Momentum and change in momentum

Which would you rather get hit by? 1 bowling ball? 1 marble ?

On what information does your answer depend?

Car Crashes Why do some people survive and others do not?

DEFINITION OF MOMENTUM

Momentum A quantity of motion found by multiplying an object’s mass by its velocity Is a vector value (Magnitude and direction are important)

Momentum “Pain upon impact” “Inertia in motion”

Units of momentum Kg m/s

What has momentum?

What has more momentum? The statue of liberty or a SUV moving at 60 mph down the road?

Examples of momentum Anything with mass that is in motion Any object that is not moving has NO momentum

DETERMINATION OF AN OBJECTS MOMENTUM VALUE

Equation of momentum P = m v

How an object’s momentum changes is more useful than the momentum value at any point in time

CHANGE IN MOMENTUM “Impulse”

Newton’s Cradle

Impulse The measure of a change in momentum Symbol ∆p, units are the same Any object that changes its mass or velocity over time changes its momentum Any change in momentum requires a net force, acceleration Any application of a net force, results in a change of momentum of the object

Examples of net force changing momentum Hockey stick on a puck Wall on a car Bat on a softball

WHAT CAR HAS THE GREATER IMPULSE? The Red car that was going 45 mph stopped by the Brick Wall Or The same red car that was going 45 mph and stopped by application of Brakes

Answer They have the same change in momentum But the results of the change in momentum to each car is very different The car hitting a brick wall will have more force applied over a shorter time

Newton’s second law and ∆p How does 2 nd law relate to momentum? Acceleration = the change in velocity over change in time a = ∆v / ∆t Rewrite the 2 nd law in terms of the change of momentum (This is how Newton presented the law)

The Impulse momentum theorem Fnet = ma = m ∆v / ∆t, rearrange to form theorem mΔv = Δp = F net ∆t ∆v = v f - v i

Which parts of the equation = the impulse? Impulse = F ∆t Impulse = m ∆v Impulse = pf - pi

Important For a given crash involving vehicles with identical masses, undergoing identical changes in velocity… the impulse is constant regardless of how the crash occurs Impulse = mΔv

Time and force The length of time it takes for the crash to be complete determines the amount of force applied during the crash All of the measure found below extend the time of the crash, reducing applied force to passengers Seat belts Foam padding Air Bags Crumple zones

Time and force The longer the time allowed to exert a force, the less force is exerted

Again What causes a change in the momentum?

Change of momentum and Sports Baseball/ softball Golf

Catching a ball

To catch a ball Your hand must apply force to the ball to make it stop moving, The longer you can make the time spent applying force to the ball, the less force is needed

APPLICATIONS OF MOMENTUM

What determines if you live or die in an auto accident?

Safety features

Safety features in cars that protect you during a crash Seat belt Air bags Cushioned dashboard, steering weel Padded headrest Crumple zones

The way to survive an accident Drive a car with: – Seat-belts – Air bag – Crumple zones – Soft dashboards/padded steering wheels What benefit do these features provide?

What value do safety features extend? The time of the crash Impulse = Force x time

What value is decreased as a result of those safety features? The amount of force needed to stop the car (and you)

The purpose of most safety features in a car is to lengthen the time of the accident Air bags

Air Bags The air bag increases the time of the collision It will also absorb some of the energy from the body It will spread out the area of contact – decreases the pressure – helps prevent penetration wounds

Pressure P = F / A F = total force applied A = area over which the force was applied Units: N/m or Pascals

Seat belts

Padding on dashboard, seats and steering wheel

Crumple zones It takes time for the parts of the car in the crumple zone to be crushed, less force applied to the passenger section

Any other means to protect the passengers during a collision?

Other examples of change in momentum Catching a Foul Ball Being hit by a foul ball

Again The main point of all safety devices in cars is to extend the time of the impact between human and car

Answer The amount of force applied is related to the length of time required to bring the driver to a stop The longer the time, the less force required

Average Force in Impulse The average force can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval

Average Force cont. The impulse imparted by a force during the time interval Δt is equal to the area under the force-time graph from the beginning to the end of the time interval Or, to the average force multiplied by the time interval

Homework Pg 233 problems 1-5 Do not do 3 if we have not discussed no constant forces

Homework answers 1a) 23,200 kg m/s eastward 1b) 38.4 km/h eastward, 10.7 m/s eastward 3a) 2.7 m/s same direction as original velocity 3b) 1.3 m/s in the same direction as original velocity 5a) 7,800 N opposite direction of motion 5b) 800 kg (too heavy to lift)

ANGULAR MOMENTUM

Definition If something has mass and is rotating, it has angular momentum How much depends on: – Amount of mass, location, shape (MoI) – Rotational velocity L = Iω where I = MoI, ω = ang velocity

EXAMPLES OF ANGULAR MOMENTUM IN REAL LIFE

Angular momentum

Skaters in a spin How do skaters spin faster? Is there an outside force-torque being applied?

Change in angular momentum ∆L = L f – L I = I∆ω Just like linear momentum, change in angular momentum requires a Net force that causes change in rotation (Thus a net Torque) over time. T ∆t = I ∆ω

Question A old fashioned top (with a moment of inertia of 4.2 Kg m 2 )is spun by a rope that applies 155 Nm of torque when pulled. If Susie pulls on the rope for 1.2 seconds: A) What is the change in the angular momentum? B) What is the change in the angular velocity if top starts from rest?

Homework Pg 235 Questions 6-12