Newton's 1st Law
a.k.a The Law of Inertia
A body at rest will remain at rest, and a body in motion will remain in motion at a constant speed in a straight line, unless it is acted on by a net, external force.
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Newton's 1st Law
a.k.a The Law of Inertia A body at rest will remain at rest, and a body in motion will remain in motion at a constant speed in a straight line, unless it is acted on by a net, external force. |
What do we mean by a "net" force? an "external" force? Here's a little animation to illustrate these two terms. Note that there are several complex forces involving the ropes & hanging sphere. These are all internal forces & have no effect on the motion of the box. The box has 2 external forces acting on it. It will move as if a single force of 1 N is acting on it– the net force.
In Physics, we define inertia as follows:
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Inertia: The resistance to change in motion.
The mass of a body is a measure of its inertia. (More on this later.) |
Why would we choose to call Newton's first law the "Law of Inertia"?
Here are some questions that may help you find the essence of this law.
| 1. A ball is thrown upward with an initial speed of 30 m/s. You know that it is moving at about 20 m/s after 1 s. But, why does it keep going at all?
We say that there is a downward force of gravity slowing it down, but must there also be an upward force to keep it moving?
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2. A frictionless elevator is rising at a constant speed.
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| 3. A heavy ball is attached to a string & swung in a circular horizontal path. Here's a top view. When the string is just horizontal, on the right, it breaks. Which path indicates the path the ball will take after the string breaks? |
| 4. If a body has an acceleration of zero, does this imply that there are no forces acting on it?
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Here are some puzzlers to help you confront some important details.
| 5. Incorrect: A net force causes an object to move.
Correct: A net force causes an object to |
| 6. When you push on something, it pushes back. The more mass (inertia) is has, the better it will be at pushing back. Is inertia some sort of force? |
| 7. A force is applied to a body & it has a certain change in velocity. How could that same force be used to cause a greater change in velocity? |
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Newton's 3rd Law
For every action (force) there is an equal and opposite reaction (force). |
Newton's Third Law is probably one of the most well-known statements in science. This is not to be confused with well-understood. Let's find out what it really means.
There are several key points to understand in relation to this law.
• Forces occur in matched pairsFor example, if you run and collide with a wall you obviously exert a force on the wall. From the fact that you decelerate we also know that the wall exerted a force back on you. Notice the graphs of the forces these blocks experience when they collide each other. The spikes indicate the force when they collide. The heights of the spikes are equal. Their opposite orientations indicate their directions.
Look at the wavy graph of the force on the blue block. What do you think a graph of the force the spring exerts on the wall would look like?
If you extend your arms to bring yourself to a halt more slowly, you'll exert less force on the wall and it will exert less force on you. Here's an animation that illustrates how one force changes with any change in its opposing force.
We refer to these pairs of forces as action-reaction pairs. One body exerts a force (the action force) & the body it acts on exerts an equal, opposing force (the reaction force) back on the first body. We sometimes call the initiating force an active force. The reaction is called a passive force because it just acts in response to the first force.
Sometimes it seems tricky to identify the reaction force. Look at the nouns. They exert the forces.
For example, if a ball falls and hits the floor, the ball exerts a force on the floor and the floor exerts a force on the ball. It's just that simple.
How about a ball falling through the air? If the earth is pulling the ball downward (the gravitational force), what exerts the reaction force? (Look at the nouns. It's not the air.)
Although the forces are always the same, the effects on the two objects may differ. If you run into a rice paper wall, you'll do great damage to the wall, but be unhurt yourself, paper cuts (ouch) notwithstanding. Note that the force on both is equal & quite small. It just doesn't take much force to damage such a wall. If you run into a brick wall, the (equal) forces will most likely be much larger, and you'll receive the most damage.
• Action-Reaction Forces act in opposite directions
This was pretty obvious from the two previous animations, but it can get a little tricky when you get into two or three dimensions. First we'll look at a pool ball colliding head on with another ball. Notice the directions of the forces on the two.
