Acceleration, Force, and Impact (Egg drop)
Today’s Goal: To understand the relation between force, mass, and acceleration
(Newton’s second law).
Discussion:
Each group should hand in one copy of this page at the end of class
Group:
Names of group members present:
> Hannah is weighing a cantaloupe using a weightless scale. There
are many forces acting, as indicated by the diagram.
A. Some of these forces are related to others by the Law of
Interaction. List these relationships (please give the full name of each
force).
B. Some of these forces are related to others by the Law of Inertia.
List these relationships.
C. Suppose the scale has weight (this force is not indicated on the diagram). How does
this change any of the answers to parts A and B?
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What to do
1. Set up an inclined track, so that the upper end is 5 cm higher than the lower end.
Make five measurements of how long it takes for a metal ball to roll the length of the
track.
2. Raise the upper end of the track so that it is 10 cm higher than the lower end. Make
five measurements of how long it takes for the ball to roll the length of the track.
3. Raise the upper end of the track so that it is 15 cm higher than the lower end. Make
five measurements of how long it takes for the ball to roll the length of the track.
4. Raise the upper end of the track so that it is 20 cm higher than the lower end. Make
five measurements of how long it takes for the ball to roll the length of the track.
5. Determine the median time to roll down the incline for each of the cases, and enter
this in the table below (the last two columns are explained below).
Steepness
Distance
Time
Average
Final Speed Acceleration
Speed
(see below)
0 cm
56 cm
0 sec
0 sec
0 m/sec
0 cm/sec2
5 cm
56 cm
10 cm
56 cm
15 cm
56 cm
20 cm
56 cm
6. Calculate the average speed for each steepness.
Tip
The final speed is different from the average speed. After all, it was going more slowly
at first, so it didn’t go as far in a small time interval than it did later. It turns out that for
this system the average speed actually is the average of the initial speed and the final
speed
Average speed = (Final speed + Initial speed)/2
In the experiments you just did, the initial speed was zero. Then
Final speed = 2 × Average speed
Use this to fill in the 4th column.
The acceleration is calculated by dividing the change in velocity (or speed, in the present
case) by the time it takes to change the speed. The initial speed was zero (if you just let
the ball go), so
Acceleration = (Final speed – Initial speed)/(Time interval)
= (Final speed)/(Time interval).
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Now calculate the acceleration for the ball rolling down the ramp, for each steepness.
6. Draw a graph showing how the acceleration varies with the steepness.
Please summarize the graph in words.
7. When you weighed the cart on the incline, gravity was pulling the cart down the
incline and the scale was providing a balancing force, to keep the cart from moving.
How did the downhill force vary with the steepness?
Comparing this with the results of today’s experiment, how is the force on a ball related
to its acceleration?
Check #1: Discuss about your thought with an instructor.
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Mass Effect
Why big things seem to go slowly.
Materials
 Pasco cart
 Rubber bands
 A ceramic ball and a Styrofoam ball
1. Attach a chain of three rubber bands to a Pasco dynamics cart. Use this to get the
cart moving, and to stop it again. What do you have to do to make the cart accelerate?
2. Put a weight on the cart, or even two
acceleration?
How does mass affect your ability to cause
3. Hold a blue ball in one hand and vigorously shake it. Compare this to shaking a
Styrofoam ball. Explain how the difference between the balls is related to the difference
in the way they shake.
4. The velocity of a ping pong ball is not constant during a game. When is the
acceleration the largest?
5. How is the large acceleration achieved?
6. When you use a hammer to drive a nail, the velocity of the hammer is not constant.
When is the acceleration the largest?
7. What causes this large acceleration?
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8. Why do hammers have heavy heads?
9. According to what you have observed, how are force, motion, and mass related?
Check #2: Explain the results of these activities.
Representing motion with graphs
How does a graph of position versus time reveal speed and acceleration?
On a graph of position versus time, the slope tells us the
speed. A steep slope means the object went a large
distance in a time interval (fast), and a small slope means
that it went a small distance (slow). Acceleration means
the speed is changing; then the curve is steep some places
and less steep others: it is not a straight line.
10. The graph at right represents the position of an object
at various times.
When was the object moving the fastest?
0 to 1 sec
1 to 2 sec
2 to 3 sec
3 to 4 sec
When was the object moving at nearly constant speed?
0 to 1 sec
1 to 2 sec
2 to 3 sec
3 to 4 sec
When was the object accelerating?
0 to 1 sec
1 to 2 sec
2 to 3 sec
3 to 4 sec
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Summary of this unit (so far):
We have met three laws that relate force and motion. These are called "Newton's Laws
of Motion" and are usually referred to by number ("The Second Law").
The Law of Inertia (The First Law): In the absence of external net forces, an object
moves with constant velocity.
The Law of Force and Acceleration (The Second Law): An unbalanced force will cause
an object to accelerate, so that
Net Force = Mass × Acceleration.
If the mass is measured in kilograms and the acceleration is measured in m/sec2, the
product of mass and acceleration is in newtons. An unbalanced force of 1 N force will
cause 1 kilogram to accelerate at 1 m/s2.
