Download Stacey Carpenter

Newton’s 2nd Law of Motion
PPT
Developer Notes
 Prediction summary. Nerf darts? Mass carts (nice lead-in to momentum)?
 Force and acceleration (but no mass):
a. Mixer through thick or thin mashed potatoes
b. Bank account accelerating at $10/wk, then steady at $1000 when you start taking out
$10/wk. Accel, decel?
 Need exercises using 9.8 m/s2.
 Need exercises with Fnet.
 Should we discuss net acceleration? Fnet = manet . This is like an object sitting on a table. It
has a downward acceleration due to gravity, but it has an equal and opposite upward
acceleration due to the table. Actually due to the force from the table, and force = ma.
Version
08
Date
20031217
Who
dk




Revisions
Added version table
Moved Nerf warm-up to a summary activity
Goals
 Students should understand that force causes acceleration and that mass (inertia) resists
acceleration.
 Students should understand that acceleration and force are directly proportional.
 Students should understand that acceleration and mass are inversely proportional.
 Students should know the equation Fnet = ma
 Students should be able to manipulate the equation Fnet = ma.
Concepts & Skills Introduced
Area
physics
Concept
Newton’s 2nd Law of Motion
Time Required
Warm-up Question
Presentation
This is a very rich activity, and you could spend a lot of time on it. It is a good candidate for a
full lab report.
The summary questions are critical to understanding. They are meant to make sense of the setup
first (a diagram should help, and the review of vectors is good), then to look at what is happening
582713314
dk
Page 1 of 8
PPT
Newton’s 2nd Law of Motion
qualitatively, following Newton's lead. After the qualitative analysis, students can look at their
numbers to find the patterns.
The main thing to get out of it is that F = ma. At last we define force as more than a push or pull
- we can assign units to it. The definition came from Newton, who saw that a  F and a  1/m.
He put the two together to make a  F/m. Be sure to emphasize the qualitative aspects with the
students. The students may or may not be familiar with directly and inversely proportional. This
is a good opportunity to teach those concepts.
 If F, then a. If force goes up, acceleration goes up - they are directly related.
 If m, then a. If mass goes up, acceleration goes down - they are inversely related.
In fact, from the data,
 If F doubles, then a doubles - they are directly proportional.
 If m doubles, then a halves - they are inversely proportional.
 If force quadrupled, acceleration would quadruple, too. If force was times 10…
When the two are put together in one equation, the relationships still work. Since we know the
units for mass and acceleration, we can now make a new unit for force, called the Newton. The
units for the Newton are kgm/s2.
F = ma. So, if m is kg and a is m/s2, F is kgm/s2.
Graphs help here.
1. A graph of force vs. acceleration works nicely, ending up with straight lines through the
origin. Do separate lines for each cart setup. In this case, force (the weight) is the
independent variable, acceleration is dependent, and the mass of the car is a control. (Don't
worry about the slope on this graph. If acceleration was on the x-axis and force was on the yaxis, then the slope would be the total mass, F = ma, but it will read as more because of
friction.)
2. You can also graph total mass vs. acceleration. You'll get a hyperbola because they are
inversely related. That's a good lesson. If mass is the independent variable, 1/acceleration is
the dependent variable, and force is a control, you'll get a straight line through the origin.
(Don't worry about the slope on this graph. If a was on the x-axis, and 1/m on the y-axis, then
the slope would be force, a = F1/m, but it will read as less due to friction.)
3. A third graph would be acceleration vs. force/mass (the weight/total mass). The result is a
straight line through the origin. Force/mass is independent, acceleration is dependent, and the
slope is - well, it will be close to the acceleration of gravity! It should be about 6 or 7 rather
than 9.8. The difference is friction. A nice lesson. A mathematical treatment is shown below.
Lead a discussion to find the effect of the acceleration due to gravity in the activity. Here is a
sample of leading questions:
1. In our laboratory activity, we found the acceleration of a cart under a variety of conditions.
What causes an object to accelerate? (Force)
2. What provides the force that makes the cart accelerate? (the mass on the string)
3. What makes the mass on the string accelerate? (gravity)
4. If there were no string tied to the mass, how fast would it have accelerated? (9.8 m/s2)
582713314
dk
Page 2 of 8
PPT
Newton’s 2nd Law of Motion
5. Using the formula F = ma, what was the force on the mass? (mg. Be sure to put all units in
the mks system.)
