Momentum and Impulse. Calvin Liu and Maribel Maria

Transcription

1 Momentum and Impulse Calvin Liu and Maribel Maria

2 Momentum Momentum is the quantity of motion an object has, p. It can be found by the formula p=mv (mass x velocity) Momentum ~ Velocity Momentum ~ Mass It is a vector quantity, and goes in the direction of the object's velocity

3 Momentum, continued. Generally, the momentum of an object moving towards the right is positive, and the momentum of an object moving towards the left is negative. Momentum can be measured in kg m/s or N s. The momentum of an object can be changed by altering the mass or velocity of that object.

4 Newton's 3rd Law Newton's Third Law states that every action produces an equal and opposite reaction. When an object exerts a force on another object, the second object exerts a force of equal magnitude back to the first object in the opposite direction. When two objects interact, they change in momentum due to forces applied that change v. *Since time (t) would be the same for both objects, the impulse that each object exerts on each other are also equal.

5 Conservation of Momentum Momentum is neither created nor destroyed. It can only be changed. If no external force acts on system, the system is closed, and the total momentum remains constant. Therefore, in a system involving two objects, Total momentum before = total momentum after p before = p after m 1 v 1 +m 2 v 2 =m 1 v' 1 +m 2 v' 2 v' 1 v' 2 = velocities after the collision

6 Impulse Impulse is the change in momentum, J. It is also a vector quantity. It is measured in the same unit as momentum, kg m/s or N s. The formula for impulse is: J= p= F t = m v.

7 Collisions Collisions can happen in many different ways: a) Two objects moving in opposite directions collide b) One object moving faster than another object moving in the same direction collide Momentum change can also differ based on the results of the collision: a) The objects collide, then separate b) The objects collide and stick to each other

8 Notes To Remember The formula m 1 v 1 +m 2 v 2 =m 1 v' 1 +m 2 v' 2 can be used for most Regents problems dealing with collisions or recoil. If the objects stick to each other after the collision, then their final velocities are equal, and the mass is the sum of the mass of both objects. The right side of the above formula can be rewritten as (m+m)v'. If the objects are moving in the same direction, all velocity vectors are positive. However, if the objects are moving in the opposite direction, the velocity of the object moving to the left side is negative. The final momentum can be either positive or negative. -v +v

9 Other Notes If an object is at rest, its momentum is 0 because it has no velocity. Two repulsive objects bound together by ropes, for example, have a total momentum of 0 kg m/s at the start. When the ropes are cut, they move in opposite directions, but their momentum has the same magnitude. In recoil problems such as shooting a gun, the direction of the two objects are always opposite. Don't forget that m1 would be the mass of the bullet, while m2 is the combined mass of the person and the gun.

10 Practice Problem 1 The magnitude of the momentum of an object is 64 kg m/s. If the velocity is doubled, the magnitude of the momentum of the object will be (1)32 kg m/s (2)64 kg m/s (3)128 kg m/s (4)256 kg m/s

11 Answer Problem 1 Since p = mv, p and v are directly proportional. This means that if the velocity is doubled, then the momentum doubles as well. p'= (64 kg m/s) x 2 = 128 kg m/s Answer is (3)

12 Practice Problem 2 A tow-truck applies a force of 2000N on a 2000-kg car for a period of 3 seconds. What is the magnitude of the change in the car's momentum?

13 Answer Problem 2 p= F t = (2000 N) (3s) p= 6000 N s

14 Practice Problem 3 In a car crash, a 44-kg passenger moving at 15 m/s is brought to rest by an airbag during a 0.10-second interval. What is the magnitude of the average force exerted on the passenger by the airbag during this time?

15 Answer Problem 3 Know m= 44kg v i = 15 m/s v f = 0 m/s, t=0.1 s Want F p= F t F= p/ t = p f -p i / t F= (0 kg m/s)-(44kg 15m/s) 0.1 s F= N Magnitude= 6600 N

16 Practice Problem 4 If a 3.0-kilogram object moves 10. meters in 2.0 seconds, what is the object's average momentum?

17 Answer Problem 4 p = mv v = d/t p = md/t p = (3kg)x(10m)/(2s) p = 15kg-m/s

18 Practice Problem 5 An impulse of 30.0 newton-seconds is applied to a 5.0-kilogram mass. If the mass had a speed of 10. meters per second before the impulse, what is the speed of the mass of the impulse?

19 Answer Problem 5 J = p = p f - p i 30Ns = p f - p i p i = mv i p i = (5kg)(100m/s) p i = 500kg-m/s p f - 500kg-m/s = 30Ns p f = 530kg-m/s p f = mv f v f = p f /m v f = (530kg-m/s)/(5kg) v f = 106m/s