Download Stacey Carpenter - University of Hawaii System

PPT Activity
Mass, Weight, and Gravity
Developer Notes
 Working in Newtons is a bit frustrating because the students don't have a feel for a Newton.
They don't even really have a feel for a kilogram. They will never use Newtons in their daily
lives, so it seems a waste to teach it to them. Maybe it's a good preparation for chemistry and
biology.
 Does a person in a weightless situation have weight? Check Hewitt's glossary definition vs.
his definition in the text. The text says you need a support force while the glossary says
weight is the force on a body due to the gravitational attraction of another body. Thus a
falling object would have weight.
Goals
 Students should understand the difference between mass and weight.
 Students should understand that weight is a force.
 Students should be able to calculate the weight of an object in Newtons, given the
acceleration of gravity.
 Students should understand that all objects have gravity, and the more mass an object has, the
more gravity it has.
 Students should understand that gravity is the force of attraction between two objects.
 Students should understand that the force of gravity decreases as the inverse square of the
distance between the objects.
Concepts & Skills Introduced
Area
physics
physics
physics
math
Concept
mass
weight
gravity
inverse square
Time Required
min
Warm-up Question
Place a bowling ball in the middle of the floor. Tell them its mass. Have the students draw a
picture of the ball, then calculate and draw the force vectors on it.
Explain mass and weight and the differences between them.
Make a table of x and 1/x2 for x = 1 to 5.
Presentation
This activity is a follow-up to the Newton's 2nd activity. By the end of that activity, students
should be comfortable with Fnet = ma. They should also know that the force causing the cart to
move was gravity acting on the hanging mass. Here we expand a little and revisit mass and
weight, which they should already know. This should give them a deeper understanding.
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PPT Activity
Mass, Weight, and Gravity
There are no hands-on activities here. This is intended as a short lecture, a set of exercises, and
discussion. A lot more could be done with gravity, but there isn't time in the course for that,
although advanced students could look at the equation for gravity, which is shown in the
extension problem set.
The main thing about gravity is that all objects have it. All objects are attracted to each other.
Gravity is unlike electromagnetic forces in that it works over any distance. Like many other
things (light, sound, magnetism), the strength of gravity decreases with the inverse square of the
distance between the objects.
There is the potential for confusion because gravity is a force, and so is weight. How can a force
cause a force? Actually, the force of gravity causes you to accelerate down - pull your chair out
and see what happens! It's just that the chair or scale gets in the way, causing a counter-force,
and a net force of zero, so there is no actual change in motion. Force tends to cause a change in
motion! Or, force tends to cause acceleration.
Extra material:
Gravity is very weak in comparison to the other three fundamental forces (electromagnetic,
strong nuclear, weak nuclear), but it works over the longest distance. While gravity results in
attraction between like objects, electromagnetic force results in attraction between unlike
particles and repulsion between like particles. At long distances, the pluses and minuses at the
atomic scale blur together to look like zero charge, while gravity still looks the same. That is
why it can operate at long distances. At short distances, the pluses and minuses at the atomic
scale become more obviously separate from each other, so electromagnetic forces tend to
dominate. That's why you don't fall through the earth.
Assessment
Writing Prompts
1.
Relevance
Summary
Exercises
Why is there no weight in orbit? Because acceleration is relative (just like motion). In orbit, you
and the scale are accelerating at the same rate. Imagine the scale as part of Earth, being held still.
You are accelerating relative to the motionless scale, so you exert a force. Of course, you and the
scale are both motionless, but if you assume the scale isn't moving, then you would move
relative to it, like if you step off. In a weightless condition, it doesn't matter if you step off.
Challenge/ extension
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PPT Activity
Mass, Weight, and Gravity
Background / History
You should already know the difference between mass and weight. Now that you understand
force better, you should be able to explain the difference between mass and weight more
accurately.
Mass is a property of matter (stuff). Anything that has mass also has inertia.
Weight is a force. It is mass and acceleration multiplied. But where does the acceleration come
from? Gravity. Just like all mass has inertia, all mass has gravity. All objects are attracted to each
other by gravity. It is the force of gravity between Earth's mass and the mass of your body that
causes you to fall (accelerate down). When you stand on a scale, the scale measures the force of
attraction between you and Earth.
When we looked at the center of mass of an object, we found that the object acted as if all of its
mass was at the center. Not surprisingly, objects act as if all their gravity is at their center, too.
The further you get from the center, the weaker the gravity, just like a light gets dimmer as you
get further away. The force gets weaker proportional to the inverse square of the distance
between the two objects. Similar to acceleration being inversely proportional the mass,
a  1/m,
gravitational force is inversely proportional to the square of the distance between the objects
F  1/d2
For example, an object which moves twice as far away has 1/4 the gravitational force on it.
Problem
Materials
Procedure
Summary
Exercises
1. What is the force of gravity on a 1 kg mass on Earth?
2. What is your mass? Calculate your weight in Newtons on Earth.
3. How much force would you exert on a scale on the moon? (The acceleration due to gravity
on the moon is 1.6 m/s2.) What would your mass be on the moon?
4. What would your weight be on Jupiter? (The acceleration due to gravity on Jupiter is 25
m/s2.) What would your mass be on Jupiter?
5. Imagine yourself in space in a weightless situation. You have two identical boxes. One is
empty and one is full. How can you tell which is which without opening them?
6. If your weight on Earth is 900 N, what would the force of gravity on you be if you were three
times as far from the center of Earth? Why?
7. You have seen pictures of astronauts in a weightless condition in space stations. Space
stations orbit Earth at an altitude of about 200 km in order to get above the atmosphere and
avoid air resistance. The radius of Earth is 6,371 km. If the force of gravity on an astronaut
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PPT Activity
Mass, Weight, and Gravity
on the ground is 800 N, would the force of gravity on the astronaut in orbit be closer to 0 N
or 800 N?
8. If you were in orbit, how much force would you exert on a scale? Why?
9. Is there a gravitational attraction between you and your chair? Then why doesn't it stick to
you when you stand up?
10. Earth has a mass of 6.01024 kg. In the picture, the person has a mass of 50 kg. The scale
measures in Newtons. How much does the person weigh? In the second picture, how much
does Earth weigh? Explain.
Earth
Earth
Challenge/ extension
1. The radius of Earth is 6,371,000 m. Satellites circle Earth at an altitude of about 200,000 m
in order to be outside the atmosphere. If the force of gravity on a satellite on the ground is
10,000 N, what would the force of gravity on it be at an altitude of 200,000 m?
2. Newton's Law of Universal Gravitation states:
Every body in the universe attracts every other body with a force that is proportional to the
product of their masses and inversely proportional to the square of the distance between
them. This force acts along the line joining the two bodies.
This can be written in a formula:
F  m1m2/r2 or F = Gm1m2/r2
G is a constant, 6.710-11 m3/(kgs2). The mass of Earth is 6.01024 kg.
Calculate the force of attraction between you and Earth.
Vocabulary
 Mass - the amount of material in an object. All objects with mass have inertia and gravity.
 Weight - the force on an object due to its mass and the acceleration of gravity. Weight is
measured in Newtons (like pounds in the US system).
 Gravity - a force of attraction between all objects which have mass. Gravity decreases as the
inverse square of the distance between the objects. gravity  1/d2. (Gravity is one of four
fundamental forces.)
 g - the acceleration due to gravity on Earth, 9.8 m/s2
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