Download REVIEW 10 Force and Motion Just as Alicia was about to kick the

REVIEW 10
Force and Motion
Just as Alicia was about to kick the soccer ball, Kim said, "It won't go anywhere."
This threw Alicia off her stride. She stopped and glared at her sister. "What did you say?"
"The soccer ball. It won't go anywhere. That's Newton's third law. When you kick the ball,
you're exerting a force on the ball, right? But the ball also exerts a force that's equal and
opposite to your kick. So, the forces cancel each other out. The ball won't go anywhere."
Alicia thought about this for a moment. Then she kicked the ball, which flew into the goal. "I'm
not sure you've got that third law quite right," she said, smiling.
Words to Know
acceleration
average speed
contact force
force
friction
gravity
net force
newton
Newton's first law of motion
Newton's second law of motion
Newton's third law of motion
noncontact force
normal force
velocity
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All motion is relative
How do you know when an object is moving? This might seem like a strange question, but let's
think about it a moment. Imagine that you are asleep in a car that is traveling on the
interstate. (Your driver, fortunately, is wide awake, with hands firmly on the wheel.) Your
car moves at a constant speed in a straight line to the east. After a while, you wake up,
groggy and scrunched down in your seat. The only thing you see (at first) is another car
next to yours. This other car is moving at the exact same speed and direction as your car—
in other words, at the same velocity. This other car does not pull ahead of your car or drop
behind it. It appears to be completely motionless. So, you might think for a moment that
your car is not moving at all. And, in a way, you'd be right. Your car is not moving,
relative to the location of the other car.
But what happens when you sit up and look at the rest of the world? Suddenly you see trees,
road signs, and buildings zipping by. It turns out that, relative to the ground, your car is
traveling to the east at 80 km/hr! It's that phrase "relative to" which is so important here.
Motion is the change in the position of an object over time. And motion is always judged
and described relative to a chosen reference point. Most drivers (and all speedometers and
police officers) choose the ground as the reference point. But this need not be. If you
choose the other car as your reference point, your position relative to the other car's
position does not change in time.
Suppose that the driver of the other car speeds up to 90 km/hr, relative to the ground. What
is the speed and direction of the other car, relative to you?
Suppose that a cocker spaniel is looking out the back window of the other car. Describe the
speed and direction of your car, relative to the cocker spaniel.
Newton's first law
Scientists used to believe that objects had a natural tendency to be at rest. They also believed
that objects in motion needed a force to keep them in motion. Isaac Newton, however,
showed that this is not true. Newton's first law of motion says that the object will
continue doing what it is doing (whether it is in motion or at rest) if the forces acting on an
object are balanced (equal and opposite). This means that an object at rest will stay at rest.
However, it also means that an object in motion will continue that motion unless acted on
by an outside force.
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Gabe kicked a soccer ball across a field. The ball rolled for a while but eventually stopped. If
Newton's first law of motion is true, it seems that the ball Gabe kicked should continue
rolling forever. Why does the ball stop?
Once an object is in motion, it stays in motion until it is acted on by another force. When you
roll a ball, it is slowed by friction and will eventually stop. In outer space, which is a
practically frictionless vacuum and has very little gravity, an object will keep going,
practically forever. So remember: Don't let go of the tether the next time you are on a
spacewalk!
Suppose you are playing baseball and hit a home run. What forces slow down the ball
while it is in motion? If you hit the home run in space, what would happen?
Describing motion
Scientists have many ways of describing an object's motion: position, speed, direction,
acceleration, and so on. You've certainly heard speed described in terms of miles per hour.
An object's average speed is how far it travels in one unit of time—say, how many meters
it can travel in one second. The following is the formula for finding an object's average
speed:
---see formula
Sharon bicycles 44 km in 2 hours. What is her average speed, in km/hr?
If Dave drives a car at an average speed of 85 km/hr for 3 hours, how far does he travel?
