Force and Motion

Here is a Kahoot to practice the concepts of Force AND Motion

or try this link…

A FORCE is a push or a pull.

It sounds like an oversimplified definition, but it works in college just as well as in kindergarten. Without forces, nothing would be able to move or stop moving. Before, we learned that “energy is the ability to make things move”, SO energy is the ability to make a force.

Forces are measured in NEWTONS.

We honor Sir Isaac with the unit of force called the Newton. It should be capitalized (like all other units named for people). Besides, lower-case “n” is taken. It stands for “nano” or one billionth of something.

The Newton is the amount of force required to make a 1 kilogram mass accelerate at a rate of 1m/s2.

The “net force” is the total amount of force acting on an object after all forces have been considered. Sometimes forces are added together while other situations require that they be subtracted from each other.

A “net force” is calculated by adding or subtracting.

Forces in the SAME direction are ADDED together.

When forces are moving an object in the SAME direction they are helping each other. Because of this cooperation (and not competition) we must ADD the forces together to determine the net force. When you help someone move a large piece of furniture you are each lifting half of the object. One person is pushing while the other is pulling on the sofa. Cooperation forces are added.

Forces in DIFFERENT directions are SUBTRACTED.

When opposing force are in COMPETITION with each other the net force is calculated through subtraction. An arm wrestling challenge requires two pushing forces into the center where the hands are clasped. The opponent with the larger force is the one that will win.

In the situation pictured, a two equal forces would cancel each other out. The net force would be 0 Newtons.

If one of the contestants pushes with a force GREATER than the other, the unbalanced force cause the clasped hands to accelerate in the direction of the winner’s force.

A “tug-O-war” is often thought of as a competition between PULLS. The team with the greater force wins. In this case, the team on the right

Most people only consider the pulling of hands on the rope but in reality, winning at tug of war requires another set of forces. Without the push of your feet into the ground to create friction, a team will slide across the field to lose the “competition “war”. The team that has the greatest friction with the ground AND that can hold on to the rope the best will win.

Opposing forces are either BALANCED or UNBALANCED

When forces are compared in opposite directions, we can identify what kind of motion (if at all) the objects will have. Sir Isaac Newton tells us a great deal about force and the motion caused by forces in his THREE LAWS of MOTION. Newton’s FIRST Law is mostly about BALANCED forces while the SECOND Law refers to UNBALANCED forces. You’ll want to commit the following to memory…

  • 1st Law – An object at rest remains at rest. An object in motion remains in motion at a constant velocity until an unbalanced force acts on it.
  • 2nd Law – An unbalanced force will cause a mass to accelerate.
  • 3rd Law – Every action force has an equal and opposite reaction force.

“An object at rest remains at rest….”

This is the first part of Newton’s first Law of motion. I like to remember this as the Law of Balanced Forces. Imagine a book on a table. The weight of the book gives a force downward while the table supports the book with exactly the same amount of force. The book is at rest because forces are BALANCED.

In the arm wrestling and the tug of war examples above the forces were balanced. This means they were the same magnitude (size) in opposite directions. They “canceled” each other out. As a result of balanced forces an object can be totally still (at rest).

“… an object in motion will remain in motion at a constant velocity…”

This is the second part of Newton’s first Law of motion. It also gives us an understanding of how matter responds to balanced forces. An object CAN be moving when forces are balanced but the motion will be at the SAME SPEED in the same direction. This is what we mean by the phrase “constant velocity”.

In outer space, there is nothing out there to slow you down. If you put on your space suit and walked outside the International Space Station you could tee off a golf ball into the unknown darkness. That golf ball would keep going at THAT speed in THAT direction forever (until Newton’s 2nd Law takes over).

On Earth we have a great deal of friction that slows us down. We can put our vehicle on “cruise control” and that will keep us at the same speed. Running through the snow and then sliding across a frozen driveway would be close to a constant velocity but we’d have to ignore the little bit of friction between your shoes and the ice. Eventually, you would slow down on the ice.

