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### 601-I: Collision Energy

• Topic Cluster: Momentum
• Topic: Collisions and Explosions
• Objective: Given a collision or explosion, analyze the collision quantitatively, determine if kinetic energy is lost, gained, or conserved; analyze the source of work done on a system.
• Content: While momentum is always conserved in a collision or explosion, energy can be gained or lost depending upon the individual situation.
• Level: 3

#### BACK to Ladder Collisions and Explosions

In all of the previous sections of this unit, we have analyzed only three quantities: mass, velocity, and momentum. But only other quantity is crucial in understanding momentum: kinetic energy.

The total amount of energy added to the system is the WORK DONE on the system.

• If kinetic energy is lost, it is an inelastic collision. (negative work done on the system)
• If kinetic energy is conserved, it is an elastic collision. (zero work done on the system)
• If kinetic energy is gained, it is an explosion (positive work done on the system).
• Before the collision...
• Car A has a mass of 300 kg and is moving RIGHT with a speed of 12 m/s.
• Car B has a mass of 100 kg and is moving LEFT with a speed of 6 m/s.
• After the collision...
• Car A is stationary.
• Car B is moving at an unknown velocity.
1. Write an equation based on the conservation of momentum that relates all the variables in this problem. Write the equation in full before plugging any numbers into it.
2. Determine the speed (magnitude only) of car B after the collision.
3. Determine the total amount of kinetic energy in the two car system before the collision.
4. Determine the total amount of kinetic energy in the two car system after the collision.
5. Determine the amount of work done on the two car system during the collision.
6. What type of collision is this?
1. A cannon with mass of 400 kg fires a cannonball with a mass of 2 kg at a speed of 50 m/s. The cannon was not moving before it fired.
1. Determine the recoil speed of the cannon.
2. How much kinetic energy did the cannon-cannonball system have before it was fired?
3. How much kinetic energy did the cannon-cannonball system have after it was fired?
4. What is the change in kinetic energy $$\Delta KE$$ for the system?
5. According to the Law of Conservation of Energy, any new energy added to the system must come from some other source. What is the source of the energy added to this system?
2. A toy car with a mass of 10 kg is moving 5 m/s left when it runs into toy truck with a mass of 40 kg that was moving 2 m/s to the right. A little kid covered the toy truck in flex tape, so the two toy cars stick together following the collision.
1. What is the speed of the two cars after the collision?
2. What is the change in kinetic energy of the system before and after the collision?
3. According to the Law of Conservation of Energy, if energy was lost from the system, it needed to become some other form of energy outside the system. Where did the energy lost from this system go?
4. What is it called when two objects stick together after a collision, and why?
5. Look at the kinetic energy formula. Based on the mathematics of this formula, why is so much energy lost when two objects stick together following a collision?
3. A blue golf ball with a mass of 200 grams and a speed of 2 m/s rolls into a stationary red golf ball with the same mass. After the collision, the blue golf ball is stationary and the red golf ball begins moving.
1. Determine the speed of the red golf ball following the collision.
2. Determine the change in kinetic energy of the system of two golf balls during the collision.
3. What type of collision is this?