Question

1. A 1,000 kg car moving north at 30 mph collides into a 2,000 kg truck which is also moving north, but at 10 mph. Immediately after the collision, the truck’s speed is 13 mph. What is the speed of the car after the collision? Express your answer in mph and input the number only.

2. Was kinetic energy conserved in this collision? A. Yes B. No

3. What type of collision was this? A. Perfectly inelastic B. Inelastic C. Elastic

4. Imagine finding yourself stranded, at rest, in the middle of a large patch of ice, which is completely frictionless. In order to try to get off the ice, you throw one of your shoes to the right. What will happen to you after you throw the shoe? A. Nothing B. You will also move to the right C. You will move to the left

5. Suppose that your total mass (including clothing and shoes) is 50 kg, the mass of the shoe is 1.4 kg, and you throw the shoe at a speed of 6.0 m/s. What is the initial momentum of the system (you + shoe) before you throw the shoe? Express your answer in kg m/s and input the number only.

6. Suppose that after you throw the shoe, your speed is ??. Which of the following equations correctly expresses the momentum of the system (you + shoe) after you throw the shoe? Hint1: Use your answer to question 5; and pay attention to signs Hint2: After you throw the shoe, you are no longer wearing it A. 50?? + 1.4 ∙ 6.0 D. −48.6?? + 1.4 ∙ 6.0 B. 48.6?? + 1.4 ∙ 6.0 E. 50?? − 1.4 ∙ 6.0 C. −50?? + 1.4 ∙ 6.0 F. 48.6?? − 1.4 ∙ 6.0

7. What is your velocity after you throw the shoe? Express your answer in m/s and input the number only. Hint: Sign matters! 8. Suppose that now, you decide to throw your other shoe, which also has a mass of 1.4 kg, and you also throw it to the right at 6.0 m/s. What is the initial momentum now of the system (you + second shoe)? Express your answer in kg m/s and input the number only. Hint: Sign matters!

Answer 1

1.

m = mass of the car = 1000 kg

v = velocity of the car = 30 mph

M = mass of the truck = 2000 kg

V = velocity of truck = 10 mph

V' = velocity of truck after collision = 13 mph

v' = velocity of car after collision

using conservation of momentum

mv + MV = mv' + MV'

(1000)(30) + (2000)(10) = (1000) v' + (2000)(13)

v' = 24 mph

2.

Kinetic energy before collision is given as

Ki = (0.5) (mv2 + MV2) = (0.5) ((1000)(30)2 + (2000)(10)2) = 550000

Kinetic energy after collision is given as

Kf = (0.5) (mv'2 + MV'2) = (0.5) ((1000)(24)2 + (2000)(13)2) = 457000 J

clearly , final kinetic energy is not same as initial kinetic energy , hence the kinetic energy is not conserved.

3.

Inelastic collision

4.

initially both me and shoes was at rest. so initial total momentum of me and shoes was zero. after throwing the shoes to right , the shoes has some momentum in right direction. as per conservation of momentum , sum of momentum must be zero as it was initially.. hence i gain equal momentum in left direction so that total momentum remains zero.

C. You will move to the left