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Speed and velocity
Speed is different than velocity. Speed refers only to an object's rate of motion. Velocity refers
to both an object's rate of motion and the direction in which the object moves—basically,
speed plus direction. So, if your teacher says that an object's velocity is changing, that
could mean a change in the object's speed, a change in the object's direction, or both.
State whether the following examples refer to speed, velocity, or neither.
A cactus wren flies west.
A javelin sails north at 5 m/s.
A western white-tailed dove flies to a saguaro cactus at 4 m/s.
Acceleration
On Earth, an object's motion rarely stays constant. When an object's speed or direction changes,
the object undergoes an acceleration. When most people use the word accelerate, they
mean "to speed up." When scientists use the word accelerate, they mean any change in
either the rate or the direction of an object's motion. So, acceleration can be defined as the
amount of change in velocity per unit of time.
Scientists often express acceleration in the units meters per second for each second, or meters
per second squared (m/s2). Does it seem strange to "square" a second? All this means is
that the rate of motion (m/s) is changing for each unit of time (s) that passes.
Suppose that Sharon is riding her bike, and her speed is 10 m/s. As she rides down the
street, her speed decreases to 5 m/s. Is her acceleration positive or negative? Why?
Now, suppose Sharon rides her bike in a straight line for 20 seconds. During this time, her
speed remains constant at 5 m/s. What is the value of her acceleration during this time?
How do you know this without using a formula?
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So, what causes an object to accelerate—in other words, to go faster, or slower, or in a different
direction? Only a force can do this. A force is a push or a pull that can cause the motion of
an object to change.
Give an example of a situation in which you apply a force to something and it does the
following.
goes faster:
goes slower:
changes direction:
Contact and noncontact forces
A contact force must touch an object to change its speed or direction. When a bat hits a ball,
they exert a contact force on each other, causing the speed and direction of both to change.
One example of a contact force is friction, which slows down objects due to particles of
two materials rubbing against or catching on each other. Normal force is the force exerted
by an object to balance an outside force acting on it. This is easier than it sounds: When
you sit in your chair, the chair exerts a normal force on your body that is equal to the force
of gravity pulling you toward Earth.
Dave is driving down the street. If Dave steps on the brakes, what force slows his car?
Some forces, called noncontact forces, can act on objects from a distance. For example,
gravity is a force that pulls two bodies that have mass toward each other: The more mass a
body has, the greater the force of gravity it can exert. Gravity from the center of the Milky
Way galaxy influences the movements of our solar system, which is thousands of lightyears away. Gravity is a universal force, meaning that every object that has mass exerts
gravitational pull on every other mass. Magnetism and electricity are other examples of
noncontact forces.
What force causes a ball to speed up as it rolls down a hill?
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Newton's second law
Newton determined the relationship between the forces acting on an object and the object's
motion. Newton's second law of motion states the following: The acceleration of an
object is related to the net force acting on it and the object's mass. Scientists use the
following formula to relate force, acceleration, and mass:
force = mass X acceleration or F = ma
In the metric system, the units for force are kg X m/s2. Scientists have given this group of units
a simple name: the newton (N). Many forces can act on an object at the same time. When
you add up all of the forces, you get the net force. If all of the forces acting on the same
object add up to 0 N, the forces are balanced. If the forces are balanced, then the object is
at rest or moving at a constant speed in a straight line. If the net force is anything other
than 0 N, the forces are unbalanced. If the forces are unbalanced, then the object is
accelerating—its speed and/or its direction is changing.
The net force acting on a 50 kg crate is 0 N. What is the crate's acceleration?
What net force will make a 5 kg bowling ball accelerate by 1.5 mis2?
Suppose that the net force you found in the last problem is applied to a 10 kg bowling ball.
What is the acceleration of the 10 kg bowling ball?