Now look at a glancing collision. At the instant the balls collide, the force is perpendicular to the two balls at the point where they make contact. (The arrows have been moved to the centers of the balls to make them easier to see.)
• Inanimate objects can exert forces
Although all the forces we've seen acting have been between inanimate objects, people often have trouble accepting this. If I push on a wall, I do it because I intend to. The wall does not have to intend to push back.
A wall is able to exert a varying force because it is slightly compressible like a spring. The harder you push on the wall, the closer its molecules get together. The closer they get together, the more they repel one another and the object pushing them.
• Forces do not require contact
This may seem very odd to you, but look at this interaction between two oppositely charged spheres. Planetary motion is another obvious example.
Actually, in cases where contact is "obviously occurring," a look at the microscopic level will always bring disappointment. Actual "stuff" touching "stuff" just doesn't occur. Sorry!
We'll ignore this & use the everyday idea of contact when things touch in our usual sense of the terms.
Now that those details are out of the way, let's try some 3rd Law practice questions.
| 1. When a golf club hits a ball, we might say the action force is the club pushing forward on the ball. The ball's acceleration is evidence of this force. What is the reaction force & what is the evidence of this force?
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When you need a force to make yourself move, you have to "force" some other object to exert it. (This is not like whipping a horse.)
| 2. What exerts the force that makes a car move along the road? What active force causes this passive force? |
| 3. There was some feeling among non-physics-types that a rocket would never work in the vacuum of space. A U.S. president even asked for a clarification on this issue. Well, it works (unless you're some alt.conspiracy wacko). Think about the rocket and the burnt fuel blasting out the back as the two objects. What makes rockets go? |
| 4. Some lazy parental unit decides that you need to mow the lawn. Armed with physics you make this argument:
"If I push forward on the lawn mower, it will push back equally. Thus the net force is zero so nothing will move." If the L.P.U. worked a little harder in Physics than you do, what would his/her argument-winning response be? |
The Law of Inertia forced us to look at the world in a new way. We found that the motion of a body is determined by the net force on it. If there is a net force the body will accelerate.
Usually a moving body has some force opposing its motion–friction, air resistance, etc. If that force exactly cancels the force pushing it along, a constant velocity results (a=0).
| 1. What would a graph of net force vs. time look like for this case? A graph of velocity vs. time? | |
| 2. Suppose we pulled with the same force, but got rid of most of the friction. What will our force & velocity graphs look like in this case? |
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Our force sensor has been calibrated in newtons (N), which are the SI units of force. When you hold a quarter-pound hamburger in your hand, you're exerting an upward force of about one newton to hold it up.
Here you see the cart being pulled by the string. The UMD is to the left. The string exerts a fairly constant force to the right. There is a small amount of friction to the left. We'll ignore it for now.
| 1. What sort of motion is indicated by the rising, straight, velocity graph? |
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Make sure that you can see how our observations indicate the following:
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A constant (net) force produces a constant acceleration. |
What if we double the net force. It's fairly clear that the acceleration will increase, but by how much? Let's do some more trials with our cart and get some data. We need to vary the force on the cart and measure the resulting acceleration. A plot of a vs. F will show us the relationship. If we get a straight line, we know that a is directly proportional to F. If it is curved, we'll have to use some of our other graphing skills to find the relationship.
Copy down this data table.
Let's get our data. There are six trials with increasing applied force. Here are three movies showing three of the six trials. As in the previous graphs, we have F vs. t on top and a vs. t on the bottom in each graph pair.
Each trip starts with a transition period when the force had not yet stabilized. We just need the interval where the constant acceleration occurred. Each graph is fairly horizontal during this interval. The later runs are much quicker since the increased force is causing larger accelerations.