Getting a ride on my “hovercraft” is another way to closely experience a constant velocity. I use a vacuum cleaner in reverse to push air through a round board that we sit on. Underneath the board is a skirt of plastic that allows the air to rush out underneath, bringing friction to almost zero! If we had a long enough flat floor and an infinite battery pack we could ride the hovercraft FOREVER after just one push to get us going!

Summary: BALANCED forces on an object means there will be NO CHANGE in its motion. Either at rest or constant velocity.

The last part of Newton’s First Law is really just a preview of the SECOND LAW. Think of this as the Law of UNBALANCED forces. Changing the velocity of a mass requires an unbalanced force. Acceleration is any change in velocity and there are THREE ways to do that:

“An unbalanced force will cause a mass to accelerate.”

1. SPEEDING UP – If you were to ask 100 people on street what the term “acceleration” meant, the vast majority of them would say “it’s when something speeds up”. Increasing speed is absolutely a form of acceleration. It occurs most often when the applied force is greater than the force of friction holding back motion. While most “normal people” think that is the end of the story, you are now a physics student and you’ll have to think differently. There are TWO other definitions to “acceleration”.

2. SLOWING DOWN – Unbalanced forces cause acceleration and “acceleration” is any change in velocity. Slowing down is certainly a change in your velocity. Whether you apply the brakes on a bike or open a parachute, the frictional forces against forward motion are GREATER than the forces of motion. The object slows down.

3. CHANGING DIRECTION – Unbalance forces cause a change in velocity (acceleration) and DIRECTION is a key component of velocity. Changing directions requires an unbalanced force in the opposite direction of the motion. This extra friction alters the motion of the object. Imagine roller skating in a straight line and you want to turn to the left. You’d use your right skate and push to the side and back. If you wanted to turn to the right, your left skate would push to the side. Unbalanced forces can cause a change in direction.

Summary: Unbalanced forces cause masses to speed up, slow down, or change directions … That’s called acceleration!

We can visualize the different forces acting on a mass using a “force diagram”.

Forces are written as arrows called “vectors”. They have a direction and magnitude.

Gravity

Newton is credited with having a greater understanding of gravity than anyone before him. Only until Einstein did we have to modify his theories. Let’s learn a bit about the complexity of the man, Sir Isaac Newton…

ALL objects we diagram will need to show the force of GRAVITY.

GRAVITY – The force of gravity shows us how attracted objects are to other objects. The center of mass of the object will be described as a bold DOT. All object’s near Earth will need to have the force of gravity drawn. For most of our diagrams we will draw a vector that points FROM the center dot TO the center of Earth. This will typically be shown as an arrow that is drawn straight down. The size of the vector will describe the object’s weight.

The example diagram describes an object that ONLY has gravity acting on it. The bowling ball in the vacuum chamber from the video below would be drawn this way.

1. GRAVITATIONAL FORCE – (we’ll spend a bit more time discussing this one below)

The attraction between any two masses in the universe. Gravity is increased when at least one of the two masses increases OR the distance between the center of each object decreases. Overall, gravity is the weakest of the four forces but it can be calculated over limitless distances.

The BBC clip above is really well done, except for ONE fairly major thing. They cut to slow motion the moment the bowling ball and feather are dropped in a vacuum. Make no mistake, both the bowling ball and the feather should drop at 9.8 m/s2 without air. I did some math and the reworked the shot to look much more like it would in real time.

Apollo astronauts did something similar on the Moon. They dropped a hammer and feather at the same time to prove everything falls at the same rate (though it is just 1.6 m/s2 instead of 9.8 m/s2

While gravity itself is a force between masses, we often MEASURE and COMPARE the acceleration of an object when they are brought close to each other. EARTH’s gravity pulls on objects so that they all fall at 9.8 m/s2 . The only reason something WOULD NOT fall at this rate is if our atmosphere slows it down with a parachute or some other type of air friction. On the Moon there is no air at all. All objects fall at the same rate to the surface.

