Momentum and Inertia
Formulas you need to know:
(REMEMBER: P = Momentum and J = Inertia)
p = mass x velocity ----> momentum is measured in kgm/s
∆p = mass x ∆velocity
J = F x ∆time ----> inertia is measured in NS
J = p
mava + mbvb = mava + mbvb ------> finding the total momentum of a system
mava + mbvb = (ma + mb) (Vab) ----> total momentum when the objects stick together
ptotalinitial = ptotalfinal
Momentum and Inertia Questions that are frequently seen:
1) What is the momentum of an 8kg bowling ball rolling at 2m/s?
p = mv
p = 8 (2)
p = 16kgm/s
2) What's the momentum of a 50kg cart sliding at 7 m/s across a tile floor?
p = mv
p = 50(7)
p = 350 kgm/s
3) Which has a greater momentum, a heavy truck at rest or Julian Martin on a skateboard rolling at 4 m/s?
Julian has a greater momentum, because of his velocity. If you were to calculate this, you would see that the truck's velocity would be 0, thus making his momentum 0 as well.
4)Describe the change in momentum in this situation: A small bee hits a big mac truck's windshield.
The change in momentum of any action/reaction scenario stays the same; therefore, the bug and the mac truck lose the same momentum. The truck has a big mass and a small acceleration, where the bug has a small mass and a big acceleration. This concept is proven through Newton's 3rd Law, saying each action has an equal and opposite reaction. See below:
Mava = mbVb
mac truck ∆momentum = bee ∆momentum
5) If you throw a ball horizontally while standing on a skate board, you will roll backwards. If you go through the motions of throwing the ball, but hold onto it instead, will you still roll backwards?
You theoretically shouldn't and won't move backwards because there's no Newton's 3rd Law force pushing back on you. The net force would have to be something other than 0, because in order to have that acceleration, there can't be a balanced force.
6) While being thrown, a net force of 100 Newtons acts on a baseball with a mass of 0.5 kg for a period of 1 second. What's the change in momentum of the ball?
F∆t = J
(100N) (1) = 100NS
J = p
p = 100kgm/s
7) If a bat hit a baseball, how large would the ball's force be on the bat?
The forces, according to Newton's 3rd Law, would be equal and opposite.
8) An astronaut with a mass of 60kg carries a cooler of CapriSun with a mass of 15kg in space. By using the cooler away with a speed of 3 m/s, the astronaut floats in the opposite direction. Solve for the total system's momentum and find the speed at which the astronaut moves away from the cooler.
ptotalinitial = ptotalfinal
(ma + mb) (Vab) = mava + mbvb
(75kg) (0) = 60 (va) + 15 (3)
-45 = 60va
Va = - 0.75 m/s
9) On an icy road, a 7000 kg mac truck hits a 1000 kg car that had been previously traveling at 15 m/s, causing the truck to slow from 20 m/s to 14 m/s and the car to speed up. Find the total momentum and find the final velocity of the car.
ptotalinitial = ptotalfinal
mava + mbvb = (ma + mb) (Vab)
7000 (20) + 1000 (15) = (7000+1000) (Vab)
290000 = 8000 Vab
Vab = 36 m/s
Big Question!
Why would you bend your legs when jumping off a roof? (This question is very similar to the Egg Toss and padded dashboard scenarios).
- You are going from some amount of velocity to completely stopped no matter if your legs are bent of not
- The mass and change in velocity are the same with or without bent legs
- ∆p = m∆v and the ∆p is the same with or without bent legs
- Since the ∆p is the same, and the ∆p = J, the J is the same too
- Since J is constant, bending legs will increase the time, which decreases the force (leading to a safer landing)
- Bad landing: J = F∆t (Big force on you with little time)
- Good landing: J = f∆T (Small force on you with greater time)
From my orange sheet:
- Mava = mbVb (Big momentum and little velocity equals little momentum and big velocity)
- ∆p = J
- When two objects hit, the momentum is equal and opposite. So is the impulse. However, the acceleration may be different for an object (for example, if a bug hit a car windshield, it's acceleration would be greater)
- F∆t = m∆v
- The ∆p is the same no matter if the ∆p is fast or slow
- Remember to convert weight to kg before using it in a formula
- ptotalinitial = ptotalfinal
- Use SOHCAHTOA when finding the sides of an angle (for example, if two balls collided and bounced off at different angles).
- Individual objects can have a change in momentum, but when working with a system, the momentum of two objects has to be equal and opposite.