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Force diagrams
Scientists draw pictures called force diagrams to help them understand all of the forces acting
on an object. These pictures include arrows called vectors that represent the forces. Forces
have both a magnitude (size) and a direction. Look at the table below. In the first example,
a 10 N force and a 20 N force pull on an object to the right. The net force on the object is
30 N to the right. In the second example, a 10 N force pulls on an object to the left and a
25 N force pulls on the object to the right. The net force on the object is 15 N to the right.
---see table
A force diagram does not show an object's motion. The arrows show the sizes and directions of
the forces acting on an object, not the speed or direction of the object itself. Look at the
first example in the table. The diagram shows a net force of 30 N to the right acting on the
object. It says nothing about the speed or direction of the object. That object could be
moving to the left at 10 m/s and slowing down because the net force is acting to the right.
Or, the object could be at rest and just starting to move to the right because the net force is
acting to the right.
In the space below, draw a picture in which a single object experiences a force of 15 N to
the left and another force of 45 N to the right.
What is the net force acting on the object you just drew? (Give both magnitude and
direction.)
If the object has a mass of 15 kg, what is its acceleration, in m/s2?
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It is fairly easy to see that the net force acting on an object at rest is zero. It may be harder to
see how an object moving at a constant speed in a straight line also experiences a net force
of zero. This idea may become clearer when you consider Sharon on her bicycle. Look at
the following diagram.
---see diagram
In the first panel, Sharon is at rest. In the second panel, she starts accelerating. To start moving,
the first few pushes she gives the pedals must provide a force that is greater than the
friction force from the road. In other words, the pushing and friction forces are unbalanced.
A net force greater than zero acts in the direction of her motion to make her go faster. By
the third panel, Sharon's pushing force is equal to the force of friction from the road. The
forces are balanced, the net force is zero, and Sharon moves at a constant speed in a
straight line.
Sharon cruises east at 5 m/s. She then uses her brakes and comes to a gentle stop. As
Sharon slows, how does the direction of the net force compare to that of her motion?
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Newton's third law
Newton's third law of motion states that forces come in pairs: For every action, there is a
reaction that is equal in magnitude (size) but opposite in direction. This sometimes
confuses people: If the forces are equal and opposite, then why don't they cancel each other
out? How does anything move? The key is to remember that the "equal and opposite"
forces act on different objects, and that those objects often have greatly different masses.
Look at the illustration of a hammer pounding a nail into a board.
The hammer supplies an action force, one that pushes on the nail toward the left. The nail
supplies a reaction force, one that is equal to the action force and pushes on the hammer
toward the right. Because the hammer is more massive than the nail, the nail moves away
from the point of contact, into the wood. However, the same quantity of force works on the
hammer by stopping it; you might even feel a slight rebound as the hammer moves away
from the point of contact. That is the reaction force that the nail exerts on the hammer.
Think back to the introduction of this review and the story of Alicia and the soccer ball.
Using Newton's third law of motion, explain how she could kick the ball into the goal.
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Graphing constant velocity
An object's velocity and acceleration can both be expressed on graphs. Take a look at the graph
on the right. This is called a distance-time graph because the y-axis shows distance and the
x-axis shows time. Suppose that an object moves at a constant velocity to the south. The
line on the graph represents the distance the object moves in an amount of time. At 1 s the
object has moved 10 m south, at 2 s the object has moved 20 m south, and so on.
On a distance-time graph, a straight line means that an object's velocity is constant. In the
example above, the object's velocity is neither increasing nor decreasing—it is staying
exactly the same. If you want to use a distance-time graph to find the velocity of an object,
just find the slope of the line. First, pick two points—an initial point with the coordinates
(ti, di) and a final point with the coordinates (tf, df). Put these coordinates into the following
equation.
---see formula
Notice that the values for distance (m) are in the numerator, and the values for time (s) are in
the denominator. This results in the proper units for velocity: m/s. Remember, any time
you refer to an object's velocity, you have to mention both the rate of motion and the
direction in which the object moves.
The moving object represented in the graph above is moving south at a constant velocity.