Gravity between objects INCREASES when the mass (or masses) INCREASES

Imagine taking a trip to our Moon or another planet like Jupiter. Your mass would remain basically the same throughout the trip (assuming you don’t binge on Twinkies the for entire flight).

If you step on a mass like the MOON you would feel only about 1/6th of your weight. This is because the Moon has about 1/6th of the mass of Earth and has a gravity of 1.6 m/s2 . With less mass, there is less to attract you to the surface so your same ol’ mass FEELS lighter. If you’ve seen footage of astronauts on the Moon you can see they have a bounce to their step. Less mass on the moon = less gravity = easier to push off the surface.

What about Jupiter? If you COULD step on the surface of the planet (it’s just gas so good luck) you would find that you are next to a body of mass that is significantly more massive than Earth. Jupiter’s gravity is 24.79 m/s2 which means your weight is about 2.5 times that on Earth!

Click on the picture below to determine what your weight would be on different worlds.

Gravity between objects DECREASES when the distance between masses INCREASES.

Mass isn’t the only thing that can change the amount of gravity between objects. It’s a good thing too. The SUN has more mass than everything else in the solar system…combined! If we were only attracted to the object of greatest mass we would fly up from our seats, through the ceiling, into outer space, and eventually become crispy critters on the Sun.

Johannes Kepler (1571-1630) discovered that objects in space don’t always travel at the same rate. The force of gravity INCREASES when objects get closer to each other. Comets typically have a very elliptical path around the Sun. When they are farther away from each other there is less gravity and the comet’s velocity is low. As it gets closer to the Sun in orbit, the gravity increases. The comet speeds around the Sun and launches itself back out into space.

Click on the picture to the left to make your own gravitational simulations. You’ll be able to can change the mass and velocity of stars, planets, and comets to design your own solar system model. It’s pretty cool. Time to play…and learn!

Gravity is just ONE of FOUR main forces in the universe.

NUCLEAR STRONG and WEAK FORCES –

Put simply, the NUCLEAR STRONG force holds the nucleus of atoms together. Uranium for example has 92 positive protons all confined in a tiny place. The protons SHOULD repel other positive protons and fly apart in 92 different directions! But this doesn’t happen. SOMETHING must be stronger than the repelling force of protons. The NUCLEAR STRONG FORCE keeps positive protons and neutral neutrons together when there is no electrical reason to be that way. This is the STRONGEST of the four forces but it only exists over extremely short distances.

The WEAK force is “weaker” but still quite strong compared to the other forces. Inside every proton and neutron there are three even smaller particles called quarks. The quarks determine if the particle will be a proton or a neutron. The weak force is involved in holding these quarks together.

ELECTROMAGNETIC FORCE–

The attraction and repulsion due to electric or magnetic charges. Positive and negative, North and South. These terms describe the two opposing natures of electromagnetic energy. Opposite charges attract while “like” charges will repel. This force can be increased by either increasing the size of the charge(s) OR by decreasing the distance between the charges.

Positive repels positive but attracts negative

North repels North but attracts South

Electromagnetic repulsion can account for how MOST matter interacts with other matter.

Most of the interaction we witness between matter is a result of electromagnetic forces. Remind yourself of the fast moving ELECTRONS. These are the tiny little negatively-charged particles that are found in swarms or “clouds” around the nucleus of every atom. Electrons DO NOT want to be in the same space as another electron. They repel each other electromagnetically.

This may mess with your mind a bit but matter doesn’t ever really touch other matter. Even when a baseball is hit by a bat. The outermost electrons of the baseball do not want to enter the space of the outer electrons of the bat. Do you believe that you are actually touching the chair you are sitting in? INSTEAD, understand the outer particles of your clothes are repelling the out particles of the chair keeping them from passing through one another. Your nerve cells take that electrical interaction and send signals to the brain to let you know that something is there.

The following forces may seem like “contact forces” but at their core they are a result of electrons needing their own space.

