9th Grade Physical Science #8
Unit 6: Collision Course
Activity #8 Conservation of Momentum PHeT
Learning Goals
Students will be able…
· To define momentum and describe the variables that affect momentum.
· Diagram representations of "before-and-after" collisions using momentum vectors.
· Apply the law of conservation of momentum to solve problems of collisions.
To Begin
The sports announcer says,
"Going into the playoffs, the Seahawks have the momentum." The headlines declare "Seahawks Gaining Momentum."
Momentum is a commonly used term in sports. A team that has a lot of momentum is really on the move and is going to be hard to stop. Momentum is a physics term; it refers to the quantity of motion that an object has. A sports team that is on the move has the momentum. If an object is in motion (on the move) then it has momentum.
Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. Momentum is a vector quantity.
You will be using vectors to represent many quantities in this course. A vector is best described as a mathematical quantity that has both a magnitude (size) and a direction. Many quantities in physics are vector quantities (force and velocity!). A vector diagram uses an arrow drawn to scale and pointing in a specific direction to show the vector.
Vector Conventions
1. Showing Direction: Be neat. Use straight lines. For simplicity sake, our vectors will be drawn horizontally or vertically. Vectors pointed up (North) and to the right (East), will be positive, and, vectors pointed down (South) and to the left (West) will be negative.
2. Showing Magnitude: The magnitude (size) of a vector is shown by the length of the arrow. The longer the arrow the greater the magnitude. Always label the vector with the magnitude value (actual number and units)
Preliminary Questions
1. Define vector.
2. Define momentum and list the variables that affect momentum.
3. Consider the collision between a car and a truck. Is it possible for the car to have a greater momentum? How? What information would you need to decide which vehicle has the greater momentum?
Process and Procedures
Using Chrome, google ‘phet collision’. Select the first choice that appears. Click on ‘Download now’.
1. Before you play: Choose ‘Advanced’ tab. In the green box on the right side of the screen, select the following settings: 1 dimension, velocity vectors ON, momentum vectors ON, center of mass OFF, reflecting borders ON, momenta diagram ON, kinetic energy OFF, show paths OFF, show values OFF, elasticity 100%.
2. Drag the red ball (ball 1) and green ball (ball 2) further apart from each other on the screen. Observe the GREEN (velocity) and YELLOW (momentum) vectors that represent their motion.
a. Which ball has the greater velocity? ______
b. Which has the greater momentum? ______
c. Make a sketch of these two balls, with the appropriate labeled vectors (please use simple line arrows, where the momentum vector is below the velocity vector).
3. Before you play: Explain why the green ball (ball 2) has more momentum but less velocity than the red ball (ball1) (HINT: what is the definition of momentum?).
4. 100% elastic collisions mean the objects will bounce off each other without losing any energy. Push “play” and let the balls collide. Only let them collide once!!! After they collide and you see the vectors change, click ‘pause’. Click ‘restart’ and watch the ‘momenta box’ (at the bottom right) during the collision.
5. Before you hit ‘play’, zoom in on the vectors in the ‘momenta box’ using the control sliders on the right of the box. Notice that the pink vector in the ‘momenta box’ is the result of adding vector 1 and vector 2. It is the total momentum of the system.
Use the “play”, “restart”, and “pause” to watch the collision and the vectors in the ‘momenta box’ several times.
a. What happens to the momentum of the red ball after the collision?______
b. What about the green ball (ball 2)? ______
c. Explain what happens to the total momentum (pink vector) of the system (both the red and green ball)?
6. When the motion is paused, change the mass of the red ball to match that of the green ball. Do NOT play!
a. Which ball has greater momentum now? ______Explain why:
b. How has the total momentum of the system changed? ______
c. Predict what will happen to the motion of the balls after they collide.
7. Push “play” and watch the simulation. Pause it once the vectors have changed.
a. What happens to the momentum of the red ball after the collision? (discuss magnitude & direction)
b. What about the green ball? ______
c. What about the total momentum of both the red and green ball?
8. Change the elasticity to 0% (no bouncing off each other) and the masses back to the original mass. Predict the motion of the balls after the collision.
9. Watch the simulation, and then pause it once the vectors have changed.
a. What happens to the momentum of the red ball after the collision?
b. What about the green ball?
c. What about the total momentum of both the red and green ball?
10. Experiment a little by running additional simulations. Vary the situations as much as possible.
Mass of Red Ball / Mass of Green Ball / % elasticity / Is there a change in the velocity of the red ball after crash? Green ball? / Is there a change in the momentum of the red ball after crash? Green ball? / Is there a change in total momentum during simulation? (yes or no)11. Complete this summary of the Law of Conservation of Momentum:
When two objects collide the total momentum of the system (2 objects) before the collision is ….Stop and Think
In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object. Momentum = mass • velocity
In physics, the symbol for momentum is the lower case "p". Thus, the above equation can be rewritten as
p = m • v
where m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.
Variable / What it represents / SI Unitp / momentum (vector quantity) / kg•m/s
v / Velocity (vector quantity) / m/s (meters/second)
m / Mass / Kg (kilograms)
The units for momentum would be mass units times velocity units. The standard metric unit of momentum is the kg•m/s.
1. In the scenario above the mass of the truck is 44,000 kg and the mass of the car is 10,000 kg. Both vehicles are traveling at 25 m/s. (car has a + velocity, truck has a -velocity)
a. During the collision, which force is greater? The force of the truck on the car or the force of the truck on the car. Draw labeled force vectors above the car and truck (you will not know the magnitude of F).
b. Calculate the momentum of the truck prior to the collision? Show your work and use units! Draw this value as a labeled vector (p truck initial) above the truck diagram.
c. Calculate the momentum of the car prior to the collision? Show your work. Draw this value as a labeled vector (pcar initial above the car diagram.
d. Calculate the total momentum of the car- truck system before the collision by adding ptruck initial
and pcar initial. Draw this value as a labeled vector (ptotal initial) below the car-truck diagram.
e. The car and truck are stuck together after the collision. What is the final total momentum of the car-truck system? Which direction would you expect the car-truck system to travel? Use the law of conservation of momentum!
f. Represent this momentum value and momentum direction as a labeled vector on your drawing
(ptotal final).
g. You should be able to calculate the mass of the car-truck system; and, you know the momentum. Can you use some algebra to figure out the velocity of the car-truck system after the collision?