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Rolling downhill, again
How are forces and acceleration related?
Materials:
 inclined track and ball
 timer
 Pasco cart
 Rubber bands
 A ceramic ball and a Styrofoam ball
 Ball of clay
 2 N weight
Questions:
The world record for running 100 m is about 10 seconds. What is the average speed?
Red 5 m/sec Yellow 0 m/sec Green 10 m/sec Blue 0.1 m/sec
When is the runner accelerating?
Red Mostly at the very beginning of the race
Yellow The acceleration is constant
Green All the time, but more at the beginning
Blue All the time, but more towards the end
What is the largest acceleration (numerical value)?
Red 10 m/s2 Yellow 10 m/s Green 5 m/s Blue 20 m/s2
How far does the runner go in the first second?
Red 10 m Yellow more like 5 m Green barely 1 m Blue Not clear
At the start of the race, the runner has one foot on a starting block.
Red She pushes herself forward
Yellow She pushes back on the block, and the block pushes her forward (Law of Inertia)
Green She pushes back on the block; the block pushes her forward (Law of Interaction)
Blue The starting block prevents a false start
What is the acceleration of a car starting
from a stoplight?
Red 10 m/s
Yellow 0
Green 2 m/s2
Blue 10 m/s2
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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 5 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
5 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
5 measurements of how long it takes for the ball to roll the length of the track.
4. 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)
5 cm
56 cm
10 cm
56 cm
15 cm
56 cm
5. Calculate the average speed for each steepness.
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 = ½ (final speed + initial speed)
In the experiments you just did, the initial speed was zero. Then
final speed = 2 x 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)
Now calculate the acceleration for the ball rolling down the ramp, for each steepness.
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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?
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Mass Effect
Why big things seem to go slowly
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?
8. Why do hammers have heavy heads?
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9. According to what you have observed, how are force, motion, and mass related?
Check: 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.
8. 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 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 x 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.
Egg Drop
Why do things break when they fall to the floor?
Materials
A ball of clay
2 N weight
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?
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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?
6. A car is going 15 m/s (33 mph) but then comes to a stop at a red light.
process there is a force on the passenger in the car. Estimate its size.
During this
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: Please discuss this activity with an instructor
Check: Please do not do the activity 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:
9. How fast do cars drive on Euclid Avenue?
How long does it take for a car to get up to speed after the light turns green?
Make a graph showing the velocity of a car driving on Euclid Avenue after the light turns
green.
10. According to your graph, what is the acceleration of the car during the first second?
11. What forces act on a passenger in the car, right after the light turns green? (name,
direction, and numerical magnitude)
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*If you were to move the level along the track you made for the rolling ball, taking the
same path as the ball and going the same speed, where would the bubble be centered and
where not? When the bubble was off-center, which direction would it be pointing?
Explain by drawing a diagram showing the track and the bubble level.
Bubble is centered when the level is moving
in a straight line at constant speed. It is offcenter, pointing towards the center of the
curve, when it is changing direction
>What is the acceleration of a car starting at a stoplight?
It takes 2 to 4 seconds to get to 22 mph (10 m/s), so the acceleration is more than 2.5 m/s2
and less than 5 m/s2. The larger acceleration will be a little uncomfortable for the
passengers.
*Suppose we were on a bus, and had a carpenter’s level which we put on a level spot on
the floor. What would be bubble do
>when the bus starts moving?
It points forwards, because the bus is accelerating.
>when the bus is traveling down Euclid Avenue at constant speed?
It is centered, because the bus is not accelerating
>when the bus stops?
It points backwards.
>when the bus makes a right turn?
It is off-center to the right.
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