NORMAL FORCE – This is the force that supports an object. It is always 90O from the surface that the object is sitting on. Sir Isaac Newton’s THIRD LAW of motion says that “every action force has an equal and opposite reaction force”. The normal force is that reaction force. Right now you are likely sitting in a chair while reading this page. Your weight down MUST be equally supported in the opposite direction. If your weight was greater…you would accelerate downward with the unbalanced force and break the chair. If the chair gave a greater force than your weight, you we launched into the sky. Neither of these are likely happening. The normal force is EQUAL and OPPOSITE to the force of gravity.

If the object is on an incline (a ramp), then the normal force will be 90O from that slanted surface. Notice that the force of gravity is STILL drawn straight down to the center of Earth. Because the force of gravity and the normal are not directly opposite on this ramp the object has a net force down the ramp. If the object is sitting still on the slanted ramp we will need to add a third force…FRICTION.

FRICTIONAL FORCE – The force of friction opposes motion. It occurs when matter comes into contact with other matter. Friction can be balanced or unbalanced depending on the type of motion demonstrated. If the object is at rest or at a constant velocity the force of friction will be balanced. If we are witnessing matter that is slowing down or changing directions however, we would need to draw the frictional vector larger than the force causing motion. Imagine a box that was given a shove to the right at some point. Now we see the box moving to the right but SLOWING DOWN. This means the unbalanced force of friction must be pointing to the left. Friction opposes motion.

APPLIED FORCE – This a force that is given to an object due to direct contact causing a push or pull interaction. This force could represent an engine pushing a car or a hammer striking a nail. When a force is applied by another object, we use Fa in the force diagram.

In this example, the box is speeding up to the right. Notice that the gravity and normal forces are the same sized vectors. This means forces are balanced up and down. The box is not falling or being launched into the sky. Speeding up requires that an unbalanced force be applied to the box. We show this unbalanced applied force by making the vector to the right (Fa) larger than the force of friction (Ff) to the left.

TENSIONAL FORCE- Tension occurs when a rope or chain is applying a force and not another object directly. Hanging an object or pulling one along with a rope creates tension. While there is an “applied” force on the rope, the object does not receive it. From the point of view of the object, it experiences only a force from the rope. For example, the speaker in the picture is being held by one chain. That’s not a very safe idea at a concert because ALL of the weight of the speaker is being supported by the tension on one chain. If the chain fails at any of the links, the unbalanced force of gravity will cause the speaker to accelerate downward.

In a real situation we should install a speaker with redundancies. This means we have multiple chains or ropes in case one of them fails. In this new installation, the speaker has TWO chains with tension holding the weight. Each chain is holding one HALF of the weight of the speaker. We show this on the force diagram by drawing two vectors that when added together will EQUAL the weight due to gravity.

At Six Flags, the SkyScreamer is a ride that lifts swings up into the air. Each double chair is held up by EIGHT chains. This means that each individual chain is hold ONE EIGHTH (1/8) of the total weight including both people and the weight of the chairs. Notice that the weight due to gravity down is balanced by the tension of the chains up. When you sit on the chair you are not falling or being launched into the air.

BUOYANT FORCE – Buoyancy occurs when an object is floating in a fluid. Boats have a weight downward due to gravity and are supported by the weight of the water it displaces. If the boat is heavier it will sit deeper in the water to get its equal and opposite force. If the boat CANNOT displace enough water it will sink deeper and deeper until it sinks for good.

A hot air balloon receives a buoyant force from the fluid surrounding it as well. The weight of the cooler air displaced by the hot air in the balloon forces up to keep it aloft. As drawn, this balloon could be hovering or changing height at a constant velocity. Assuming the balloon isn’t speeding up or slowing down, the forces on it would be balanced.

Distance and Displacement: it’s all perspective

“Distance” refers to the actual path traveled. Running a marathon typically implies that started at one point and ended 26.2 miles away from that point. That means your final position was “displaced” 26.2 miles from the your initial position.

Training for a marathon may require some treadmill time. Using VR goggles and a treadmill you may think you actually moved that distance but in reality you haven’t moved at all. “DISPLACEMENT” refers to the actual change in your position.

