Initial velocity of the cart (V12)= 0 (that means cart 2 was in rest position)

Now, after the collision

The avg final velocities of cart 1,2 are (V1f, V2f)= 0.1067= V (As I already stated in an inelastic collision there is common final velocity

In an Inelastic collision, there is always a loss of Kinetic energy after the collision.

Initial K.E = 1/2m1*V1i + 1/2 m2*V2i

K.E(Initial)= 1/2*0.5302*(0.89)^2+0 , (avg V2i is 0 so K.E is also 0)

K.E(i)= 0.20

Now, K.E(Final or after collision)= 1/2 (m1+m2)*V

K.E(f)= 1/2*(0.5302+0.5293)*0.427

K.E(f)= 0.09

Loss of K.E is = 0.20-0.09= 0.11

But Total K.E energy of system is = 0.20+0.09= 0.29

And in inelastic collision K.E is not conserved.

Now do the same calculations for setting(3).

Question (2)

Final momentum (Setting 2)

Here we know that for Inelastic Collision the final velocities of the cart after the collision is same (V)

As we know the Momentum = Mass*Velocity

Momentum(final)= (m1+m2)*V

=(0.5302+0.5293)*0.4267

Final Momentum =0.4520

Similarly, for setting (3)

Momentum(Final)= (m1+m2)*V

=0.5302+0.5293)*0.27

Final Momentum = 0.2860

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