The sports announcer says “Going into the all-star break, the Detroit Red Wings have the momentum.” Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. Momentum is a physics term; it refers to the quantity of motion that an object has. Momentum can be defined as “mass in motion”. Momentum = mass x velocity p = m v Momentum depends upon the variables mass and velocity. The equation illustrates that momentum is directly proportional to the object’s mass and directly proportional to the object’s velocity.

10 kg 6 kg Momentum is a vector quantity. As discussed previously, a vector quantity is a quantity which is fully described by both magnitude and direction. “A”“B” p = 24 kg m east s p = 24 kg m west s Question: Each object above has the same momentum. What can you say about the relationship between the objects’ velocities? Answer:_____________________________________________ Object “B” has a greater velocity than object “A”. Why did you answer as you did? Since object “B” is less massive but has the same momentum as object “A”, it must have a greater velocity than object “A”.

Answer:____________________________________________________ The green truck has the greatest “m” and “v”, therefore the greatest “p” as well.

Objects that have momentum are hard to stop. The more momentum an object has the harder it is to stop. In order to stop an object, its momentum must be changed. Since mass is constant the factor that must be changed is velocity. Remember, a change in velocity is an acceleration, and accelerations are caused by a net force. So, in order to change an an object’s momentum, a net force must be applied for a certain amount of time. The stronger the net force applied to an object, the less amount of time will be needed to stop the object. The weaker the net force applied to an object, the more time will be needed to stop the object.

The impulse-momentum change theorem can be represented with an equation. Below we will derive this equation together. Net force:F net = ma or F net = m(  v) t Change in Momentum:  p = m (  v) or F net (t) = m (  v) F net (t) =  p Impulse = Change in Momentum

Observe that the greater the time over which the collision occurs, the smaller the force acting upon the object. Thus, to minimize the effect of the force on an object involved in a collision, the time must be increased. Real World Application: Air bags are used in automobiles because they are able to minimize the effect of the force on an object involved in a collision. How?___________________________________________________ By extending the time required to stop the momentum of the driver.

When a boxer recognizes that he will be hit in the head he relaxes his neck and allows his head to move backwards upon impact. Why? Answer:______________________________ ____________________________________ A boxer “rides the punch” in order to extend the time of impact which in turn decreases the force of impact. Rock climbers attach themselves to the steep cliffs by means of nylon ropes. If a rock climber should lose her grip on the rock, she will begin to fall. In such a situation, her momentum will ultimately be halted by the means of the rope, thus preventing a disastrous fall to the ground. Why Nylon ropes? Answer:________________________________________ _______________________________________________ Nylon has the ability to stretch. If the rope is capable of stretching upon being pulled taut by the falling climber, then it will apply a force over a longer period of time. Time Force

Which collision is best for the driver of a car? A) a car collides with a wall causing the front of the car to crumple and eventually stop. B.) a car collides with a wall causing the car to bounce backwards or (rebound). Answer:___________________________ _______________________________________________________ The crumpling car is the safest type of collision. If a car rebounds upon collision, the momentum change will be LARGER than if it were to crumple and stop. A larger momentum change causes a larger impulse which is commonly associated with a larger force.

Imagine that you are hovering next to the space shuttle in earth-orbit and your buddy of equal mass, who is moving at 4 m/s (with respect to the ship), bumps into you. If he holds onto you, then how fast do the two of you move after the collision?

When a collision occurs in an isolated system (isolated from all other net forces), the total momentum of the system of objects is conserved. p 1 + p 2 = p 1 + p 2 Before the CollisionAfter the Collision

(m 1 v 1 ) + (m 2 v 2 ) = (m 1 v 1 ) + (m 2 v 2 ) p 1 + p 2 = p 1 + p 2 If the masses of the objects are the same, you do not need to factor them into the equation: v 1 + v 2 = v 1 + v 2 Before CollisionAfter Collision 4 km/hr + 0 km/hr = v 1 + v 2 v 1 & v 2 = 2 km/hr

The animation below portrays the inelastic collision between a very massive fish and a less massive fish. Before the collision, the big fish is in motion with a velocity of 5 km/hr and the little fish is at rest. The big fish has four times the mass of the little fish. After the collision, both the big fish and the little fish move together with the same velocity. (Collisions such as this, where the two objects stick together and move with the same post-collision velocity, are referred to as INELASTIC collisions.) What is the after-collision velocity of the two fish?

5 km/hr 4 (m 1 v 1 ) + (m 2 v 2 ) = (m 1 v 1 ) + (m 2 v 2 ) m 1 v 1 = v (m 1 + m 2 ) 4m x 5km/hr = v (4m +m) 4m x 5 km/hr = v (5 m) 4 m x 5 km/hr = v 5m 4 km/hr = v

A perfectly inelastic collision, as seen below, is one in which objects stick together upon colliding. Kinetic energy (energy of motion) is converted to other forms of energy during a perfectly inelastic collision. These different forms may include heat, and sound.

