Unit 08 “Impulse and Momentum” Problem Solving: Watermelons and Car Accidents Impulse: Force and Time

Impulse Δp = pf - pi Δp = mvf - mvi Δp = FΔ t Definition Equation Definition Equation Impulse is the amount of change in an objects momentum. Impulse is the product of the force applied to an object and the amount of time applied Δp = pf - pi Δp = mvf - mvi 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.

Cushion “Sinks in” “Stretches out” “bends” or “breaks” Suspension More time to change the momentum of an object means less force applied to the object. Types of Protection When the object hits … Examples   Pillow, Fun noodle, air bag Cushion “Sinks in” “Stretches out” Bungee cord Elastics Seatbelt Suspension “bends” or “breaks” Jump off table Crumple zone Bed of nails Crumple Zone

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 = 2kg Vi = 10m/s Vf = 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 =

Δp =FΔt Δp =FΔt -20kgm/s=F(2.5s) -20kgm/s=F(0.20s) -8N = F -100N = F Force from Concrete Δt = F= ? Δp = Force from Water Δt = F= ? Δp = 0.20s 2.5s -20kgm/s -20kgm/s Δp =FΔt Δp =FΔt -20kgm/s=F(2.5s) -20kgm/s=F(0.20s) -8N = F -100N = 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

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 Person

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 Person m = 68kg Vi = 40m/s Vf = 0m/s Δp =? Δp = mvf – mvi Δp = 68kg(0m/s) – (68kg)(40m/s) Δp = 0kgm/s – 2720kgm/s Δp = -2720kgm/s

Force from Steering Wheel Δp = Force from Seatbelt Δt = F= ? Δp = Force from Airbag Δt = F= ? Δp =

Force from Steering Wheel Δp = Force from Seatbelt Δt = F= ? Δp = 0.50s 3.78s -2720kgm/s -2720kgm/s Δp =FΔt Δp =FΔt -2720kgm/s=F(3.78s) -2720kgm/s=F(0.50s) -719N = F -5440N = F Force from Airbag Δt = F= ? Δp = 7.2s Δp =FΔt -2720kgm/s=F(7.2s) -2720kgm/s -378N = F

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.