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?

(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 sam

See previous post: Mon, 11-23-15, 1:20 PM.

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

1. Momentum: Momentum is conserved before and after the collision. The total momentum of the system before the collision is equal to the total momentum after the collision. Mathematically, it can be expressed as:

(mass of cart A * velocity of cart A) + (mass of cart B * velocity of cart B) = (total mass of the system * final velocity of the system)

2. Kinetic energy: In this case, kinetic energy is not conserved as there is an external force acting upon the system during the collision (the velcro), which does work and converts some of the kinetic energy into other forms, such as potential energy in the compressed velcro.

(b) To determine the final velocity of the system after the collision, we can use the conservation of momentum equation mentioned above. Since the carts stick together, their final velocity will be the same. Mathematically, it can be expressed as:

(mass of cart A * velocity of cart A) + (mass of cart B * velocity of cart B) = (total mass of the system * final velocity of the system)

(0.500 kg * 40.0 cm/s) + (0.750 kg * 0 cm/s) = (0.500 kg + 0.750 kg) * final velocity of the system

20 + 0 = 1.250 kg * final velocity of the system

final velocity of the system = 20 / 1.250 kg
final velocity of the system = 16 cm/s

Therefore, after the collision, the carts will be moving together at a velocity of 16 cm/s.

(c) As mentioned earlier, the kinetic energy is not conserved in this case due to the work done by the external force (velcro) during the collision. Therefore, there will be a decrease in the kinetic energy of the system compared to the initial kinetic energy before the collision.

The deformation in this case is due to the compression of the velcro. The velcro acts as a spring-like object, storing some of the initial kinetic energy as potential energy in the compressed velcro. This deformation can be characterized as elastic deformation.

(d) If the carts are equipped with magnets so that they repel each other, the collision will be different. Since the carts don't touch each other during the collision, there will be no deformation of either cart. Instead, they will experience a repulsive force due to the magnets.

In this case, the conservation laws will still apply, but the collision will be more like an "ideal" collision. The conserved quantities will be:

1. Momentum: Momentum will still be conserved, and the total momentum before the collision will be equal to the total momentum after the collision.

2. Kinetic energy: Since there is no external force doing work on the system, and the collision is elastic (assuming no other energy losses), the kinetic energy will be conserved. The total kinetic energy before the collision will be equal to the total kinetic energy after the collision.

To determine the final velocities in this case, the specific details of the collision, such as the distance between the carts and the strength of the repulsive force, would need to be considered.