Elastic collisions, as seen below, occur when two objects rebound upon colliding with one another. During an elastic collision kinetic energy is conserved (no energy is lost). Elastic collisions are not realistic. Partially inelastic collisions are ones in which some energy is lost, but the objects do not stick together. Partially inelastic collisions are realistic.

Scenario: A moving cart, of mass=1.0 kg, moves along a frictionless surface at a velocity of 60.0 cm/s before a brick of mass=2.0 kg is added to its top surface. Question: What will happen to the momentum of the cart after the brick is added? Answer:______________________It will decrease Why?___________________________________________________ ___________________________________________________ The “p” of the brick increased. This “p” must have come from the cart (isolated system). Therefore, the “p” of the cart decreased.

Grandma (mass = 80 kg) skates along at 6 m/s before picking up her grandson who has a mass of 40 kg. Determine the velocity of both Grandma and her grandson after she picks him up. (m 1 v 1 ) + (m 2 v 2 ) = (m 1 v 1 ) + (m 2 v 2 ) (80 kg x 6 m/s) + (40 kg x 0 m/s) = v (80 kg + 40 kg) (480 kg m/s) = v (120 kg) v = (480 kg m/s) 120 kg = 4 m/s

A large truck slams into the back of a compact car. Determine the velocity of the truck after the collision with the car. (m 1 v 1 ) + (m 2 v 2 ) = (m 1 v 1 ) + (m 2 v 2 ) (3000 kg x 10 m/s) + (1000 kg x 0 m/s) = (3000 kg x v) + (1000 kg x 15 m/s) (30000 kg m/s) = (3000 kg x v) + (15000 kg m/s) (30000 kg m/s) - (15000 kg m/s) = 3000 kg x v kg m/s = v 3000 kg V = 5 m/s

Newton’s third law states that if one object applies a force to another object that object will apply an equal but opposite force.

The force acting on the truck caused the truck’s momentum to change. The force acting on the car caused its momentum to change as well. The momentum lost by the truck was gained by the car. Why was the change in the car’s velocity not the same as the change in the truck’s velocity. Answer:________________________________________________ _______________________________________________________ The car has less mass than the truck. If the car received the momentum that the truck lost it must have a greater change in “v”.

Answer:____________________________________________ __________________________________________________ The force acting on each vehicle will be greater than than in the previous collision. This is due to the magnitude and direction of the objects’ momentum.

Answer:________________________________________________ _______________________________________________________ Yes, because the time of impact is increased. Also, the change in momentum of each object is decreased. Each of these factors is associated with a smaller force acting on each driver.

A 100 kg fullback leaps toward the end zone with a velocity of 5 m/s. A 75 kg linebacker moving at 4 m/s attempts to stop the forward progression of the fullback by colliding with him in mid-air. Does the fullback score?

Two girls on ice skates, originally at rest, apply a pushing force on each other. This causes the skaters to move away from each other. The mass of the first girl is 100 kg.,while the mass of the second girl is 50 kg. Answer the questions below: a.) What is the relationship between each girl’s momentum after they push each other? __________________________________ b.) What is the relationship between each girl’s velocity after they push each other? __________________________________ They are equal. The larger girl has ½ the velocity of the smaller girl.

A 4.0 kg model rocket is launched, shooting 50.0 g of burned fuel from its exhaust at an average velocity of 625 m/s. What is the velocity of the rocket after the fuel has burned? (Ignore the effects of gravity and air resistance.) (m 1 v 1 ) + (m 2 v 2 ) = (m 1 v 1 ) + (m 2 v 2 ) 0 = [(4 kg -.05 kg) x v)] + (.05 kg x -625 m/s) 0 = [(3.95 kg) x v)] + ( m/s) v = (31.25 m/s) 3.95 kg = m/s

A 1325 kg car moving North at 27.0 m/s collides with a 2165 kg car moving east at 17.0 m/s. They stick together. Draw a vector diagram of the collision. In what direction and with what speed do they move after the collision? p blue = mv = 1325 kg x 27 m/s = kg m/s p red = mv = 2165 kg x 17 m/s = kg m/s (p blue ) 2 + (p red ) 2 = (p resultant ) 2 p resultant = kg m/s p resultant = m v kg m/s = (1325 kg kg) v v = 14.7 m/s Tan  = =  Inv tan = = 44.2 degrees

A running back with a momentum of 500 kg m/s gets tackled by a linebacker with a momentum of 300 kg m/s. If both players remain connected during the tackle, determine their resultant momentum and direction of motion. p resultant = kg m/s Tan  = 300 = Inv tan.6 = 31 0 