As an extension, you can compute the acceleration of gravity from the data. It will end up too
low due to the friction, but that is a good lesson, too. In the lab data,
a  mweight/mtotal.
Change the proportionality to an equation,
a = kmweight/mtotal,
then solve for k.
k = amtotal/mweight
The students should get numbers around 6 or 7. Ask them what number near that relates to how
fast things accelerate. They should come up with 9.8. So why is their number smaller? Friction!
A return to forces and vectors.
Here is a more complete derivation, which you can use to make it easier if the previous one is too
difficult. To compute g, start with a = F/m.
a = Fweight/mtotal
Since the force on the weight is the mass of the weight times gravity,
a = gmweight/mtotal
To find g, rearrange the equation to form
g = a(mtotal kg)/(mweight kg).
Here is a good summary POE. Use two nerf dart guns. Load one dart with some paper clips to
make it heavier. Ask the students to predict which one will hit first if you shoot them straight
down at the same time. (The lighter one will hit first. Same force, less mass equals more
acceleration while on the gun. After that they both accelerate at g. If the kids don't get it, try
another POE shooting straight up. Same explanation. Or shoot straight sideways.)
Assessment
Writing Prompts
1.
Relevance
Answers to Exercises
Answers to Challenge/ extension
582713314
dk
Page 3 of 8
PPT
582713314
dk
Newton’s 2nd Law of Motion
Page 4 of 8
PPT
Newton’s 2nd Law of Motion
Background
Newton took Galileo’s concept of inertia and developed his first law of motion – inertia. But
what does inertia mean? If something isn’t moving, and you want to get it moving, you need to
push it or pull it – apply a force. What happens when you apply the force? It’s motion changes –
it either speeds up, slows down, or changes direction - it’s velocity changes. A change in velocity
is acceleration. If it’s a bigger thing - more mass, more inertia - you need a bigger force to get it
moving as quickly. So force, acceleration, and mass (inertia), are related. From these ideas
Newton developed his 2nd law of motion.
Problem
Find the relationship between force (F), mass (m), and acceleration (a).
Materials
1
mass cart with ball bearing wheels
1
string about 1m in length
1
table pulley
1
mass set
1
meter stick
1
stopwatch
1
2000 gram spring scale
(1
c-clamp)
(1
1x3 6” long)
Procedure
1. Work in groups of three.
2. Set up the equipment as shown.
a. The table or bench surface should be as clean, smooth, and level as possible.
b. The cart should make as long a run as possible before the weight hits the floor.
c. Be sure that the string pulls parallel to the table surface, not up or down.
3. Hold the cart so that the weight is just below the pulley. Release the cart and time how long it
takes to go a distance (the distance depends on your setup - the longer, the better).
582713314
dk
Page 5 of 8
PPT
Newton’s 2nd Law of Motion
4. Record the following data:
a. Mass of cart
b. Mass on cart
c. Mass of weight on string
d. Total mass: (mass of cart) + (mass on cart) + (mass of weight on string)
e. Distance cart traveled
f. Time cart traveled
5. Test the following 9 combinations (take multiple samples for each and average them):
a. Weight on string:
30 g, 60 g, 90 g.
b. Cart: empty, with 500 g, loaded so that its total mass is double the empty mass
Summary
1. Draw a diagram of the setup showing the vectors for the forces on the weight and on the cart.
2. The cart is initially not moving. Due to the cart’s inertia, a force is required to start it moving.
What supplies the force?
3. As the force pulls on the cart, does the cart maintain the same speed, or does it accelerate?
4. Why do we need to add up the mass of everything in the system? (Hint: what other mass
accelerates at the same rate as the cart?)
5. Make a new table to summarize your data. Make 3 columns for the force and 3 rows for the
total mass as shown. Compute the acceleration of the cart for each combination and enter it
in the table.
Table of acceleration
0.03 kg
0.06 kg
0.09 kg
empty cart kg
cart + 0.5 kg
double cart kg
6. As the force increases with (almost) the same mass, does the acceleration increase or
decrease?
a. What happens to the acceleration when the pulling force doubles?
b. Look at the rest of your data as the force increases. What's the pattern?
c. Describe the relationship in a formula.
7. As the mass increases (with the same force), does the acceleration increase or decrease?
a. What happens to the acceleration when the total mass doubles?
b. Look at the rest of your data as mass increases. What's the pattern?
c. Describe the relationship in a formula.
