Momentum problems

Question

1.Bobby has a mass of 55 kg and he runs down the length of a football field at 3.8 m/s in an effort to catch the football being passed to him. What is his momentum?

2.A car is driving on highway 78 and has a momentum of 47,400 kgm/s. If the car is 1,800 kg, what is the velocity of the car?

3.A golfer swings the club with a force of 8,000 N. If the club makes contact with the golf ball for only 0.22 s, then what impulse is given to the golf ball?

*answer and explanation please*

Answer 1

1. Momentum is the product of mass and velocity. It's good to get in the practice of using algebra for these sorts of problems: Let M = mass. Let V = velocity. Let P = momentum (because we already used M). Then the equation for momentum is P = M x V. Just plug in M = 55 kg and V = 3.8 m/s to find P. So his momentum is just P = 55 kg x 3.8 m/s = 209 Kg m/s.
2. Using the same formula, P = M x V, we have P = 47,400 kg m/s and M = 1800 kg. So we have: 47,400 = 1800 x V. Divide both sides of the equation by 1800 to get 47400/1800 = V. So V = 26.33 m/s.
3. This requires a different formula, relating momentum to force. If you apply a constant force F for a time of T seconds, then the product of the two is the change in momentum over that time. As an equation: F T = Delta P. Delta P means the change in momentum, from the start to the finish. In this case, F = 8000 N, T = 0.22 s. So plugging in, we get: 8000 x 0.22 = Delta P. So Delta P = 1760 N/s. That's the change in momentum for the golf ball. But since initially, the momentum was zero, (the ball had zero velocity at the start), then Delta P in this case is just the final value of P. So the momentum is 1760 N s. Note the units: Newton - seconds. Earlier, we said that the dimensions of momentum in the metric system was kilogram-meters per second. So the unit of force, the Newton, is equal to a kilogram-meter per second-squared.

Answer 2

1. Note: A summary is below:

Just as displacement is the change of position from one time to another and is measured in the same units so impulse is the change in momentum from one time to another and is measured in the same units.

Both momentum and impulse are measured in Kg•m/s, but you may see impulse described in N•s - which is the same quantity ** further explanation below.

The first two questions involve the formula p=mv where p is momentum measured in Kg•m/s, m is mass in Kg and v is velocity measured in m/s.

1) The momentum asked for is the product of mass and velocity. We know 3.8 m/s is velocity because of the units as well as the implied language: p = mv = 55kg • 3.8 m/s = 209 Kg•m/s.

2) Here what is asked for is the velocity and what is given is momentum and mass. It is the same measurements and the same equation, but a different unknown so the equation must be re-arranged to define velocity.

p=mv

m m

mass cancels out and you get p/m = v or, by symmetric property v=p/m.

So the velocity can be found as the quotient of moment and mass:

v=p/m = 47,400 Kg•m/s / 1,800 Kg = 26 1/3 m/s

The final question about impulse uses the equation ∆p = F∆t where ∆ means "change in". Sometime the ∆ symbol is left out - especially when symbolizing the change in time: p =Ft and sometimes impulse is represented with an I: I=Ft, but the relationship is always the same - "impulse is the product of the force and time":

∆p = F∆t = 8000N • .22s = 1760 N-s or 1760 Kg•m/s

It might be confusing to see the compound units N•s and Kg•m/s as the same amount, but if you consider the Newton is a Kg•m/s^2 you can see how this works:

** N•s= Kg•m/s^2 • s = Kg•m/s

Summary:

1) p = mv = 55kg • 3.8 m/s = 209 Kg•m/s.

2) v=p/m = 47,400 Kg•m/s / 1,800 Kg = 26 1/3 m/s

3) ∆p = F∆t = 8000N • .22s = 1760 N-s or 1760 Kg•m/s