Question

A car carrying a suspicious amount of nitroglycerin in its trunk is rear-ended by another car. When they collide, the nitroglycerin in the first car explodes.

You are provided with dynamics carts (including one dynamics cart with a spring launcher that can be cocked to fire), masses, and Vernier motion sensors.

a) How would you model each object in this scenario with dynamics carts? What about the interaction between the objects?

b) Will momentum be conserved during the collision?

c) Will kinetic energy be conserved during the collision?

d) Classify the collision as inelastic or elastic. Is it totally inelastic or perfectly elastic? Explain why.

e) Limitations of your model.

Answer 1

a) the dynamics cart with the spring will be in the front, with a mass m1. the other cart with mass m2 will approach from the rear. the masses and velocities of the carts will be scaled as follows:

1. velocity will be scaled down in ratio with the sizes of the cars. i.e. if cars are 5m long and the carts are 5cm, then the velocity will be scaled down by a factor of 100.

2. the masses will be scaled down so that the ration of initial momentum remains constant.

the spring will be cocked to the extent so that the force exterted when uncocking is proportional to the force due to the explosion.

b) No, as the explosion results in an additional force on both the cars at the time of impact, momentum will not be conserved.

c) No, The kinetic energy is not conserved. this is because the explosion adds energy to the system.

d) Collisions are classified elastic or inelastic depending on whether the kinetic energy is conserved or not in the collision. In the current case, kinetic energy is not conserved, this is because the chemical energy in nitroglycerin and the potential energy in the spring is being released. thus we should classify this collision as inelastic. In a perfectly inelastic collision, the maximum amount of kinetic energy is lost. As the explosion will add some kinetic energy to make up the loss, we cannot confirm if the collision is perfectly inelastic without knowing the relative magnitudes of the different energies before and after the collision.