Summer School Physics —
Forces and Motion
Developed by the Cosmology
Research Group, UCB Physics Department, and Emery USD
PART II (A):
Velocity and Fractions: A Review
CONCEPT:
Velocity is a measure of how much distance an object travels in a certain
amount of time. It is really a fraction! It is distance divided
by time.
- Memorize this: v=d/t.
What does that mean? The v stands for velocity; the d
stands for distance; and the t stands for time. This equation
just says that velocity is distance divided by time.
- Memorize this: d=v*t.
This second equation is really just the same as the
first, but rearranged with algebra. It tells us that if you want to
know how much distance an object traveled in a certain time, you just
multiply the object's velocity by the time.
Discussion:
Units are important! You have just calculated a speed in units of feet
per second. What are some other common units for velocity?
Discussion:
Imagine a salesperson advertising a car for sale. The ad says that the
car's top speed is 140. Is that fast? The ad also says that the car
is very fuel efficient—40 per gallon. Would you consider buying
the car based on this information?
- Hold on! What are the units of the "140 top speed"? Miles
per hour? Kilometers per minute? Feet per year? You have to
specify the units.
- Is the efficiency really good? Forty what per gallon?
Kilometers? Perhaps the salesperson was trying to swindle you and
meant 40 inches for every gallon. Uh-oh...
You see now why the units are important. Always include the units
when writing down velocities.
Calculation:
Let's convert the baseball's velocity to other units—centimeters
per second.
[Write each of these calculations in your logbook.]
- There are 2.54 centimeters in every inch. There are 12 inches in
every foot. How far is 60 feet in centimeters?.
- Convert the baseball's speed that you calculated from units of feet
per second to centimeters per second.
- There are 5280 feet in a mile. There are about 1.6 kilometers in a
mile. Can you convert the baseball's speed to miles per hour? How about
to kilometers per hour?
PART II (B)
Three Lessons on Acceleration
and Force:
The Basics, Laws of Motion, the Force of Gravity
Lesson 1: The Basics
CONCEPT: What is acceleration?
- Acceleration is a change in velocity over time. (Velocity is a measure
of how much distance an object travels in a certain amount of time;
it is distance divided by time [v=d/t].)
- This can be speeding up or slowing down.
- Slowing down is sometimes called "deceleration," but scientists
call it a type of acceleration.
Discussion:
Name some circumstances in which you experience acceleration.
CONCEPT: Forces cause acceleration--they
cause velocity to change
- If the velocity of an object is changing, there must be a force acting
on the object.
- A famous law of physics, called Newton's Law, tells us how a force
on an object changes its velocity.
- If there are no forces acting on an object, its velocity will not
change.
Exploration: Acceleration on
the scooter
- While standing still, note that your velocity is zero.
- Now, start pushing yourself. Your legs apply force, and
your velocity changes.
- Now use your foot to stop yourself. Your foot applies a Force
again to make your velocity change from fast to zero.
- Now, get moving again, but this time don't stop using your foot. Just
let the scooter stop by itself. Why did it stop? Some force
must have acted upon you. What was it? Friction!
CONCEPT: What are Forces?
- We have seen that your legs can generate force.
- Friction is also a force.
- A force is usually a push or pull.
- There are other forces in nature. Can you name some?
- What about gravity and electromagnetic forces? They are real forces,
and they can push or pull, but they act through invisible fields.
Exploration: Force fields and
magnets
- Magnets apply forces to things, but they work through invisible
force fields. Gravity works this way too, and we will learn about
that later.
- Place one magnet on a table and then move another magnet over it
closely until you feel the magnetic force between them working.
- Magnetic fields are force fields. they almost seem magic.
the sam basic forces that make magnets work are responsible for making
all of the electronic devices work--from radios to computers. These
forces move electrical currents through wires, which is how electronic
devices work.
- Have some fun with the magnets and, as you play with them, think
about other possible uses for magnets.
Lesson 2: Laws
of Motion
CONCEPT:
You already know an important law, but you may not have
known it was really physics. It is simple. The rule is that a lighter
object is easier to accelerate than a heavier object if you apply the
same force to each object. If you push as hard as you can on a car, it
may move a little and very slowly. But if you push as hard as you can
on a skateboard, it will move fast. This is Newton's
Law, named after
Sir Isaac Newton.
Exploration: Newton's Law on
the skateboard.
- Attach a spring scale to a skateboard (with no person on it). Pull
hard enough to make the spring stretch out to a certain force. The
skateboard will accelerate because you applied a force.
- Next, put some heavy books on the skateboard. Now, pull on the
spring scale again and try to pull, just about as hard as you did
before, applying the same force as the first time. The skateboard
with the books will start moving.
- What happened? The skateboard with the books moved, but it didn't
accelerate as much as the empty skateboard. How do we understand this?
We applied a force, and the skateboard's velocity changed, but it
was moving slower. It never reached the same speed as the lighter
skateboard, even though we applied about the same force.