The data collected by the UMD (acceleration) and force sensor (duh) has been saved under the following names in the Ga-data directory:
a-f-30g
a-f-60g
a-f-90g
a-f-120g
a-f-150g
a-f-180g
Remember, you need to plot a vs. F. Open the first data file in GA. You'll notice that:
2. Work with the menus in GA to produce a graph of acceleration vs. force. You should get a very straight line. Determine the slope and use it to write an equation relating acceleration to force. Don't forget units!
It certainly appears to be a linear relationship between the acceleration and the applied force. Better still, if we could explain away that small y-intercept, we'd have a direct proportion. Ordinarily we'd just say "it looks close enough to me," and that would work here too, but there is a better response this time.
3. Let's assume that our data exactly describes what happened–no errors. How might you interpret that y-intercept given that we were using a low-friction cart? Talk about it. Be specific.
What does this information do for our a = mF + b equation? Our cart has two opposing forces acting on it. The string pulls to the right and friction acts to the left. Suppose we plotted the net force instead of the string's force. What would this do to our line?
The net force is the string's force + the negative .07 N of friction. Doing this would decrease every force value by .07 N. That is, it would move each point that much to the left on our graph. Here's what it would look like. A nice straight line through the origin!
So if we plot the acceleration vs. the net force we get a direct proportion, a much tidier result. This is the first half of Newton's 2nd Law.
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Newton's 2nd Law (Part 1)
The acceleration of a body is directly proportional to the net force acting on it. |
Note: When we say "the force acting on a body" we generally mean the net force. This is just a short hand.
(By the way, the .07 N is not far off. I found by using a very sensitive scale, that it did take about .07 N to get the cart started.)
How about the weight? Aren't heavy things harder to accelerate than light things? Yes, but we need to be careful here. We're actually letting two separate quantities merge into one.
Weight
The weight is a force that pulls an object downward, toward the earth. We can also talk about the weight of something on the moon or some other body, but we generally mean the earth when we use the term.
When this force pushes something against a surface, it influences the friction force between the surfaces. More weight means more friction (unless the surface is vertical.) But friction is already a part of the net force. Scratch weight from the list then, at least for horizontal motion.
MassWe saw this effect with Newton's 1st Law. All objects have a tendency to resist acceleration. We call this tendency the inertia of a body. The heavier object has more resistance to acceleration so we say it has more inertia. Mass is a measure of the inertia of a body.
We don't know why objects with more inertia weigh more, that is, why gravity exerts a larger force on them. Someone will figure it out some day. For now, be sure not to mix up these two.
• The weight of a body is not a property of the body. It is a force that acts on it and it is not constant. If you move it to the moon it will weigh less than it does on the earth.
• The mass, however, is a property of a body and it will be the same everywhere. Disregarding friction, it's just as hard to accelerate an object on the moon as on the earth!
What makes these two seem like the same thing is that they are proportional. Objects with a lot of mass weigh a lot. More later.
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Weight and Mass
The weight of a body is the gravitational force pulling down on it. The mass is a measure of a body's inertia. |
So much for theory. Just how does the acceleration depend on the mass of the object being accelerated? It's your turn to figure this one out.
Here are three movies of three trials where the accelerating force was kept constant, but the mass being accelerated was increased by adding more mass to the cart before each successive trial. (The graphs plot acceleration vs. time.)
Comparison of the three graphs indicates two things. The acceleration
So acceleration is not directly proportional to mass. So just what is the relationship? Let's find out.
The acceleration vs. mass data is contained in the following data files in the "Ga-data" directory.
a-m-0g
a-m-200g
a-m-400g
a-m-600g
a-m-800g
a-m-1000g
a-m-1200g
a-m-1400g
a-m-1600g
a-m-1800g
The names indicate the amount of mass, in grams, that was added to the cart. I.e., a-m-200g means that 200 grams or .2 kg was added to the .5-kg cart. The total mass would then be .7 kg.
