Chapter 6: sections 1-3

Objectives Compare the momentum of different moving objects. Compare the momentum of the same object moving with different velocities. Identify examples of change in the momentum of an object. Describe changes in momentum in terms of force and time.

QOTD Can a bee and a truck have the same momentum? Explain. What determines the momentum of an object? Momentum depends on…

Linear Momentum Momentum is defined as mass times velocity. Momentum is represented by the symbol p, and is a vector quantity. (direction counts)! p = mv momentum = mass  velocity Units: kg m/s html

Sample Problem A 2250 kg truck has a velocity of 25 m/s to the east. What is the momentum of the truck? (5.6x10 4 kg m/s) What velocity must a 1210 kg car have in order to have the same momentum as the pickup truck? (46 m/s E)

QOTD How can you change the momentum of an object? (Use physics terms.) F=ma Write down three examples of using force to change momentum…

Impulse The product of the force and the time over which the force acts on an object is called impulse. The impulse-momentum theorem – A net force applied during a time interval will cause a change in momentum. F∆t = ∆p = mv f – mv i force  time interval = change in momentum J (impulse)=change in momentum

Impulse & Change in Momentum A change in momentum creates a force during the time of the change. Examples: collisions, sudden acceleration, amusement parks To change momentum requires force during time of change. Examples: Sports – change momentum to target where want ball to go. What makes roller coasters fun? Amusement park rides – want large force, make change quick Safety features in cars – What do they do? Collisions – want small force, make change take a long time. Change in p = F(of impact) x t(of impact)

Sample Problem A 1400kg car moving westward with a velocity of 15m/s collides with a pole and comes to rest in.30s. Find the force exerted on the car during the collision. (7.0x10 4 N)

Change in Momentum Sample problem: What is the momentum of a 50kg carton that slides at 4 m/s across an icy surface? If the carton skids onto a rough surface and stops in 3s. Calculate the force of friction it encounters.

QOTD What is/can be done to lessen the force of impact in collisions? F=mv f -mv i t f -t i Force and time are indirectly proportional…to lessen F, t must increase. What are some examples of this? try/airbags/

Examples Force is reduced when the time interval of an impact is increased. Manipulating force changes momentum/acceleration (helpful in sports).

Sample Problem What is the force exerted on a 65kg passenger that is brought to stop in.75s (average stopping time by an airbag) if the initial velocity is 2.4 m/s (35 mph)? 208N Calculate the force on the passenger if the airbag is not present. The average stopping time by a dashboard is.026s. (6000N) F exerted by airbag is 29X smaller than F exerted By dashboard…increasing t is the key! How would your egg design project change with this new information?

Stopping time and distance What factors determine the amount of time required to make a complete stop? Stopping distance is mostly dependent on mass, time allowed for the stop, and change in velocity from the moment of deceleration. There is no magic to stopping…you need the distance required in order to stop safely.

Sample Problem A 2240 kg car travelling westward slows down from 20.0m/s to 5.00m/s. How long does it take the car to decelerate if the force on the car is 8410N eastward? (4.00s) How far does the car travel during the deceleration? (-50.0m)

Conservation of Momentum Describe the interaction between two objects in terms of the change in momentum of each object. Compare the total momentum of two objects before and after they interact. State the law of conservation of momentum. Predict the final velocities of objects after collisions, given the initial velocities, force, and time.

Conservation of Momentum The total momentum of objects within a closed system remains constant. total initial momentum = total final momentum

Conservation of Momentum Momentum remains constant before and after a collision or impact. momentum (before) = momentum (after) mv (before) = mv (after) /fca.cfm /fcb.cfm

Cases for Studying Collisions “The explosion” …when two or more objects are initially at rest, and final momentum of objects is equal and opposite to each other. Energy may be conserved. Momentum (before) = Momentum (after)

Practice Problem A 65kg clown is fired horizontally from a 200kg cannon. If the clown travels at a velocity of 18m/s, what is the recoil velocity of the cannon?

Cases for Studying Collisions “Hit and Stick” (Inelastic) …when two or more objects collide and stick together after impact. Energy is not “conserved”. Some of initial energy is transferred into heat and sound. Momentum (before) = Momentum (after)

Practice Problem Sample Problem: A 6kg fish swims at 1m/s to eat a 2kg fish that is swimming toward him at 2m/s. What is the velocity of the big fish after lunch?

Cases for Studying Collisions “Hit and Separate” (perfectly elastic) …when two or more objects collide and separate after impact. Energy is conserved as less is transferred into other forms. momentum (before) = momentum (after)

Practice Problem A 1500 kg truck collides with a 750 kg car which is initially at rest. If the truck is moving at 10 m/s before impact, and 5 m/s after impact, what is the velocity of the car after impact? What could be done to lessen the force of impact on the cars?

Divide & Conquer Problem Solving Are you a 3, 2, or 1? “Conservation of Momentum Problems” Sheet 3’s-Solve the problems in any order 2’s-Solve in the following order: 2,5,4,3,1 1’s-Work with me