3. A low friction cart (similar to what you use in the lab) collides with a second low friction cart.

Cart A has a mass of 0.500 kg and cart B has a mass of 0.750 kg. Glider A was moving at 40.0
cm/s before the collision. Glider B was at rest.
(a) The carts have velcro on them so that they stick together during the collision. What quantities
are conserved in this collision?
(b) How fast are they moving after the collision?
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PHYS 1101 Assignment #9 Due: Thurs., Nov. 19
(c) Compare the kinetic energy of the two-cart system before the collision with the kinetic energy
after the collision. Was there any “deformation” of the carts? If so, what was the nature of
this deformation?
(d) Now suppose the carts are (like the ones in the lab) equipped with magnets so that they
repel each other. Now the carts don’t even touch each other during the “collision” and so
no deformation of either cart can take place. Suppose the collision is otherwise the same as
before (same initial velocities). Find the velocities of the carts after the collision now.

3a. Momentum conserved.

b. Ma*Va + Mb*Vb = Ma*V + Mb*V.
0.50*0.40 + 0.750*0 = 0.50V + 0.75*V.
V = ?

c. Before: KE = 0.5Ma*Va^2.
After: KE = 0.5(Ma+Mb)*V^2.
KE will be less after the collision.

To answer these questions, we can use the principles of conservation of momentum and kinetic energy.

(a) In this collision, the quantities conserved are:

1. Momentum: The total momentum of the system before the collision is equal to the total momentum after the collision, provided no external forces act on the system.

2. Kinetic Energy: The total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision if no external work is done on the system.

(b) To find the velocity of the carts after the collision, we can use the principle of conservation of momentum.

Before the collision, cart A is moving at 40.0 cm/s, and cart B is at rest. So the initial momentum of the system is:

Initial momentum = (mass of cart A * velocity of cart A) + (mass of cart B * velocity of cart B)
= (0.500 kg * 40.0 cm/s) + (0.750 kg * 0 cm/s)
= 20.0 kg·cm/s

After the collision, the carts stick together and move as one unit. Let's assume their final velocity "v".

Final momentum = (mass of the combined carts * final velocity)
= (0.500 kg + 0.750 kg) * v

Since momentum is conserved:
Initial momentum = Final momentum

20.0 kg·cm/s = (1.250 kg) * v

Solving for "v":
v = (20.0 kg·cm/s) / (1.250 kg)
v ≈ 16.0 cm/s

So they are moving at approximately 16.0 cm/s after the collision.

(c) To compare the kinetic energy of the two-cart system before and after the collision, we calculate them separately.

Before the collision, the kinetic energy is given by:

Initial kinetic energy = (1/2) * (mass of cart A * (velocity of cart A)^2) + (1/2) * (mass of cart B * (velocity of cart B)^2)
= (1/2) * (0.500 kg * (40.0 cm/s)^2) + 0
= 400.0 J

After the collision, since the carts stick together, their combined mass is (0.500 kg + 0.750 kg) = 1.250 kg.

Final kinetic energy = (1/2) * (mass of the combined carts * (final velocity)^2)
= (1/2) * (1.250 kg * (16.0 cm/s)^2)
= 320.0 J

Therefore, there is a decrease in kinetic energy. The "deformation" of the carts refers to the loss of kinetic energy, indicating that some energy was transferred elsewhere, likely as heat or sound, due to an inelastic collision.

(d) In this scenario, since the carts don't touch each other, there is no deformation or transfer of kinetic energy through the collision. Instead, we can use the principle of conservation of momentum to find the velocities of the carts after the collision.

Using the same initial momentum calculation as before:

Initial momentum = (mass of cart A * velocity of cart A) + (mass of cart B * velocity of cart B)
= (0.500 kg * 40.0 cm/s) + (0.750 kg * 0 cm/s)
= 20.0 kg·cm/s

After the collision, the carts repel each other, and their final velocities will depend on the strength of the repulsive force between the magnets and the initial velocities.

As the problem states, the initial velocities are the same as in the previous scenario. However, since the carts don't touch, their final velocities will have opposite signs.

Let's assume their final velocities are "v_A" for cart A and "v_B" for cart B:

Final momentum = (mass of cart A * final velocity of cart A) + (mass of cart B * final velocity of cart B)
= (0.500 kg * v_A) + (0.750 kg * v_B)

Since momentum is conserved:
Initial momentum = Final momentum

20.0 kg·cm/s = (0.500 kg * v_A) + (0.750 kg * v_B)

We don't have enough information to find the exact values of v_A and v_B without more details about the strength of the repulsive force.