9th Grade Physical Science #9
Unit 7: Collision Course
Activity #9: Sticky Situation
Learning Goals
Students will practice concepts relating to force, velocity and momentum that they have already encountered.
Students will apply those concepts in solving problems.
To Begin
In Activity #7 you developed a way to quantify the amount of force an object experiences during a bouncing collision. This type of collision is called an elastic collision. Elastic collisions occur when colliding objects rebound or bounce off each other. But not all collisions result in bouncing. In Activity #8, you also experienced a collision where objects hit and stick. This type of collision is called an inelastic collision.
When a variable does NOT change in a before-and-after event then that variable is conserved. Remember, how the total momentum of the system in both our tennis ball activity and in the Collision PHET did not change? This illustrated that momentum is conserved! If you look at data, you will see that yes, momentum is conserved within the range of uncertainty. Even though the velocities of two objects can change during a collision, total momentum never changes in any interaction between two objects. Momentum is conserved in both elastic and inelastic collisions. This is called the Law of Conservation of Momentum.
Preliminary Practice
Let’s develop a mathematical expression for predicting what happens to objects during a hit-and-stick (inelastic) collision. See the figure below.
Complete the statements in the first column and second column by using appropriate mathematical symbols (+, -, =) or words. Be sure to work through these thoughtfully with your group and see how each statement is connected to the statement above and below it.
Expression / DescriptionF1on2 ______-F2on1 / Expression that demonstrates that forces come in ______that are equal in ______and opposite in ______(Newton’s 3rd Law)!
∆t1 = ∆t2 / Objects experience the ______contact time with each other in a collision.
m1∆v1 = - m2∆v2
∆p1=-∆p2 / Change in momentum of one object in a collision is ______the change in ______of the other object. This equation is one statement of the Law of Conservation of ______.
How can we use this equation to predict the velocity of a system after an inelastic collision?
m1∆v1 = - m2∆v2
becomes
(m1v1f - m1v1i) = - (m2v2f - m2v2i) / We can rewrite m∆v because ∆ is calculated by ______minus ______.
Remember, f means ______and i means ______.
m2v2i + m1v1i = m1v1f + m2v2f
p(1+2)i = p(1+2)f
ptotal i = ptotal f / We can rearrange the equation to show that the initial momentum of the system ______the final momentum of the system (Law of Conservation of Momentum).
m2v2i + m1v1i = msystemvsystem i
m1v1f + m2v2f = msystemvsystem f / The momentum of car 1 + momentum of car 2 ______the momentum of the system (both cars added together)
msystemvsystem i = msystemvsystem f / Law of conservation of momentum states that the total momentum of the system before the collision ______the total momentum of the system after the collision.
msystem = m1 + m2
ptotal I = (m1 + m2)vsystem f / In this scenario, if we know the the initial momentum of the system (total initial p) we can solve for the final velocity.
ptotal I = vsystem f
(m1 + m2) / Now we have an equation we can use to predict the final velocity of an ______collision! Rearrange the variables to solve for the final velocity of the system.
1. Two volleyball players on opposite sides of the net jump into the air and hit the ball at the same time, and the ball does not move but comes to rest midair. What can you say about the momentum of each of the player’s hands:
a. What does the law of conservation of momentum say must be true about Δp of each hand?
b. After the collision, if each hand has a vf = 0, then what can we say about the pf of each hand? Explain HOW you know.
c. What must be true about the pi of each hand? Explain HOW you know.
d. Does that mean the vi of each hand was the same? Explain why or why not. (Hint: p = m•v)
2. A baseball player swings a 1-kg baseball bat at 50 m/s and collides with a 0.15-kg baseball that is pitched at 40 m/s. Use the directions that are modeled in the image (bat is moving to the right, ball to the left). An elastic collision.
a. Complete the before-and-after collision table below. Show your work in the space provided.
/ Momentum Before Collision (kg·m/s) / Momentum After Collision (kg·m/s) / Momentum Change(kg·m/s)
Baseball Bat / +35
Baseball
Total Momentum
b. Draw a vector diagram of the momentum of the baseball bat-baseball collision. Include initial momentum and the change in momentum for each.
Bat kg•m Ball
s
pi
pf
Δp
c. Determine the velocity of the ball (vball f)after the collision. Use pball f and mball. Show your work, equations and units!
3. Two hockey players collide mid-rink and slide together into the wall. The mass of Player A is 80-kg and the mass of Player B is 95-kg. Player A was traveling to the right at 15 m/s and Player B was traveling to the left at 10 m/s. Is this an elastic or inelastic collision? ______
a. Complete the before-and-after collision table below. Show your work in the space provided.
Momentum Before Collision (kg·m/s) / Momentum After Collision (kg·m/s) / Momentum Change(kg·m/s)
Player A
Player B / +135
Total Momentum
b. Draw a vector diagram of the momentum of the hockey player collision. Include initial momentum of Player A, initial momentum of Player B, and the change in momentum for each.
Player A kg•m Player B
s
pi
pf
Δp
c. Determine the velocity of both players (vsystem f)after the collision. Use ptotal and msystem. Show your work, equations and units!