The Law of Interaction (The Third Law): If object A exerts a force on object B, object B
exerts an equal and opposite force on object A.
Falling Object
1. If you a drop a nickel and a steel ball at the same time from the same height, predict
which one will arrive at the floor first. Explain your prediction.
2. Do the experiment, and use the Law of Force and Acceleration to explain the result.
3. Determine how long it takes for the nickel to fall two meters, repeating the experiment
five times.
Use the median time to determine
the average velocity of the nickel
the final velocity of the nickel
the acceleration for the falling nickel.
4. You measured the mass and weight of a nickel in a previous activity. What were the
results?
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What is the unbalanced force acting on the nickel while it is falling? (What causes it, and
a numerical value)
What should the acceleration be, according to the Law of Force and Acceleration?
(numerical value)
5. While the nickel is falling, how is the velocity changing? On the graph below, draw
this relationship.
6. Alice threw an orange straight up. After a while, it came down again. Her group is
trying to decide when the acceleration was the largest.
Barb said, “The acceleration was largest just after it left her hand.”
Clara said, “The acceleration was the largest when the orange was at the highest point,”
Danielle said, “The acceleration was the largest just before the orange touched the floor.”
Eva said, “The orange wasn’t accelerating.”
Fern said, “The orange had constant acceleration.”
Who is right? What does the Law of Force and Acceleration have to say about the
orange?
Check #3: Discuss these questions with an instructor.
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Egg Drop
Why do things break when they fall to the floor?
Materials
A ball of clay, 2 N weight
What to do:
Make two balls of modeling clay, about 2 cm (1 inch) in diameter. They don't need to be
exactly spherical, but they should be smooth and round.
1. Gently place one ball on the table top. Then drop another ball from a height of 50 cm
(18 inches) onto the table. Compare the flat spots on the bottoms of the two clay balls.
What does the difference imply?
2. The clay ball weighs about 0.1 N. Gently lay the 2 newton weight on the ball that was
not dropped (don't drop the weight on the ball!). What size flat mark does this make on
the ball? What does this tell you about the size of the force on the ball as it hits the table?
3. Similarly drop a ball onto the floor from as high as you can reach. Or throw the ball at
the floor! Again, consider the force that is needed to squash the ball a similar amount.
4. Describe the forces acting on the ball and the acceleration of the ball at various times:
 before you dropped it;
 while it was falling;
 just as it hit the floor;
 1 second after hitting the floor.
What does the Law of Force and Acceleration say about these forces?
5. Why does a glass break when you drop it on a concrete floor, but might not break if
you drop it on the rug?
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6. A car is going 15 m/s (33 mph) but then comes to a stop at a red light, which takes
about 2 sec. During this process there is a force on the passenger in the car. Estimate its
size.
7. A car is going 15 m/s (33 mph) but then comes to a stop when it runs into a tree. The
seat belt and air bag stop the passenger in less than a meter, which takes less than 0.1
second. This involves a force on the passenger in the car. Estimate its size.
8. A car is going 15 m/s (33 mph) but then comes a stop when it runs into a tree. The car
doesn’t have an air bag and the seat belts are not in use. The passenger stops when he
encounters the windshield, which takes 0.001 second. Estimate the size of the force on
the passenger.
Check #4: Please discuss this activity with an instructor
Check #5: Please do NOT do the activities described in Q7 and Q8.
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Each group should hand in one copy of this page at the end of class
Group:
Names of group members present:
1. The speed limit in Centerburg is 35 mph (15 m/sec); at the city limit there is a sign
saying “Resume safe speed.” Maria starts accelerating at the sign but it is 5 seconds
before she reaches about 70 mph (31 m/sec). What is her acceleration?
2. How far does Maria go before she gets up to speed?
Andrea says, “75 meters from the city limits.”
Betsy says, “115 meters from the city limits.”
Carla says, “155 meters from the city limits.”
Who's right, and why?
3. On nice Saturdays there is a juggler at the Farmer's Market in downtown Lexington.
He can juggle 6 balls at once. Part of his secret is that he throws the balls very high, so
that he has lots of time after he throws a ball before he has to deal with it again. If it is 4
seconds between throwing the ball and catching it, how high did it go?
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Check #3
The gravitational force on a 0.005 kg nickel is 0.05 N. This is the only force on the
nickel while it is falling, so
Net force = 0.05 N (down) = mass × acceleration = 0.005 kg × acceleration
Therefore the acceleration is 10 m/s2 (down).
Since it is true for all masses in Lexington, KY that the weight (in newtons) is 10 times
the mass (in kilograms), all objects have the same acceleration while falling, and it is
constant (Fern was right about Alice’s orange).
This calculation shows why we don’t use “the weight of a kilogram” as a force unit. We
would get “The weight of a kilogram = the mass of a kilogram × the acceleration of a
falling kilogram”, which doesn’t tell us what the acceleration actually is.
The velocity of the falling nickel increases constantly in time
Velocity = acceleration × time
so that after 0.6 seconds it will be going 6 meters/second. The average velocity will be
smaller, and in fact is exactly half as large (3 m/s). Then, the distance the nickel has
gone is (average velocity)×(time interval) = 3 m/s × 0.6 s = 1.8 m.
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