Your task is to determine the relationship between acceleration and total mass. (Note that the mass is found from the name of the file as explained in the paragraph above.) You'll need to:
Your data should have lead you to the second part of Newton's 2nd Law.
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Newton's 2nd Law (Part II)
The acceleration of a body is inversely proportional to the mass of the body. |
So a ~ F and a ~ 1/m
Which leads to a ~ F/m
Adding a constant we have a = kF/m
By defining our unit of force, the newton (N) such that one newton is the amount of force required to give a 1-kg object an acceleration of 1 m/s2, we get a constant of one and can drop it. (It's really a bit more involved than this.)
So here's what our hard work got us & Newton.
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Before we can put our new equation to use we need to address its vector nature. 
is a vector equation, that is, both sides are equal in magnitude and direction.
For example, remember all the trouble we had with the direction of the acceleration? This new equation, , gets to the answer in a much more satisfying manner.
Suppose a car is traveling to the left and slowing down. What is the direction of its acceleration? We found that when things are slowing down, the acceleration is opposite the direction of travel. Thus the acceleration is to the right. Yuck!
How would answer this question? Remember, the acceleration must be in the same direction as the net force.
If you're going to the left & slowing down, in what direction would the wind be blowing if it was the force slowing you down? That's easy, it would be to the right. Follow that? Here's an animation.
Let's use a Free-Body Diagram (FBD) to see why.
Newton's 2nd Law refers to the forces acting on a single body we've chosen to study. Let's consider the cart and look at all the forces acting on it. (Click each 
button in the animation as indicated below.)
a. Clearly, the string pulls to the right.
b. We also found that a small friction force opposed our pull. So that force is to the left.
c. The weight is the downward pull of gravity. So let's add that.
Why doesn't the cart fall? Could our two horizontal forces somehow be balancing it? No way! Something must be pushing upward. It's easy to see that without the table, the cart would fall.
d. The table must be pushing upward with a force that just balances the cart's weight. We call this force a Normal Force, a force acting perpendicular to both the surfaces at their point of contact.
These are the four forces acting on the cart. To make it easier to see their combined effect we show them in a FBD. In a FBD we
a. represent the object being studied (the cart) as a point.
b. draw all forces acting on the object as vectors radiating outward from it. The magnitudes of the forces are indicated by the lengths of the vectors. 
c. The net force is found by adding these vectors (in any order). That is,
Looking at our diagram, it's clear that the the weight and normal force are equal and opposite; so they add to zero. The two horizontal forces are all that's left. So the net force is just the string's force plus the friction force. (Added with a negative direction.)
Let's look again at our a vs. F graph. The net force, the blue line, was created by subtracting the .07 N friction force from each Fstring value. Thus our graph indicated a direct proportion between the net force and the acceleration.
You try a few FBD's.
1. Our cart was accelerated by running the string over a pulley and hanging a weight from the end of the string. Draw a FBD for this weight.
2. When you throw a ball upward in a vacuum, the force of gravity is the only force acting on it. What is the direction of its acceleration while it is rising?
| up |
| down |
| There is no force. |
3. What is the direction of its acceleration while it's falling?
| up |
| down |
| There is no force. |
4. What is the direction of its acceleration while it's at the top of its flight?
| up |
| down |
| There is no force. |
One reason why you had heard of Isaac Newton long before taking a Physics class is because of the far-reaching importance of his 2nd Law. is used to determine everything from the maximum tension that must be withstood by a climbing rope to the acceleration of the space shuttle and the deceleration of the pathfinder ship that carried Sojourner to Mars in the summer of 1997.
Let's try a few examples to get the hang of it. Be sure to draw a FBD for each problem.
1. A glider is being towed behind an airplane. The tow rope exerts a forward force of 8.0x104 N on the glider. Air resistance exerts a force of 5.0x104 N. The glider's mass is 2.0x104 kg.
