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# Collisions

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### Collisions

1. 1. Collisions January 14th, 2009
2. 2. <ul><li>This clip clearly gives the driver a good reason to make sure occupants in the rear of the car are wearing their seat belts. Not wearing a seatbelt not only puts your life in danger but also anyone else who happens to be riding with you. </li></ul>The force from the seatbelt safely decelerates the driver, but the child in the back seat follows Newton's Law of Inertia and continues moving in the absence of a net force. The 60mph &quot;kid&quot; not only breaks its own neck but also the neck of the driver.
3. 3. <ul><li>This clip illustrates what happens to children in a car accident if they or their car seat are not properly belted in. (This particular car seat was flawed.) Remember, if the car was going 55mph, then any person or object in the car is also going that fast and will continue to go that fast until a net force acts on them to slow them down. </li></ul>It should be pointed out that the rotating dial makes 1 rotation in 1/10th of a second. It was used to measure small intervals of time on the film (pre-digital clock)
4. 4. <ul><li>In this clip we see a &quot;parent&quot; holding a &quot;child&quot; and neither of them wearing a seatbelt. As you can see, the &quot;parent&quot; not only allows harm to come to the &quot;child&quot; but actually hurts the child more as the child becomes an ineffective &quot;air bag&quot; for the parent. </li></ul>
5. 5. <ul><li>In this clip, we see that seat belts and child seats not only protect you in a frontal impact, they could also prevent a tragedy in rear end collision. </li></ul>They were at rest originally, and in the absence of a net force (from the seat belt) they remained at rest while the car they were in was accelerated by the net force from the car that hit them. Newton's first law can be a killer! In this clip, the station wagon literally gets accelerated out from under the &quot;kids&quot; sitting in the back.
6. 6. <ul><li>Cars are designed with crumple zones so they may slow down over a longer period of time, which keeps the force smaller (see impulse). However, this safety feature alone will usually not prevent serious injury or death to the occupants of a car during an accident. The crumple zone only slows the car more gradually. </li></ul>The only way it slows the occupants more gradually is if they are attached to the car. Otherwise, the car may come to rest more slowly but the people come to rest immediately upon striking the already stopped interior of the car. Stopping in a small amount of time means the force must be very large. This video clip shows some very dramatic scenes of car crash tests with test dummies who are not wearing seat belts. Specifically look for cars crumpling and people stopping in very small amounts of time.
7. 7. <ul><li>Seatbelts use two main ideas to protect passengers during a car accident. First, they slow the passenger down more slowly than the passenger running into steering wheel or dashboard. </li></ul>This keeps the force required to stop them smaller. (see impulse) It also prevents the person from contacting any of the glass windows in the car or continuing on to be stopped abruptly by the road, tree, or another automobile. The video clip above shows the role of the seatbelt during an accident.
8. 8. Momentum Conservation Principle <ul><li>One of the most powerful laws in physics is the law of momentum conservation. The law of momentum conservation can be stated as follows. </li></ul><ul><ul><li>For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. </li></ul></ul><ul><ul><li>That is, the momentum lost by object 1 is equal to the momentum gained by object 2. </li></ul></ul><ul><li>The above statement tells us that the total momentum of a collection of objects (a system) is conserved - that is, the total amount of momentum is a constant. </li></ul>
9. 9. <ul><li>Consider a collision between two objects - object 1 and object 2. For such a collision, the forces acting between the two objects are equal in magnitude and opposite in direction (Newton's third law). This statement can be expressed in equation form as follows. </li></ul><ul><li>The forces act between the two objects for a set time. Since they are colliding, this time must be the same! </li></ul><ul><li>If force and time are the same, impulse must be the same! </li></ul><ul><li>If impulse is the same, change in momentum must be the same </li></ul>
10. 10. <ul><li>The above equation is one statement of the law of momentum conservation . </li></ul><ul><ul><li>In a collision, the momentum change of object 1 is equal to and opposite of the momentum change of object 2 . </li></ul></ul><ul><ul><li>That is, the momentum lost by object 1 is equal to the momentum gained by object 2 . </li></ul></ul><ul><ul><li>In most collisions between two objects, one object slows down and loses momentum while the other object speeds up and gains momentum. </li></ul></ul>
11. 11. Vector Representation of Conservation of Momentum
12. 12. Practice! <ul><li>When fighting fires, a firefighter must use great caution to hold a hose which emits large amounts of water at high speeds. Why would such a task be difficult? </li></ul><ul><ul><li>The hose is pushing lots of water (large mass) forward at a high speed. This means the water has a large forward momentum. In turn, the hose must have an equally large backwards momentum, making it difficult for the firefighters to manage. </li></ul></ul>
13. 13. <ul><li>If a 5-kg bowling ball is projected upward with a velocity of 2.0 m/s, then what is the recoil velocity of the Earth (mass = 6.0 x 10^24 kg). </li></ul><ul><ul><li>Since the ball has an upward momentum of 10 kg*m/s, the Earth must have a downward momentum of 10 kg*m/s. </li></ul></ul><ul><ul><li>To find the velocity of the Earth, use the momentum equation, p = m*v. This equation rearranges to v=p/m. By substituting into this equation, </li></ul></ul><ul><ul><ul><li>v = (10 kg*m/s)/(6*10^24 kg) </li></ul></ul></ul><ul><ul><ul><li>v = 1.67*10-23 m/s (downward) </li></ul></ul></ul>