University:
California Institute of Technology
Course:
EE/APh 40 | Physics of Electrical Engineering
Academic year:

2022
Views:

490

Pages:

26
Author:

SpaceCadet101

8.5 Collisions Whenever objects collide in the absence of external forces, the net momentum of the objects before the collision equals the net momentum of the objects after the collision. 8.5 Collisions The collision of objects clearly shows the conservation of momentum. 8.5 Collisions Elastic Collisions When a moving billiard ball collides head-on with a ball at rest, the first ball comes to rest and the second ball moves away with a velocity equal to the initial velocity of the first ball. Momentum is transferred from the first ball to the second ball. 8.5 Collisions When objects collide without being permanently deformed and without generating heat, the collision is an elastic collision. Colliding objects bounce perfectly in perfect elastic collisions. The sum of the momentum vectors is the same before and after each collision. 8.5 Collisions a. A moving ball strikes a ball at rest. 8.5 Collisions a. A moving ball strikes a ball at rest. b. Two moving balls collide head-on. 8.5 Collisions a. A moving ball strikes a ball at rest. b. Two moving balls collide head-on. c. Two balls moving in the same direction collide. 8.5 Collisions Inelastic Collisions A collision in which the colliding objects become distorted and generate heat during the collision is an inelastic collision. Momentum conservation holds true even in inelastic collisions. Whenever colliding objects become tangled or couple together, a totally inelastic collision occurs. 8.5 Collisions In an inelastic collision between two freight cars, the momentum of the freight car on the left is shared with the freight car on the right. 8.5 Collisions The freight cars are of equal mass m, and one car moves at 4 m/s toward the other car that is at rest. net momentum before collision = net momentum after collision (net mv)before = (net mv)after (m)(4 m/s) + (m)(0 m/s) = (2m)(vafter) 8.5 Collisions Twice as much mass is moving after the collision, so the velocity, vafter, must be one half of 4 m/s. vafter = 2 m/s in the same direction as the velocity before the collision, vbefore. 8.5 Collisions The initial momentum is shared by both cars without loss or gain. Momentum is conserved. External forces are usually negligible during the collision, so the net momentum does not change during collision. 8.5 Collisions External forces may have an effect after the collision: • Billiard balls encounter friction with the table and the air. • After a collision of two trucks, the combined wreck slides along the pavement and friction decreases its momentum. • Two space vehicles docking in orbit have the same net momentum just before and just after contact. Since there is no air resistance in space, the combined momentum is then changed only by gravity. 8.5 Collisions Perfectly elastic collisions are not common in the everyday world. Drop a ball and after it bounces from the floor, both the ball and the floor are a bit warmer. At the microscopic level, however, perfectly elastic collisions are commonplace. For example, electrically charged particles bounce off one another without generating heat; they don’t even touch in the classic sense of the word. 8.5 Collisions An air track nicely demonstrates conservation of momentum. Many small air jets provide a nearly frictionless cushion of air for the gliders to slide on. 8.5 Collisions think! One glider is loaded so it has three times the mass of another glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion of the gliders after the collision. 8.5 Collisions think! One glider is loaded so it has three times the mass of another glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion of the gliders after the collision. Answer: The mass of the stuck-together gliders is four times that of the unloaded glider. The velocity of the stuck-together gliders is one fourth of the unloaded glider’s velocity before collision. This velocity is in the same direction as before, since the direction as well as the amount of momentum is conserved. 8.5 Collisions do the math! Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch? 8.5 Collisions do the math! Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch? Momentum is conserved from the instant before lunch until the instant after (in so brief an interval, water resistance does not have time to change the momentum). 8.5 Collisions do the math! 8.5 Collisions do the math! Suppose the small fish is not at rest but is swimming toward the large fish at 2 m/s. 8.5 Collisions do the math! Suppose the small fish is not at rest but is swimming toward the large fish at 2 m/s. If we consider the direction of the large fish as positive, then the velocity of the small fish is –2 m/s. 8.5 Collisions do the math! The negative momentum of the small fish slows the large fish. 8.5 Collisions do the math! If the small fish were swimming at –3 m/s, then both fish would have equal and opposite momenta. Zero momentum before lunch would equal zero momentum after lunch, and both fish would come to a halt. 8.5 Collisions do the math! Suppose the small fish swims at –4 m/s. The minus sign tells us that after lunch the two-fish system moves in a direction opposite to the large fish’s direction before lunch. 8.5 Collisions How does conservation of momentum apply to collisions?

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