Part 2: Complete the following math problems by using the Law of Momentum Conservation.
Formulas:
i. Momentum = (mass) * (velocity)
ii. Impulse = (Applied force) * (time) and Impulse = Change in Momentum
iii. Applied Force = (Change in Momentum) / (time)
iv. For multiple objects: Total Momentum of everything before interaction = Total Momentum of everything after
6. A car of mass 1100kg moves at 24 m/s. What is the braking force needed to bring the car to a halt in 2.0 seconds? (Use i and iii)
7. What is the force on a 0.025 kg egg from a bed sheet as the egg hits the sheet at 4.0 m/s and takes 0.2 seconds to stop? (Use i and iii)
8. A 8.0 kg shell leaves a 2.0 x 103 kg cannon, at a speed of 4.0 x 102 m/s. What is the recoil speed of the cannon? (Use i and iv)
9. A 1.0 kg dart moving horizontally at 10.0 m/s makes impact and sticks to a piece of wood with a mass of 9.0 kg, which then slides across a friction free surface. What is the speed of the wood and dart after the collision? (Use i and iv)
10. A 10,000-kg train car coasting at 10 m/s collides with a 2000-kg automobile coasting at 30 m/s in the opposite direction. If the stick together after the impact how fast and in what direction will they be moving? (Use i and iv)
I will be happy to critique your work. Consider the hints, they tell you how to do them.
Najan
6. To find the braking force needed to bring the car to a halt, we can use the Law of Momentum Conservation.
First, we calculate the initial momentum of the car using the formula Momentum = mass * velocity.
Momentum_initial = (1100kg) * (24 m/s) = 26,400 kg*m/s
Since the car comes to a halt, the final momentum of the car is 0 kg*m/s.
Now, we can find the change in momentum using the formula Impulse = Change in Momentum.
Change in Momentum = Final Momentum - Initial Momentum = 0 kg*m/s - 26,400 kg*m/s = -26,400 kg*m/s
Next, we can calculate the braking force using the formula Applied Force = Change in Momentum / time.
Applied Force = (-26,400 kg*m/s) / (2.0 s) = -13,200 N
Therefore, the braking force needed to bring the car to a halt is -13,200 N (negative sign indicating it acts in the opposite direction of motion).
7. To find the force on the egg from the bed sheet, we can again use the Law of Momentum Conservation.
First, we calculate the initial momentum of the egg using the formula Momentum = mass * velocity.
Momentum_initial = (0.025kg) * (4.0 m/s) = 0.1 kg*m/s
Since the egg stops, the final momentum of the egg is 0 kg*m/s.
Now, we can find the change in momentum using the formula Impulse = Change in Momentum.
Change in Momentum = Final Momentum - Initial Momentum = 0 kg*m/s - 0.1 kg*m/s = -0.1 kg*m/s
Next, we can calculate the force on the egg using the formula Applied Force = Change in Momentum / time.
Applied Force = (-0.1 kg*m/s) / (0.2 s) = -0.5 N
Therefore, the force on the egg from the bed sheet is -0.5 N (negative sign indicating it acts in the opposite direction of motion).
8. To find the recoil speed of the cannon, we can use the Law of Momentum Conservation.
First, we calculate the initial momentum of the system (shell + cannon) using the formula Momentum = mass * velocity.
Initial Momentum = (2.0 x 10^3 kg) * (0 m/s) + (8.0 kg) * (4.0 x 10^2 m/s)
Initial Momentum = 0 kg*m/s + 3.2 x 10^3 kg*m/s = 3.2 x 10^3 kg*m/s
Since the system comes to a stop (recoil speed of the cannon), the final momentum of the system is 0 kg*m/s.
Now, we can find the recoil speed of the cannon using the formula Total Momentum before = Total Momentum after.
(2.0 x 10^3 kg) * (V_recoil) + (8.0 kg) * (4.0 x 10^2 m/s) = 0 kg*m/s
(2.0 x 10^3 kg) * (V_recoil) = -3.2 x 10^3 kg*m/s
V_recoil = (-3.2 x 10^3 kg*m/s) / (2.0 x 10^3 kg)
V_recoil = -1.6 m/s
Therefore, the recoil speed of the cannon is -1.6 m/s (negative sign indicating it is in the opposite direction of the shell's initial velocity).
9. To find the speed of the wood and dart after the collision, we can use the Law of Momentum Conservation.
First, we calculate the initial momentum of the system (dart + wood) using the formula Momentum = mass * velocity.
Initial Momentum = (1.0 kg) * (10.0 m/s) + (9.0 kg) * (0 m/s)
Initial Momentum = 10.0 kg*m/s + 0 kg*m/s = 10.0 kg*m/s
Since the dart and wood stick together, they have the same final momentum.
Now, we can find the final velocity of the dart and wood using the formula Total Momentum before = Total Momentum after.
(1.0 kg) * (V_final) + (9.0 kg) * (0 m/s) = 10.0 kg*m/s
V_final = (10.0 kg*m/s) / (1.0 kg)
V_final = 10.0 m/s
Therefore, the speed of the wood and dart after the collision is 10.0 m/s.
10. To find the final speed and direction of the train car and automobile after the collision, we can use the Law of Momentum Conservation.
First, we calculate the initial momentum of the system (train car + automobile) using the formula Momentum = mass * velocity.
Initial Momentum = (10,000 kg) * (10 m/s) + (2,000 kg) * (-30 m/s)
Initial Momentum = 100,000 kg*m/s - 60,000 kg*m/s = 40,000 kg*m/s
Since they stick together, they have the same final momentum.
Now, we can find the final velocity of the train car and automobile using the formula Total Momentum before = Total Momentum after.
(10,000 kg + 2,000 kg) * (V_final) = 40,000 kg*m/s
12,000 kg * (V_final) = 40,000 kg*m/s
V_final = (40,000 kg*m/s) / (12,000 kg)
V_final = 3.33 m/s
Therefore, the train car and automobile will be moving together with a final speed of 3.33 m/s in the direction of the train car's initial motion.