Hitting a home run in baseball allows you to “run the bases”. Your distance from home plate around to each base and back again would be 360 ft. Because you started and ended in the same spot, your displacement would be zero.

Motion requires a stationary reference point in order to be described properly. From the perspective of the slinky (or the toddler), a great deal of distance has been traveled. From an outside observer, the displacement is close to zero. Perspective matters.

how do you know WHAT is moving?

Looking at the graphic can you know for certain WHAT is moving? Is the bus in the window moving forward? Is the bus you are riding moving backward?! You need a reference point to truly analyze the motion of objects.

Speed and Velocity

When an object moves, it changes its position. No change is instantaneous so it must take some amount of time for a mass to move. The SPEED of an object can be calculated by dividing the change in position by the change in time.

VELOCITY is mathematically the same as speed. The major difference between the two is direction. Velocity can be positive (+) or negative (-) depending on which direction the object is traveling.

acceleration

As we discussed earlier, acceleration is a change in velocity. There are THREE ways that this can occur. Speeding up, slowing down, and changing direction. Each of these can occur when unbalanced forces are applied to an object.

Because this is a change in velocity over time we label accelerations as a ratio. Imagine that you are stopped (0 m/s) and over the next 4 seconds you increase your speed to a rate of 8 m/s. The change in velocity was 8 m/s and the time it took was 4 seconds. This means your speed changed by 2 m/s each second. We write that as 2m/s /s OR 2 m/s2 .

Remind yourself that Earth’s gravity pulls all objects down at a rate of 9.8 m/s2. This means that in each second of freefall an object is going an ADDITIONAL 9.8 m/s !

Like velocity, acceleration can also be a positive number or a negative number. This sign tells us which direction the unbalanced force is going. If a ball rolls down a ramp that positive acceleration. If a car slams on the brakes, the unbalanced force would be in the negative direction to slow it down.

Graphing motion

There are THREE main graphs to look for when an object is moving. The first is a “position – time” graph also referred to as x/t . “X” stands for the position of the object away from the origin at ZERO. Time is always moving to the right.

The SLOPE of these lines will tell us a great deal. Slope is calculated as “rise over run” or the change in y over the change in x. In this case the change in position divided by the change in time will equal…VELOCITY. The slope of an x/t graph will tell us the velocity of the object.

The second graph will be looking at the change in velocity over time. Positive velocity typically means moving “to the right” on a graph while negative velocities are moving “to the left”. The slope of a velocity/time graph will tell us the ACCELERATION of the object.

The third graph you will see is the change in acceleration over time. Positive accelerations mean that the unbalanced force is in the “positive” direction while a negative acceleration would have that force in the opposite (negative) direction.

The following graphics are from the physics classroom website. They do a fantastic job of visualizing what the three main graphs would look like for SIX different motion types.

CONSTANT VELOCITY in the positive direction.

Position and velocity are both positive numbers while acceleration is zero. No change in velocity means no acceleration…”0″.

CONSTANT VELOCITY in the negative direction.

Position and velocity are both negative while acceleration is zero. Again there is no change in the velocity of the ball.

SPEEDING UP in the positive direction.

Notice that the x/t graph is curved upward and that both velocity and acceleration are positive numbers. When velocity and acceleration are the same sign, the ball will be speeding up.

SPEEDING UP in the negative direction.

Notice that the x/t graph is curved downward and that both velocity and acceleration are negative numbers.

SLOWING DOWN in the positive direction.

Notice that the x/t graph is curved upward as the ball moves away from the origin. Also notice that before the ball stops the velocities are always positive while the acceleration is a negative number. When velocity and acceleration are different signs, the object will be slowing down.

SLOWING DOWN in the negative direction.

Notice that the x/t graph is curved downward as the ball moves away from the origin. Also notice that before the ball stops the velocities are always negative while the acceleration is a positive number. When velocity and acceleration are different signs, the object will be slowing down.

This interactive lab will help you see the relationship between moving objects and the graphs that describe them.