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### 601-D: Conservation of Momentum 2: Perfectly Inelastic Collisions

• Topic Cluster: Momentum
• Topic: Collisions and Explosions
• Objective: Use the conservation of momentum to analyze crashes in which two objects stick together.
• Content: When two cars crash and stick together, it is called a perfectly inelastic collision; a perfectly inelastic collision can also be analyzed using the principles of conservation of momentum.
• Level: 2

#### BACK to Ladder Collisions and Explosions

In the previous section, you used information given and the conservation of momentum to fill out a table of information relating two cars. This section continues building the same skill, but focuses on a particular type of collisions: perfectly inelastic collisions.

In a perfectly inelastic collision, the two objects that collide stick together following the collision.

These tables are actually slightly easier to figure out, because there aren't as many boxes. Just remember that because two objects stick together, after their collision their mass is combined!

• Before the collision...
• Car A has a mass of 400 kg and is moving right with a speed of 10 m/s.
• Car B has a mass of 200 kg and is stationary before the collision.
• After the collision, the two cars stick together. It is a perfectly inelastic collision.
• What is the speed of the cars after the collision?
• Before the collision...
• Car A has a mass of 200 kg and is moving right with a speed of 15 m/s.
• Car B has a mass of 200 kg and is stationary before the collision.
• After the collision, the two cars stick together. It is a perfectly inelastic collision.
• What is the speed of the cars after the collision?
• Before the collision...
• Car A has a mass of 500 kg and is moving right with a speed of 20 m/s.
• Car B has a mass of 300 kg and is moving right with a speed of 15 m/s.
• After the collision, the two cars stick together. It is a perfectly inelastic collision.
• What is the speed of the cars after the collision?
• Before the collision...
• Car A has a mass of 1000 kg and is moving with a speed of 12 m/s.
• Car B has a mass of 1200 kg and is moving with a speed of 6 m/s.
• After the collision, the two cars stick together. It is a perfectly inelastic collision.
• What is the speed of the cars after the collision?
• Before the collision...
• Car A has a mass of 200 kg and is moving at an unknown velocity.
• Car B has a mass of 300 kg and is moving at 5 m/s.
• After the collision, the two cars stick together and move at a speed of 4 m/s.
• What was the initial speed of car A?
• Before the collision...
• Car A has a mass of 400 kg and is moving at a velocity of 8 m/s.
• Car B also has a mass of 400 kg and is moving at an unknown velocity.
• After the collision, the two cars stick together and move at a speed of 10 m/s.
• What was the initial velocity of car B?
1. A truck with a mass of 4000 kg is speeding at a rate of 30 m/s. It slams into a compact car with a mass of 1000 kg driving safely at a rate of 18 m/s. The compact sticks to the truck after the collision. What is their speed?
2. A linebacker with a mass of 120 kg runs at a rate of 8 m/s into a running back. The running back has a mass of 90 kg and is running in the same direction at a rate of 6 m/s. The linebacker wraps his arms around the running back so they stick together following the collision. What is their speed?