CONCEPT:
Let's actually express this law in a formula, which is how scientists
express ideas. What we are about to do is avery important in science,
and you can do it yourselves. Imagine going back in time—you would
have amazed people everywhere by explaining your understanding of these
laws:
- Formula: a=F/m. The a stands
for acceleration; the F stands for force;
and the m stands for mass.
- This law tells us that the acceleration, which an object experiences,
is equal to the force applied to the object divided by the mass of
the object.
Calculation:
Let's see how this works. Scientists measure force with a unit called
the newton. Let's see what a force of 6.6 newton does to two
different objects.
- An empty skateboard may weigh about 3 kg, which is just under 7
lb. This number is the m in the formula above—it is
the mass of the object being accelerated. The acceleration, which
this 3 kg mass experiences when you apply a force of 6.6 newton, is
equal to the force divided by the mass.[Write down your calculation
in your logbook, please.]
- When you add some books to the skateboard, its mass may increase
to 6 kg, which is about 13 lbs. What is the acceleration that this
heavier, 6 kg skateboard, experiences when you pull on it with 6.6.
newton? (Remember, the same rule of physics applies to both skateboards—acceleration=force/mass.)
[Write down the calculation in your logbooks, please.] .
- Do you see why the lighter skateboard would have a larger acceleration
than the heavier one, even though it was pulled by the same force?
Lesson 3: The
Force of Gravity
Exploration: Gravity and the
Globe
- Look at the globe. Find where you live. Now. look away from the
globe, and look around you. Imagine, how the room around you is position
on the globe.
- Now, jump up in the air a little. What happens? Your velocity changed.
It changed twice, really. It first increased in the up direction,
and then it changed and you fell back down to the ground. Why? Your
legs applied a force to make you move up. But, another force
pulled you down—a force of gravity.
- Look at the globe again and imagine seeing yourself jumping out
from the surface of the Earth and falling back down.
- Find China on the globe. When somebody jumps in China, the same
thing happens. But notice that people jumping up and down in China
move in different directions than you did. Gravity doesn't care where
you are; it just pulls you back to the Earth.
CONCEPT:
Gravity is a force that works through in invisible force
field.
- It is almost like this: Imagine everything around you having an
invisible spring attached between it and the ground. When you lift
something off of the ground, or when you jump, the invisible spring
stretches and pulls it, or you, back down.
- This is not like any force you are used to; when you pull on the
spring, you see your hand pulling. Gravity pulls also, but it works
through an invisible force field.
- This is what gives us weight. Your body's weight, or the weight
of any object, is really caused by the Earth pulling you down The
invisible springs of gravity are attached to everything and pull every
object down to the Earth.
- The Earth actually pulls harder on a heavy object when it is lifted.
You can imagine that there are more invisible "gravity springs"
attached to heavier objects than light objects. Heavy just
means that gravity is using more strength to pull the object down.
Exploration: Falling Weights
- First, let's do a thought experiment. Imagine if you have two objects,
say, spheres. One of them is much heavier than the other, but they
are about the same size. If you were to hold them up from the same
height and drop them onto the ground, which one would hit the ground
first? Would the lighter one or the heavier one reach the ground first?
- Data:
It is good to do more than just to guess. It is good to have educated
thoughts about things. It makes you stronger to think for
yourself.
- We learned earlier that heavy objects are harder to accelerate
given the same force. A skateboard full of books accelerated more
slowly under a certain force than an empty skateboard did.
So, does this mean that the lighter ball will fall more quickly
and hit the ground first, since it is easier to accelerate lighter
things?
- But, we also just learned that gravity pulls harder on heavy
things than on light things.
Since gravity pulls harder on heavier things, maybe this means
that the heavier ball will fall quicker, since the invisible springs
of gravity are pulling harder on it.
- Now, let us actually do the experiment ourselves. Hold the balls
from the same height. Drop them and watch closely. Why did they hit
the ground at the sam time?
Discussion:
Why did the spheres hit the ground at the same time?
- Does this confuse you? That is OK. Scientists get confused all
the time. But, when we get confused, we think about things.
That is good to do even if you are not a scientist. So, let's think
about it.
- Gravity pulled stronger on the heavy thing; but it is harder to
move a heavy thing. Gravity pull was weaker on the light thing; but
it is easier to move lighter thing.
- So, the final outcome is that all objects fall with the same
acceleration when dropped.
Exploration:
Let's test if what we say is true.
- Drop a paperclip and a heavy ball at the same time from the same
height. Did they hit the ground at the same time?
- Now drop a piece of paper and a heavy ball from the same height.
Uh-oh!
- They didn't fall at the same rate because the paper "catches"the air in the room, and the air applies a force to it from
all sides—kind of like a friction force.
- Concept:This is how a parachute works!
A parachute catches the air and enables you to "defy"
gravity. It there was no air, a parachute would not work, and
a piece of paper would fall with the same acceleration as any
other object.
Prepared by Scott Armel 7/30/02
Part 1: Speed, Velocity, and Acceleration |