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### 601-E: Conservation of Momentum 3: Head-On Collisions

• Topic Cluster: Momentum
• Topic: Collisions and Explosions
• Objective: Use the conservation of momentum and guiding tables to solve problems involving cars moving in different directions.
• Content: When two cars are moving in different directions, physicists represent direction with the sign of the velocity.
• Level: 2

#### BACK to Ladder Collisions and Explosions

In the previous two sections, we used the conservation of momentum to analyze two cars in a crash. All of these were rear-end collisions, in which one car hit another moving in the same direction.

In this section, we will move to head-on collisions. In these problems, objects move in two different directions.

• 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 moving LEFT with a speed of 5 m/s.
• After the collision...
• Car A is stationary.
• What is the magnitude and direction of car B's velocity?
• 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.
• What is the magnitude and direction of car B's velocity?
• Before the collision...
• Car A has a mass of 100 kg and is moving LEFT with a speed of 8 m/s.
• Car B has a mass of 150 kg and is moving RIGHT with a speed of 4 m/s.
• After the collision...
• Car B is stationary.
• What is the magnitude and direction of car A's velocity?
• Before the collision...
• Car A has a mass of 30 kg and is moving RIGHT with a speed of 12 m/s.
• Car B has a mass of 40 kg and is moving LEFT with a speed of 6 m/s.
• After the collision...
• Car A moving to the LEFT with a speed of 2 m/s.
• What is the magnitude and direction of car B's velocity?
• Before the collision...
• Car A has a mass of 2000 kg and is moving RIGHT with a speed of 3 m/s.
• Car B has a mass of 4000 kg and is moving LEFT with a speed of 9 m/s.
• After the collision...
• Car A is moving LEFT with a speed of 8 m/s.
• What is the magnitude and direction of car B's velocity?
• Before the collision...
• Car A has a mass of 400 kg and is moving RIGHT with a speed of 5 m/s.
• Car B has a mass of 200 kg and is moving LEFT with a speed of 10 m/s.
• The collision is totally inelastic.
• What happens after the collision?
1. A railroad car with a mass of 50,000 kg is moving at a speed of 40 m/s when it smashes into a running tree trunk moving the other way at 5 m/s with a mass of 20,000 kg. The tree lodges in the railroad car. Nobody is injured, including the tree trunk. What is their speed and direction after the collision?
2. A linebacker with a mass of 140 kg is running downfield at 9 m/s towards a 120 kg running back running upfield with a speed of 8 m/s. They collide, and the linebacker wraps up the running back so they stick together. What is their speed and direction after the collision?
3. A red bumper car with a mass of 200 kg is driving to the right with a speed of 5 m/s. A blue bumper car with a mass of 200 kg is driving to the left with a speed of 6 m/s. They smash into each other. Each bumper car bounces back in the opposite direciton it was moving! If the red car has a speed of 4 m/s after the collision, what is the speed of the blue car?
4. A bumper car with a mass of 200 kg is driving forward (+) really fast, with a speed of 30 m/s. It slams directly into a truck with a mass of 4000 kg that is stationary and releases a loaded spring. The bumper car bounces backwards (-) with a speed of 30 m/s. The truck begins slowly rolling. Determine the magnitude and direction of the truck's velocity after the collision.