2. A certain (net) force applied to a 3.0-kg mass accelerates it at 4.0 m/s2. How much acceleration will the same force give a 6.0-kg mass?
3. A certain (net) force applied to a certain mass accelerates it at 4.0 m/s2. How much acceleration will the same force give an object with four times as much mass?
| 8.0 m/s2 | 16.0 m/s2 |
| 1.0 m/s2 | .25 m/s2 |
Let's try an example that brings in our acceleration equations.
4. Bobby gets loose from mom in the grocery store. He exerts a horizontal force of 50.0 N on the 40.0-kg grocery cart. Friction between the floor & wheels exerts an opposing force of 10.0 N on the cart.
4.1) How far will the cart travel during the next 2.0 s if it was initially at rest?
4.2) How much force acts on the cart when it slams into the meat counter and stops in .25 s?
That was a fun problem. Before we move to some new material, let's do a status check on your comprehension of F, v, and a.
5. Here's an animation showing a car being acted on by a constant force. Two different choices are provided describing the acceleration of the car. The top and bottom choice indicate increasing and constant accelerations respectively.
Which one is correct?
Top - Increasing Acceleration
Bottom - Constant Acceleration
What label change would make the incorrect one correct?
OK, it's the left side of the room vs. the right side. Lefties, your job is to convince the righties that the pair of bricks (tied together) will hit the ground first. Righties, you argue that the single brick will hit first.
Check this out when you're finished. Don't cheat or I'll say something really insulting!
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Weight is directly proportional to mass.
g = 9.8 N/kg |
From this activity we know the relationship between weight and mass and we also have a new form of the 2nd law that allows us to "convert" between weight and mass. That is, given the weight we can get the mass, assuming that we know g. Let's check this equation out & see where it leads us.
1. If an object has a mass of 1.0 kg, its weight would be?
| 1.0 kg | 1.0 N |
| 9.8 kg | 9.8 N |
| 2. Does this mean that 1 kg = 9.8 newtons? |
yes no |
3. Get out your mass set (if you have one) & get 1 N & 1 kg straight in your mind. That is, find a 1-kg mass and a "mass" with a weight of about 1 newton. Stare at them and shake them around until you have a weight/mass epiphany. It's a 60's kind of thing. You're sure to find inner peace.
| 4. Is "g" universal? That is, is g = 9.8 N/kg everywhere? | yes no |
5. g would be _____ 9.8 N/kg on moon.
| more than |
| equal to |
| less than |
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g = 1.6 N/kg on moon
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Note: When we refer to the weight of an object it is assumed that we mean its weight when it's on the earth. If we want to refer to its weight on the moon, the sun, etc., we have to be more specific. We'd say something like "what would it weigh on the moon.?" The following question is a typical example.
6. Determine:
7. At this NASA site you'll find the weight missing from this promo piece:
| "On the 30th anniversary of robotic exploration of Mars, NASA has selected the name "Sojourner" for the first rover slated to explore the Red Planet. The _____-pound, six-wheeled robotic explorer is now being readied for launch, and will be deployed to roam across an ancient Martian flood plain after the Mars Pathfinder lander touches down on the planet's surface on July 4, 1997." |
In case you're curious to find out more, I found this site by visiting this NASA site and searching for "Sojourner".
The value you just found was the earth weight. The Mars weight was about 9.4 pounds. Given that 1 N = .225 lbs., what is "g" on Mars? (Hint: Convert each weight from pounds to newtons. You'll still have a way to go.)
| 9.8 m/s2 | 0 m/s2 |
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| 3.7 m/s2 | 6.6 m/s2 |
Just to make sure you don't fall for another misconception..
8. When you get a flat tire, the escaping air roughly doubles in volume, that is, it takes up about twice as much space. Has its mass changed?
OK, back to the numbers.
9. A net force of 80 N gives an object of unknown mass an acceleration of 20 m/s2. What is its weight?
| 80 N | 8.2 N | |
| 4.0 kg | 39.2 N |
10. "Step right up! Your weight and mass, only one thin dime."