Use the formula for slope to find the object's velocity.
Another type of graph puts velocity on the y-axis and time on the x-axis. This is called a
velocity-time graph. A velocity-time graph for the moving object discussed in the previous
example looks like this.
This graph shows that the object has a constant velocity of 10 m/s. In other words, its velocity
is not changing over time. But on the Earth, motion is rarely constant. Acceleration
(changes to the velocity of an object) happens all the time. Let's look at how to represent
changes in velocity on distance-time and velocity-time graphs.
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Graphing changing velocity
On a distance-time graph, a curved line means that an object's velocity is changing over time.
Look at the distance-time graph on the right. The slope of the line increases between 0 and
2 seconds. This means that the velocity of the object is increasing. Then, the slope of the
line gradually decreases from 2 to 4 seconds. This means that the velocity of the object is
decreasing. The line is horizontal after 4 seconds, meaning that the object has stopped
entirely.
Now let's look at how a velocity-time graph works. On a velocity-time graph, a line with a
positive slope represents an increase in velocity, a horizontal line represents a constant
velocity, and a line with a negative slope represents a decrease in velocity.
The following velocity-time graph represents an object's motion. The object is moving
east, but the velocity at which it moves keeps changing. Study the graph, then answer the
questions.
---see graph
Describe when the object's speed increases, stays constant, and decreases.
What is the velocity of the object between 20 and 40 seconds?
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People in Science
Suppose you go outside and roll a ball on flat ground. The ball rolls in a straight line for a while
and then stops. No big deal. Now, suppose you cross the street and roll the ball on another
piece of flat ground. This time, for no reason you can see, the ball moves around and
around in a perfect circle and does not stop. It seems that the laws of nature on one side of
the street are different than the laws of nature on the other side of the street. If you can
imagine this strange situation, then you've got a sense of how scientists viewed the Earth
and the rest of the universe before Isaac Newton came along.
Before Isaac Newton, scientists believed that objects on Earth followed one set of physical
laws, and objects in the rest of the universe followed a different set of physical laws. For
example, scientists believed that objects on Earth naturally moved in straight lines, while
objects in space naturally moved in circles. Then came Newton. Between 1665 and 1667,
while in his early 20s, he overturned centuries of thought about moving objects. He united
the Earth and the universe under one law: the law of universal gravitation, which states that
every body in the universe is attracted to every other body in the universe. This law, along
with his three laws of motion and a type of math he invented called calculus, gave
scientists ways to explain and predict the motions of objects on Earth and in space. Now,
apples that fell from trees and planets that orbited the Sun both followed the same laws of
nature. By uniting Earth and the universe under a single theory and a set of laws, Newton
made modern astronomy and physics possible.
Other scientists and mathematicians would eventually have done what Newton did. For
example, a German mathematician named Leibniz developed calculus at about the same
time as Newton did. But it's a pretty good bet that no single person could have done all the
things Newton did, and done them so quickly. And Newton didn't stop there. In 1668, he
designed and built a telescope that let astronomers see farther and more clearly than ever
before. In the early 1670s, he proved through simple, brilliant experiments that white light
is made of all the colors of the rainbow. In the 1680s, he wrote the Mathematical
Principles of Natural Philosophy, usually called the Principia. This book made his ideas
about gravity and motion available to scientists everywhere.
Developing the law of gravity, inventing calculus, discovering the nature of light—for all of
these accomplishments and more, Newton is honored as one of the most important
scientists in human history. But how did Newton view himself? As an old man, this is what
he wrote of himself: "I do not know what I may appear to the world, but to myself I seem
to have been only like a boy playing on the seashore, and diverting myself in now and then
finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth
lay all undiscovered before me." Perhaps it is true that Newton only made a few
discoveries next to a "great ocean of truth." But his discoveries let later scientists explore
that ocean.
Isaac Newton
(England 1642-1727)
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Keys to Keep
 An object will keep a constant velocity unless a force acts on it.