8. If force is related to acceleration, and mass is related to acceleration, then all three must be
related.
a. Describe the relationship between acceleration, force, and mass in a formula,
based on your data.
9. Can you figure out how to graph the data? There will be multiple graphs. In each case, which
variable is independent, dependent, or a control? (Hint: acceleration is always the dependent
variable.)
582713314
dk
Page 6 of 8
PPT
Newton’s 2nd Law of Motion
Reading
Isaac Newton is one of the most famous scientists. His formula, F = ma, is the most important
formula in early physics and, along with Einstein's E = mc2, is one of the two best-known
formulas in all of physics.
Newton looked at the movement of objects, just as Galileo did. He started with inertia and
acceleration, which Galileo had defined. Newton knew that a force was needed to accelerate an
object. He experimented and found that acceleration is proportional to the force; the harder you
push, the more the object accelerates. Push twice as hard, and the object accelerates twice as fast.
aF
He also found that acceleration is inversely proportional to mass; the bigger the object, the harder
it is to get it going. If the object has twice the mass, the acceleration will be half as much.
a  1/m
Then he put the two together.
a  F/m
Later, the proportionality was made into an equation
a = F/m, or F = ma
and force was defined as more than a push or pull. The units for force are kgm/s2, which are
called Newtons, in honor of Isaac Newton. For example, a net force of 1 N acting on a 1 kg
object causes it to accelerate at 1 m/s2. On Earth, a 1 kg object weighs 9.8 N.
Exercises
1. Two identical cars start racing. One accelerates faster than the other. What can you say about
the forces on them?
2. Two cannonballs are shot with the same force and in the same direction, but one goes farther
than the other. Are they the same mass?
3. A 16 lb bowling ball is rolled down the alley. A 12 lb ball is then rolled down the alley with
less force. Can you say which will go faster?
4. If you double the force on an object, what will happen to its acceleration?
5. A car is going 60 kph down the highway and it goes around a turn but maintains its speed at a
steady 60 kph. Is it accelerating?
6. The batter in baseball hits a long fly ball to deep left field. After the ball has left the bat, and
while it is still going up, is it accelerating?
7. If you apply a net force of 10 N to a 10 kg rock, how fast will it accelerate?
8. What is the net force on a 1,000 kg car if it accelerates at 2 m/s2?
9. A rocket in space fires an engine with 10,000 N of force. It accelerates at 0.5 m/s2. What is
its mass?
10. What is the net force on a basketball at rest in your hand? What is the net force on a
basketball in the air?
11. A 3,000 kg truck is cruising straight down the highway at a steady speed of 60 kph. The
friction from the road is 200 N and the air resistance is 300 N. What force is the truck putting
out?
12. Draw a picture of a truck heading to the right. The truck weighs 2,000 kg. It is going 25 kph.
The force of friction is 700 N and the force of air resistance is 300 N. The truck is putting out
1200 N of force. Draw and label the force vectors for friction, air resistance, and driving
582713314
dk
Page 7 of 8
PPT
Newton’s 2nd Law of Motion
force. Draw and label the velocity vector. Calculate the acceleration and draw and label the
acceleration vector.
13. If a 1000 kg car, starting from rest, has a net force of 100 N applied for 10 s, how fast will it
be going?
14. You want your car to go 1 km in 10 s, starting from rest. Your car has a mass of 1,500 kg.
What force must your car put out?
15. Throw a 1 kg ball straight up in the air. When it reaches its highest point, what is the force on
it? What is its acceleration? What is its velocity?
16. If you drop a 2 kg rock, what is the force on it while it is falling? Ignore air resistance.
17. The acceleration due to gravity on the moon is 1.6 m/s2. What is the force on it while it is
falling? There is no air on the moon.
Challenge/ extension
1. What net force is needed to accelerate a 1,000 kg car at 10 km/hr/s?
2. If there's a frictionless pulley with a 5 kg mass on one side and a 3 kg mass on the other side,
what will the acceleration be?
Glossary
 Newton’s 2nd Law of Motion
The acceleration of an object is directly proportional to the net force acting on the object,
is in the direction of the net force, and is inversely proportional to the mass of the object.
This can be stated in a formula:
 a = Fnet/m (acceleration = net force / mass). This is more commonly written as:
 Fnet = ma (net force = mass  acceleration).
 Force – something that tends to cause acceleration in objects.
 Newton – the unit for force in the mks system. It is kgm/s2.
582713314
dk
Page 8 of 8