You need to get a personal image of the size of a newton relative to the more familiar weight unit–pounds. You also need to get a similar feel for kilograms. We'll use the weight that you know best–your own!
Find (or recall) your weight in pounds. Determine your weight in newtons and your mass in kilograms.
(1 newton = .225 lb.)
Remember these numbers. By doing so you'll be better prepared for questions like:
11. An average person might have a weight in _____ of Newtons.
| tens |
| hundreds |
| thousands |
12. A typical baby might weight 7 pounds. In the hospital they'll record a kilogram value. About what might this value be?
| a few kilograms |
| a few tens of kilograms |
| a few hundreds of kilograms |
There are many situations where we need to apply this process to determine the motions of bodies. We saw several examples earlier involving horizontal motion. We now turn our attention to vertical motion. We'll see that the weight of a body plays an important role here.
We all know that riding in elevators can be a bit uncomfortable, to say the least. The unpleasant feeling has to do with the relative motion of our internal organs as we accelerate upward and downward. Let's look at the physics. If you have an elevator handy to test the following, please try to do so.
Let's make some predictions first. Think about your experiences riding in elevators. Sometimes you feel heavier than normal, sometimes lighter than normal and sometimes you feel your normal weight. There are actually 2 situations that correspond to each of the first two of these experiences and 3 that correspond to the third one. Match them up. Put the correct letter in each blank. Write down your answers for use later.
| Motion | Feeling | |
| 1) Sitting Still | ||
| 2) Rising at Vconst | ||
| 3) Falling at Vconst | a) heavy feeling | |
| 4) Increasing upward velocity | b) light feeling | |
| 5) Decreasing upward velocity | c) normal feeling | |
| 6) Increasing downward velocity | d) "weightless" | |
| 7) Decreasing downward velocity | ||
| 8) Freefall |
We have a physics word for this feeling of variable weight. It's called your apparent weight. Of course your weight isn't changing. What is changing is the amount of support force applied by the floor of the elevator.
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Apparent Weight
The support force on a body while it's accelerating up or down. |
If the floor pushes upward with a force equal to your weight, you feel normal. If it pushes harder, you get sort of squished. This is because you have inertia. When the floor tries to make you speed up while rising, your mass lags behind & gets compressed more than usual. You can feel it.
It's a bit hard to think of yourself as being squishable so try this. Hold a water balloon in your hand. (I'll swear I never suggested this.) Look at how its weight makes it flatten somewhat. Now start to push it upward. It flattens more. Your hand starts to move upward, but the balloon resists. Try it for each of the eight situations above. Adjust your answers as necessary.
Let's run the numbers. We'll use an 800-N man and assume that the elevator accelerates at 1/4 g (2.5 m/s2, use g = 10 m/s2) in both directions. Our man is standing on a "bathroom" scale in an elevator. (I don't know why.) We want to know his apparent weight.
| Here's what we have to work with:
Downward Force: Weight, W = 800 N
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1. Stationary Elevator
(In the following animation, wait for the text below to tell you to go to each step. So after you click on a button, come back here for directions. Also note the floor numbers on the right-hand wall of the elevator. It starts on G - ground.)
Our rider, Vinny, is on the ground floor reading the elevator certificate. (What are those things for? Will there be a test someday?) The orange box is (obviously) the scale. The ellipse under the scale is a balloon to give you a more vivid image of force changes. The more squished it is, the greater the upward force applied on Vinny by the scale.
Let's use the 2nd law to find the apparent weight. When the elevator remains at rest, a = 0 m/s2.
Choose your answer to the question on the first page of this animation, then
In the vertical (the y-direction) the second law is written:
 |
For this case, this becomes
Wa + (-W) = may = 0
so, Wa = W = 800 N
So the force we feel, the apparent weight is equal to our actual weight. Don't we always feel our actual weight? Just wait.
