Download Name Period Date Student Sheet 3.1 Conceptual Physical Science

Name
Period
Student Sheet 3.1
Date
Conceptual Physical Science—Explorations
Acceleration from a Velocity-Time Graph
A boulder rolling downhill changes its velocity continually. In other words, it accelerates. The graph
below shows a coaster’s motion in a 10-second interval as it goes from rest to a final velocity of 25
m/s.
What is the equation that represents the rolling boulder’s motion? You can get it from the graph. Just
look at the graph to find the y-intercept. Then, to get the slope, choose two points. The difference of
the y coordinates is the “rise” and the difference of x coordinates is the “run.” Calculate the slope by
dividing the rise by the run. Plug these values into the general equation for any straight line:
y = kx + b
where k is the slope and b is the y-intercept.
The y-intercept of the boulder’s velocity-time graph is 0 as you can tell by inspection. We’ll choose two
widely spaced points to calculate the slope; (10 s, 25 m/s) and (0 s, 0 m/s) are convenient. Notice that
the rise is equal to the change in speed of the boulder (∆v = vf – v0)* and the run is the change in time
(∆t = tf – t0).
Slope = k = f(rise,run) = f(∆v,∆t) = f(vf – v0,tf – t0) = f(25 m/s – 0 m/s,10 s – 0 s)
k = f(25 m/s,10 s) = 2.5 m/s2
Can you see that the slope has units of acceleration, m/s2? This is because the slope of the velocitytime graph is acceleration! Remember that the coaster’s acceleration equals its change in velocity per
second. The graph’s slope k = ∆v/∆t —the definition of acceleration!
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The equation for the rolling boulder’s motion has the same form as the general equation for a straight
line: y = kx + b. However, we substitute the rolling boulder’s specific variables t and v for the generic
variables x and y. And we substitute the numerical values with their units for the y-intercept and
slope. So the equation for the rolling boulder’s motion is
v = (2.5 m/s2)t + 0 m/s = (2.5 m/s2)t
Now look at the graph below. It shows the velocity of an airplane accelerating down the runway. One
observer plotted the line marked (a). Another observer at a different position on the runway plotted
line (b).
1.
What is the equation for line (a)?
2.
What is the equation for line (b)?
3.
What is the acceleration of the aircraft according to line (a)?
4.
What is the acceleration of the aircraft according to line (b)?
5.
The y-intercept for observer (a) is different from observer (b). How can you explain this?
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And now look at this graph, which represents the motion of a vehicle that changes its acceleration
twice.
6.
Find the acceleration of each section of the graph, labeled (a), (b), and (c).
7.
Write a sentence describing the vehicle’s motion in as much detail as the graph allows.
8.
What is the general equation for velocity, given a nonzero initial velocity? (Hint: Use the graph and
the general equation for a line to figure this out.)
* The symbol ∆ is the Greek letter delta. It stands for difference. The symbol vf stands for final velocity
and v0 stands for initial velocity.
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Name
Period
Date
Conceptual Physical Science—Explorations
Student Sheet 3.2
Exploring Friction
Procedure
Visit each station with your group and answer the questions on the next page. Be sure to leave your
station just as you found it before you move on.
1.
Pull the brick across the board. Use a spring scale to measure the force needed. Next, rub the
board with soap. Repeat pulling the brick and measuring the force. Now, arrange pencils in a
row. Place the brick on the pencils, pull again, and record the force.
Questions: How much force did you need to pull the brick each time?
Why did the soap affect the force required?
Which pull involved rolling friction?
Which involved sliding friction?
2.
Set the can full of sand on the jar lid. Try to spin it. Now put a circle of marbles on the lid and
repeat.
Questions: What type of friction did you encounter in each case?
Why was the jar easier to spin when you placed it on the marbles?
3.
Attach the rubber band to the end of the skateboard. Pull the rubber band so the skateboard
moves at constant velocity. Ask your lab partner to measure the length of the rubber band as you
pull the skateboard. Now tape the wheels of the skateboard so they are locked. Repeat pulling the
skateboard, at the same speed as you did before. Again measure and record the length of the
rubber band.
Questions: The length of the rubber band is directly related to the force pulling the skateboard.
When did the skateboard require more force to pull?
Which produces greater force, rolling friction or sliding friction?
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4.
Crumple a piece of paper into a ball. Drop it at the same time and from the same height as a flat
sheet.
Questions: What kind of friction do the pieces of paper encounter as they fall?
Which piece of paper falls faster? Why?
5.
Make a ramp by leaning the board against some stacked books. Place the textbook on top of the
ramp. Does it slide? Have a partner lift the ramp to vary its slope. Find the angle of the board at
which the textbook begins to slide.
Questions: Estimate the angle of the board when the book begins to slide.
What force holds the book on the board before the book slides?
What forces act on the board as it slides down the ramp?
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