Can momentum change? ∆p = m ∆v Change in momentum = mass x change in velocity (Units) kgm/s = kg x m/s ∆p = m ∆v Change in momentum = mass x change in velocity (Units) kgm/s = kg x m/s
To stop an object, we have to apply a force to the object over a period of time. This is called IMPULSE. J = F ∆t Impulse = Force x change in time Ns = N x s J = F ∆t Impulse = Force x change in time Ns = N x s
Combine these two formulas and simplify: F = ma a = ∆v/∆t Combine these two formulas and simplify: F = ma a = ∆v/∆t F∆t = m∆v SO…… J = ∆p F = ∆p/ ∆t SO…… J = ∆p F = ∆p/ ∆t Short Form Useful Form
An egg dropped on a tile floor breaks, but an egg dropped on a pillow does not. Why? F Δ t= m Δ v Hint 1: In both cases, m and Δ v are the same. Hint 2: If Δ t goes up, what happens to F, the force? Answer : When dropped on a pillow, the egg starts to slow down as soon as it touches it. A pillow increases the time the egg takes to stop.
Would you rather be in a head on collision with an identical car, traveling at the same speed as you, or a brick wall? Assume in both situations you come to a complete stop.
Answer is… It Does Not Matter! Look at F Δ t= m Δ v In both situations, Δ t, m, and Δ v are the same! youyour your you The time it takes you to stop depends on your car, m is the mass of your car, and Δ v depends on how fast you were initially traveling.
Apply the force for a long time. F ∆t
Apply the force for a short time. F ∆t
It’s all about time!!! Helmet and bare head stop a 90 mph fastball, m∆v is the same for both situations F = m v Small “ t ” for head witho ut helme t Big Force F= m v Big “ t ” for head with helme t Small Force t t
Collisions that take a long time are better, because they allow for smaller forces. How do we increase the time of a collision?
5 kg mass is dropped onto an athletic surface Height of the bounce is measured G max value is determined The bigger the bounce the harder the surface Different surface has different allowable G max values basketball court > football field
Large amounts of time in a collision, results in a smaller force. Motion can be described by position, velocity and momentum. Changes in motion can be described by acceleration and changes in momentum. Changes in motion are caused by forces. Newton’s Laws help us predict changes in motion. Collisions are about momentum, and Newton’s 2 nd and 3 rd Laws.
You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do? 1) hit the other car 2) hit the wall 3) makes no difference 4) call your physics prof!! 5) get insurance!
In both cases your momentum will decrease to zero in the collision. Given that the time t of the collision is the same, then the force exerted on YOU will be the same!! If a truck is approaching at 30 mph, then you ’ d be better off hitting the wall in that case. On the other hand, if it ’ s only a mosquito, well, you ’ d be better off running him down... You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do? 1) hit the other car 2) hit the wall 3) makes no difference 4) call your physics prof!! 5) get insurance!
FF light heavy 1) the heavier one 2) the lighter one 3) both the same Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has more momentum after the force acts ?
FF light heavy av tt pp F We know: so impulse p = F av t. In this case F and t are the same for both boxes! Both boxes will have the same final momentum., 1) the heavier one 2) the lighter one 3) both the same Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has more momentum after the force acts ?
In the previous question, which box has the larger velocity after the force acts? 1) the heavier one 2) the lighter one 3) both the same
The force is related to the acceleration by Newton ’ s Second Law (F = ma). The lighter box therefore has the greater acceleration and will reach a higher speed after the 1-second time interval. Follow-up: Which box has gone a larger distance after the force acts? Follow-up: Which box has gained more KE after the force acts? In the previous question, which box has the larger velocity after the force acts? 1) the heavier one 2) the lighter one 3) both the same
1) the car 2) the truck 3) they both have the same momentum change 4) can’t tell without knowing the final velocities A small car and a large truck collide head-on and stick together. Which one has the larger magnitude of momentum change?
Because the total momentum of the system is conserved, that means that p = 0 for the car and truck combined. Therefore, p car must be equal and opposite to that of the truck (– p truck ) in order for the total momentum change to be zero. Note that this conclusion also follows from Newton ’ s Third Law. Follow-up: Which one feels the larger acceleration? 1) the car 2) the truck 3) they both have the same momentum change 4) can’t tell without knowing the final velocities A small car and a large truck collide head-on and stick together. Which one has the larger magnitude of momentum change?
1) the superball 2) the blob of clay 3) it doesn’t matter—they will be equally effective 4) you are just too lazy to throw anything You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it?
The superball bounces off the door with almost no loss of speed, so its p (and that of the door) is 2mv. The clay sticks to the door and continues to move along with it, so its p is less than that of the superball, and therefore it imparts less p to the door. 1) the superball 2) the blob of clay 3) it doesn’t matter—they will be equally effective 4) you are just too lazy to throw anything You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it?