CHAPTER 9
Motion and Force
Motion
You probably know that speed describes how fast something is moving. An object’s speed can be calculated by dividing the distance it traveled by the amount of time it was traveling. The speed equation is as follows.
speed = distance ÷ time
v = d ÷ t
Note that speed is represented by a lowercase v in the equation. This is because the equation can be used to calculate both speed and velocity. Velocity is speed in a specific direction. Think about a car traveling at a speed of 40 miles per hour (mph). Now look at the following example. Whether the car is traveling toward Location B or back toward Location A, its speed remains 40 mph. The car’s velocity, however, changes when the car’s direction changes. The car has a velocity of positive 40 mph when traveling toward Location B, but negative 40 mph when traveling back to Location A.
You probably recognize that when an object speeds up, it is accelerating. Acceleration actually describes any change in an object’s velocity. If an object speeds up, slows down, or changes direction, it is accelerating.
An object’s acceleration can be calculated by subtracting its original (old) speed from its final (new) speed, and dividing by the time it took to change between speeds. The acceleration equation is as follows.
acceleration = (final velocity – original velocity) ÷ time
a = (v2 – v1) ÷ t
Momentum and Collisions
When an object is moving, the product of its mass and velocity is called its momentum. The larger an object is and the faster it moves, the greater its momentum. The momentum equation is as follows. Note that momentum is represented by a lowercase p.
momentum = mass × velocity
p = m × v
When objects collide, they transfer momentum to one another. Look at the following example. When the cars collide, their masses do not change. Their velocities, however, do change. The cars’ velocities change because they have transferred momentum.
Notice that the total combined momentum of the two cars, however, does not change. The total momentum is always the same before and after a collision. Like energy, momentum cannot be created or destroyed, only transferred between objects.
Another important characteristic of objects in collisions is inertia. Inertia is the tendency of an object to resist change in its motion. Objects that are at rest tend to stay at rest. Objects in motion tend to stay in motion.
Think about what happens when a car stops abruptly. When the car was moving, the people inside it were also moving. When the car stops, the peoples’ inertia causes them to continue moving forward until something forces them to stop. Safety features like seat belts and airbags are designed to reduce injuries during a collision by stopping peoples’ inertia.
EXERCISE 1
Motion
Directions: Choose the best answer for each of the following items.
Questions 1 and 2 are based on the following graph.
1. Complete the statement with a number.
The object represented in the graph was moving with a speed of ____________________ miles per minute.
2. What type of acceleration is demonstrated by the object in the graph?
A. speeding up
B. slowing down
C. no acceleration
D. changing direction
3. Which object has the greatest momentum: a 60-gram tennis ball traveling at 20 meters per second or a 600-gram basketball traveling at 2 meters per second?
A. the basketball
B. the tennis ball
C. neither ball has momentum
D. their momentum is the same
Answers are on page 665.
Force
When you push or pull on something, you exert a force. All objects exert forces on each other. In fact, most objects have multiple forces acting on them at the same time.
Forces may be balanced or unbalanced. Balanced forces do not affect an object’s motion. Unbalanced forces cause an object to accelerate (speed up, slow down, or change direction). Think about two dogs pulling on opposite ends of a rope toy. If each dog pulls with the same amount of force, the forces are balanced and the rope does not move in either direction. If one dog pulls with more force, the forces are unbalanced and the rope accelerates toward the stronger dog.
Newton’s Laws
In the late 1600s, the English physicist Sir Isaac Newton developed three laws that explain how forces cause objects to move. Scientists use these three laws as the basis for understanding the movement of all objects on Earth and in the universe. The following table describes how Newton’s laws can be used to understand the motion of a skateboard.
Gravity
Sir Isaac Newton also identified the law of universal gravitation. This law says that every object attracts every other object with a force determined by the objects’ masses and the distance between them. The name for this force is gravity. The relationship between gravity, mass, and distance is shown in the following diagram.
The law of universal gravitation explains why the moon orbits Earth and Earth orbits the sun. The force of gravity keeps the smaller object orbiting around the larger object. This law also explains why, on Earth, things fall. Because Earth has such a large mass and we are so close to it, the gravity between Earth and the objects on it is very strong.
When gravity is the only force acting on an object, the object is in free fall. An object in free fall accelerates, or continually speeds up, as it falls toward the ground at a constant rate of approximately 9.8 m/s2. True free fall cannot actually happen inside Earth’s atmosphere, because the force of air resistance is always working against gravity.
Mass and Weight
Mass is the amount of matter in an object. Weight measures the force of gravity on an object. On Earth, your mass and weight are the same. In space, however, weight depends on location. If your weight on Earth is 170 pounds, for example, your weight on the moon would be about 28 pounds. The moon is smaller than Earth, so it would exert a smaller gravitational force on you than Earth does. Your mass on the moon would still be the same, though, because the amount of matter you contain does not change.
EXERCISE 2
Force
Directions: Choose the best answer for each of the following items.
Questions 1 and 2 are based on the following diagram.
1. Place a circle on the diagram to indicate the two forces that must be balanced in order for the airplane to maintain a constant altitude (height).
2. Which law can be used to determine the amount of thrust required to cause the airplane to accelerate at a certain rate?
A. first law of motion
B. third law of motion
C. second law of motion
D. law of universal gravitation
Answers are on page 665.
Work and Machines
Consider two boxes, one empty and one full of books. You push the empty box across the floor easily. You push and push on the box full of books, but you can’t get it to move. Scientists consider only one of these tasks to be work.
In science, work happens when a force causes an object to move a distance. You exerted force on both boxes, but only the empty one moved a distance. You did work only on the empty box. Even though you might have exerted more force trying to move the full box, no work was done, because the full box didn’t move.
The amount of work done on an object is calculated by multiplying the force applied by the distance the object moves. The work equation is as follows.
work = force × distance
w = F × d
Simple Machines
Simple machines make work easier, usually by reducing the applied force necessary at the expense of the distance over which that force is applied. The six types of simple machines are listed in the following table.
Mechanical Advantage and Power
When you use a simple machine, the amount of work you do stays the same, but the force you exert changes. Simple machines can change the direction of your force. Look at the examples shown in the following figure. A screw moves downward as you turn it clockwise. It is easier to turn a screw into a piece of wood than to push the screw straight into the wood. As you push downward, a wedge pushes outward to split an object. Even though you are still doing the same amount of work, splitting wood by swinging an ax downward is much easier than pulling the wood apart with your hands.
Simple machines can also change the amount of the force you need to apply. If the amount of force that comes out of a machine (output force) is greater than the amount of force you apply to the machine (input force), then the machine is said to amplify force. A machine’s mechanical advantage tells you how much the machine amplifies force.
Think about the work equation, w = F × d. Remember that simple machines cannot change the total amount of work done. If you want to reduce the amount of (input) force, there must be a trade-off. To do the same amount of work using less force, the distance traveled must increase. Look at the ramp example shown. Lifting the box directly up would require less distance, but more force. Using a ramp increases the total distance you move the box, but it lets you use less force.
Power is the amount of work a machine can do in a certain amount of time. The faster a machine performs work, the greater its power. A machine’s power can be calculated by dividing the amount of work it does by the amount of time in which it performs the work. The power equation is as follows.
power = work ÷ time
P = w ÷ t
EXERCISE 3
Work and Machines
Directions: Choose the best answer for each of the following items.
1. Connect the type of simple machine with the correct item. Some names will not be used.
2. Complete the statement using an amount based on the information in the section.
A simple machine that requires half the input force requires you to travel ____________________ the distance.
Answers are on page 665.