physics unit 5: momentum and collisions topic 5.1 – momentum and impulse topic 5.2 – elastic...
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The momentum (p) of an object is a vector quantity defined as its mass times its velocity: p = mv It doesn’t have its own derived unit to describe it like force (Newtons), or power (Watts), so we just take the units for mass (kg) and velocity (m/s) and multiply them together to get: kg x m/s, read as “kilogram meters per second”. Understanding momentum is important when trying to figure out what happens when two objects collide, as we’ll get to in topics 5.2 and 5.3. An object with more momentum will do more to influence how objects move after a collision. Two objects with the same momentum will exactly stop each other in a head-on collision. Image from Bing ImagesTRANSCRIPT
Physics Unit 5:Momentum and Collisions
Topic 5.1 – Momentum and ImpulseTopic 5.2 – Elastic CollisionsTopic 5.3 – Inelastic Collisions
Learning Goal: You will understand the concepts of momentum and impulse and how mass, velocity, and time relate to them.
Success Criteria: You will know you have met the learning goal when you can calculate the momentum of an object and the impulse imposed on an object.
Image from Bing Images
The momentum (p) of an object is a vector quantity defined as its mass times its velocity:
p = mvIt doesn’t have its own derived unit to describe it like force (Newtons), or power (Watts), so we just take the units for mass (kg) and velocity (m/s) and multiply them together to get: kg x m/s, read as “kilogram meters per second”.
Understanding momentum is important when trying to figure out what happens when two objects collide, as we’ll get to in topics 5.2 and 5.3. An object with more momentum will do more to influence how objects move after a collision. Two objects with the same momentum will exactly stop each other in a head-on collision.
Image from Bing Images
Task 5.1.1 (4 points): Calculate the momentum of the following objects.a) A .5kg soccer ball traveling at 18m/s.b) A 1200kg car travelling at 26m/s.c) A 7050kg satellite travelling at 7687m/s.d) The Earth (5.97 x 1024 kg) as it orbits the sun at 30,000m/s.
Image from Bing Images
Task 5.1.2 (4 points): Answer the following questions. They may require the use of multiple equations.a) Which has more momentum, a .16kg bullet travelling at 230m/s or a 62kg runner travelling at 11m/s?
b) What would the velocity of a 1350kg car have to be for it to have the same momentum as a 5200kg truck travelling at 15m/s?
c) You exert a 67N force (about 15 pounds) on a 35kg shopping cart for 1.5 seconds. What will its momentum be if it starts from rest?
d) A meteoroid travelling through space has momentum of 370,000 kg x m/s. How far will it travel in 18 seconds if it’s mass is 12.8kg?
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A result of newton’s third law (that every action has an equal and opposite reaction) is that momentum is conserved when two objects interact. This is called the law of conservation of momentum. We can use it to infer velocities of objects after they collide (next topic) and when they push off of each other (this topic).
For example, if two ice skaters starting from rest (p = 0) push off each other, they will both have the same momentum but in opposite directions. Thus, the mass x velocity of one skater will equal the mass x velocity of the other, but in opposite directions. Since momentum is a vector quantity, the net momentum of the two skaters is still zero (one skater is moving in the positive direction and one is moving in the negative direction).
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Task 5.1.3 (4 points): Answer the following questions.a) A 52kg skater is moving at 3.2m/s to the left after pushing off of another skater. If the other skater is 45kg, what is her velocity?
b) If a bullet is fired at 275m/s, how fast will the gun move in the other direction if the bullet is .04kg and the gun is 1.5kg?
c) A satellite needs to slow down, so it shoots a 10kg mass straight ahead at 170m/s. If the speed of the satellite decreases from 800m/s to 770m/s, what is the mass of the satellite?
d) A 74kg astronaut fixing a solar panel on the international space station gets angry and throws a 1.7kg wrench at 13m/s. If he starts from rest, what will his velocity be after he throws it?
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ImpulseBy substituting in Δv/Δt for acceleration in F = ma, and remembering that p = mv, we get F = Δp/Δt, or:
FΔt = ΔpThis is called the impulse. The impulse is the change in momentum of an object. From this we see that a force applied for a greater amount of time will induce a greater change in momentum. It also shows that to stop a moving object, it requires less force (thus it’s safer) if the force is applied over a longer time. That’s why cars are built with crumple zones; so cars come to a stop over a slightly greater distance, thus reducing the force that the occupants feel.
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Task 5.1.4 (4 points): Answer the following questions.a) What force is required to change a car’s momentum from 2500 kg x m/s to 6500 kg x m/s in 4 seconds?
b) If you push on a cart with a 100N force for 30 seconds, what is its change in momentum?
c) Suppose you throw a .25kg ball of playdoh at a wall at 18m/s and it sticks to the wall. What is the force that the wall must exert on the playdoh to stop it in .035 seconds?
d) How long does it take for a 100kg missile to be accelerated from 125m/s to 175m/s with a 660N force?
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Task 5.1.5 (4 points): Write a two-paragraph (4 sentences per paragraph) summary of what you learned in this topic.
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