Unit 08 “Impulse and Momentum”

Problem Solving: Watermelons and

Car Accidents

Impulse: Force and Time

Impulse

Definition

Equation

Definition

Equation

Impulse is the amount of change in an objects momentum.

Δp = pf - pi

Δp = mvf - mvi

Impulse is the product of the force applied to an object and the amount of time applied

Δp = FΔ t

Impulse – Momentum Theorem

The change in an object’s momentum is equal to the amount of force and the amount of time applied to the object.

FΔt = Δp

FΔ t= mvf - mvi

For a given change in momentum…The more time the object has to stop, the less force needed to stop it.

The less time the object has to stop, the more force needed to stop it.

More time to change the momentum of an object means less force applied to the

object.

Types of Protection When the object hits … Examples

Cushion

Suspension

Crumple Zone

“Sinks in”

“Stretches out”“bends” or “breaks”

Pillow, Fun noodle, air bag

Bungee cordElasticsSeatbelt

Jump off tableCrumple zoneBed of nails

Save the Watermelon!!!• Watch the video of the man dropping a watermelon

into a pool of water and onto the concrete.

• Use impulse to explain why the watermelon will be safe in the water but not on the concrete?

Water acts like a cushion. The watermelon sinks into the water, the watermelon MORE TIME to stop, so there is LESS FORCE on it to stop it.

Watermelon Accident Facts

• Mass of Watermelon = 2kg• Velocity when it hits the surface = 10m/s• Velocity after it stops = 0m/s

• Time force was applied by the concrete: 0.20s• Time force was applied by the water: 2.5s

Now, let’s prove it mathematically!

Impulse (change in momentum) for the Watermelon

Now, let’s prove it mathematically!

Impulse (change in momentum) for the Watermelon

m = 2kgVi = 10m/sVf = 0m/s

Δp = mvf – mvi

Δp = 2kg(0m/s) – (2kg)(10m/s)

Δp = 0kgm/s – 20kgm/s

Δp = -20kgm/s

Force from Concrete

Δt =

F= ?

Δp =

Force from Water

Δt =

F= ?

Δp =

Force from Concrete

Δt =

F= ?

Δp =

Force from Water

Δt =

F= ?

Δp =

0.20s

-20kgm/s

Δp =FΔt

-20kgm/s=F(0.20s)

-100N = F

2.5s

-20kgm/s

Δp =FΔt-20kgm/s=F(2.5s)

-8N = F

Car Accident Facts

• Mass of an average person = 68kg• Velocity when it gets into accident= 40m/s• Velocity after it stops = 0m/s

• Time force was applied by steering wheel: 0.50s• Time force was applied by seatbelt: 3.8s• Time force was applied by airbag: 7.2s

Wow! Time to stop really DOES matter!How about in a car – will time to stop help save you in

an accident?

Impulse (change in momentum) for the Person

Wow! Time to stop really DOES matter!How about in a car – will time to stop help save you in

an accident?

Impulse (change in momentum) for the Personm = 68kg

Vi = 40m/sVf = 0m/sΔp =?

Δp = mvf – mvi

Δp = 0kgm/s – 2720kgm/s

Δp = -2720kgm/s

Δp = 68kg(0m/s) – (68kg)(40m/s)

Force from Steering Wheel

Δt =

F= ?

Δp =

Force from Seatbelt

Δt =

F= ?

Δp =

Force from Airbag

Δt =

F= ?

Δp =

Force from Steering Wheel

Δt =

F= ?

Δp =

Force from Seatbelt

Δt =

F= ?

Δp =

Force from Airbag

Δt =

F= ?

Δp =

Δp =FΔt -2720kgm/s=F(0.50s)

-5440N = F

Δp =FΔt-2720kgm/s=F(3.78s)

-719N = F

Δp =FΔt-2720kgm/s=F(7.2s)

-378N = F

0.50s

-2720kgm/s

3.78s

-2720kgm/s

7.2s

-2720kgm/s

Explain how the seatbelt gives you more time to stop.

Explain how the airbag gives you more time to stop.

The seatbelt acts like a suspension by stretching out giving the person more time to stop. According to the impulse-momentum theorem, for a given change in momentum, the more time applied to stop an object, the less force needed to stop it. For example the steering wheel applies a big force of 5440N over a time of 0.50s, whereas the seatbelt applies a smaller 720N force over a longer time of 3.78s.

The airbag acts like a cushion by sinking in to give the person more time to stop.According to the impulse-momentum theorem, for a given change in momentum, the more time applied to stop an object, the less force needed to stop it. For example the steering wheel applies a big force of 5440N over a short time of 0.50s, whereas the airbag applies a smaller 378N force over a longer time of 7.2s.