 A net force causes a change in the velocity of an object.
 You can measure and graph the motion of an object.
 Isaac Newton's law of universal gravitation and three laws of motion are the foundation of
modern physics and astronomy.
Explore It Yourself
Joan lives in a rural area of Arizona. For exercise, she rides her bike to a small pond 5 km from
her house. Sometimes she swims in the pond, but today she just rests for a short time
before heading back home. The entire trip, including time spent at the pond, takes Joan 50
minutes. The table on the right shows the time intervals during the trip and the distance she
travels during those intervals.
---see graph
Using the data from the table, make a graph showing the total number of kilometers that Joan
traveled during her trip. Look back at the review to decide whether time should go on the
x- or the y-axis. Be sure to label your x- and y-axes, indicate what units you are using, and
give your graph a title.
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What Does It Mean?
1. Does the graph show Joan's velocity or her speed? Explain your answer.
2. On a distance-time graph, the slope of the line is related to speed. The steeper the slope, the
faster the speed. During her trip, Joan must ride down a very steep hill, and then walk her
bike up that same hill on her return. From your graph, determine the time interval in which
Joan is most likely doing the following.
riding down the hill:
walking her bike back up the hill:
3. To find the average speed from a distance-time graph, calculate the slope of the line. You
can find the slope of a line with the following formula:
---see formula
Find Joan's average speed, in kilometers per minute, for the following.
her greatest average speed:
the entire trip:
4. On a distance-time graph, what kind of slope represents an object that has stopped moving
entirely? (Give both a description and a numerical answer.)
5. Suppose you want to make a graph showing Joan's distance from her home. How could you
change the y-axis of the graph to show this information?
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AIMS Science Practice
DIRECTIONS: The following force diagram shows a crate being pulled along the floor.
Use it to answer questions 1 and 2.
---see figure
1 What is the net force acting on the crate, in newtons (N)?
A 25 N
B 35N
C 45N
D 55 N
2 At the instant depicted in the diagram, the crate was moving to the left at 0.5 m/s.
Which of the following best describes the crate's motion?
A moving to the left, speeding up
B moving to the left, slowing down
C moving to the right, speeding up
D moving to the right, slowing down
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3 Sean tries to push a parked car with a force of 80 newtons (N), but the car does not move.
Which of the following best describes the force that the car exerts on Sean in this
situation?
A no force
B less force than Sean exerts
C the same amount of force as Sean exerts
D more force than Sean exerts
4 Jacob is riding his skateboard down a hill. If his acceleration down the hill is constant for 3 s,
which of the following graphs represents his velocity?
---see graphs for A, B, C, D
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DIRECTIONS: Use the following information and graph to answer questions 5 through 7.
Lance, a 12-year-old, took a short trip on his bike around his neighborhood. The following line
graph represents how long his trip took and his distance from home.
---see graph
5 How many minutes did it take for Lance to reach his maximum distance from home?
A 2 minutes
B 7 minutes
C 10 minutes
D 18 minutes
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6 During which time interval was Lance's speed increasing?
A 0 to 2 minutes
B 2 to 4 minutes
C 4 to 6 minutes
D 6 to 8 minutes
7 At the end of Lance's trip, how far was he from home?
A 0m
B 180 m
C 300 m
D 500 m
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8 An automobile company tested how many meters it took for 7 cars of different masses to
stop from a speed of 50 km/h. Each set of brakes in each car applied the same amount of
force.
---see graph
Which of the following correctly interprets the data in the graph?
A The lower the mass of a car, the longer it takes for a car to stop.
B No matter what forces are applied, a car with a mass of 1,500 kg will always stop more
quickly than a car with a mass of 2,500 kg.
C No matter what forces are applied, a car with a mass of 3,000 kg will always accelerate
more quickly than a car with a mass of 4,000 kg.
D The distance required to stop is directly related to the mass of the car and the amount of
stopping force applied.
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