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Perfectly Inelastic collisions - by Lauren Bly, 2001

1. A 1500 kg car traveling at 15.0 m/s to the south collides with a 4500 kg truck that is initially at rest at a stoplight.  The car and truck stick together and move together after the collision.  What is the final velocity of the two vehicle mass?

Here's what you know: The car has mass 1500 kg, and initial velocity 15.0 m/s.  The truck has mass 4500 kg and initial velocity 0 m/s.  The final mass is 6000 kg (4500 kg plus 1500 kg, because they stick together) and we are looking for the final velocity.  Using the formula p = mv, and the concept that p before equals p after, the p of the car plus p of the truck equals the p of them together. So, 1500 x 15 + 4500 x 0 = 6000 x v final.  22500 = 6000 v, and v = 3.8 m/s.  The velocity is positive, and the initial velocity of the car was positive, so the two vehicles together are traveling to the south just like the car was initially.

2. A grocery shopper tosses a 9.0 kg bag of rice into a stationary 18.0 kg shopping cart.  The bag hits the cart with a horizontal speed of 5.5 m/s toward the front of the cart.  What is the final speed of the cart and bag?

Here's what you know: The rice has mass of 9.0 kg and initial velocity of 5.5 m/s.  The cart has a mass of 18.0 kg and an initial speed of 0 m/s.  Together, the bag and cart have a mass of 27 kg and we are looking for the final velocity.  Using the formula p = mv, and the concept that p before equals p after, the p of the bag before plus the p of the cart before equals the p of the cart and bag together.  So 9 x 5.5 + 18.0 x 0 = 27 x v final.  49.5 + 0 = 27 v, and v = 1.83 m/s

3. A 1.50x10^4 kg railroad car moving at 7.00 m/s to the north collides with and sticks to another railroad car of the same mass that is moving in the same direction at 1.50 m/s.  What is the velocity of the joined cars after the collision?

Here's what you know: The first car has mass of 1.5 x x10^4 kg and initial velocity of 7.00 m/s.  The second car has a mass of 1.5 x x10^4 kg and an initial speed of 1.5 m/s.  Together, the two cars have a mass of 3 x 10^4 kg and we are looking for the final velocity.  Using the formula p = mv, and the concept that p before equals p after, the p of the first car before plus the p of the second car before equals the p of the two cars together.  So 1.5 x x10^4 x 7.00 + 1.5 x x10^4 x 1.5 = 3 x x10^4 x v final.  1.27500 x 10^5 = 3 x x10^4 v, and v = 4.0 m/s to the north.  All the velocities are positive, so they al are in the same direction, which is north.

4. A dry cleaner throws a 22 kg bag of laundry onto a stationary 9.0 kg cart.  The car and laundry bag begin moving at 3.0 m/s to the right.  Find the velocity of the laundry bag before the collision.

Here's what you know: The laundry bag has mass of 22 kg and an unknown velocity.  The cart has a mass of 9.0 kg and an initial velocity of 0 m/s.  Together, the bag and cart have a mass of 31 kg and a final velocity of 3.0 m/s.  Using the formula p = mv, and the concept that p before equals p after, the p of the bag before plus the p of the cart before equals the p of the cart and bag together.  So 22 x v + 9.0 x 0 = 31 x 3.0 . 22 v + 0 = 93, and v = 4.2 m/s, to the right