2. Increasing upward velocity
Vinny presses 15. "Going up please, small appliances & hair care products." The elevator begins a constant acceleration which lasts for, say, 2 floors.
a. Draw a FBD for this case.
b. Use Newton's second law, as we did in part 1, to create an equation for this situation.
c. Answer the question in the animation, then
For this case,
Wa + (-W) = may = m (2.5 m/s2)
so, Wa - 800 N = 80 kg (2.5 m/s2)
Wa = 800 N + 200 N = 1000 N
Vinny will feel 25% heavier. Notice how this is reflected in the shape of the balloon.
3. Constant upward velocity
Vinny is traveling from floor 2 to floor 13 at a constant upward velocity.
a. Draw a FBD for this case.
b. Use Newton's second law to create an equation for this situation.
c. Answer the question in the animation, then
Wait a minute. Shouldn't that balloon be squished more? Nope, it takes no extra force to move you at a constant speed. The balloon is just squished enough to support your weight. If you were carrying some heavy packages, you'd feel their normal weight during this period.
The 2nd law says the same thing when v = constant for zero and non-zero velocities. That is, a = 0 with a constant velocity of zero or 10 m/s. In both cases the net force must be zero since the acceleration is zero.
Wa + (-W) = may = 0
so, Wa = W = 800 N
So the force we feel while at a constant upward velocity is equal to our actual weight.
4. Decreasing upward velocity
Here's the part I hate, the deceleration at the top. Let's again say that it takes 2 floors.
a. Draw a FBD for this case.
b. Use Newton's second law, as we did in part 1, to create an equation for this situation.
c. Answer the question in the animation, then
For this case,
Wa + (-W) = may = m (-2.5 m/s2)
so, Wa - 800 N = 80 kg (-2.5 m/s2)
Wa = 800 N - 200 N = 600 N
Vinny will feel 25% lighter and this has nothing to do with his lunch. Notice the shape of the balloon now.
That was a lot of work. It might be a good idea now to go through the animation again without stopping to do the calculations. Watch the balloon. It's key to understanding how the force on Vinny changes.
OK, now it's your turn. There are 5 more segments to the complete round trip. Do each case with careful FBD's and equations. Sketch the elevator with the balloon. Feel free to review the animations as needed.
You'll need to recall this important factoid.
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The Sign of the Acceleration
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Here are the situations.
5. Stationary Elevator at top.
a. Draw the elevator with the balloon.
b. Draw an FBD.
c. Use Newton's second law to determine the apparent weight.
6. Increasing downward velocity
a. Draw the elevator with the balloon.
b. Draw an FBD.
c. Use Newton's second law to determine the apparent weight.
7. Constant downward velocity
a. Draw the elevator with the balloon.
b. Draw an FBD.
c. Use Newton's second law to determine the apparent weight.
8. Decreasing downward velocity
a. Draw the elevator with the balloon.
b. Draw an FBD.
c. Use Newton's second law to determine the apparent weight.
9. Stationary Elevator at bottom
a. Draw the elevator with the balloon.
b. Draw an FBD.
c. Use Newton's second law to determine the apparent weight.
That was a lot of work. Let's see if it paid off. Get out your initial answers to these matching questions. Discuss them & see if you can get them all correct this time.
As I count them there are 2 a's, 2 b's, 3 c's, and 1 d.
| Motion | Feeling | |
| 1) Sitting Still | ||
| 2) Rising at Vconst | ||
| 3) Falling at Vconst | a) heavy feeling | |
| 4) Increasing upward velocity | b) light feeling | |
| 5) Decreasing upward velocity | c) normal feeling | |
| 6) Increasing downward velocity | d) "weightless" | |
| 7) Decreasing downward velocity | ||
| 8) Freefall |
There are many other situations where we'll use the 2nd law in a manner similar to what we did in the elevator problem. Here are some typical steps.
to create an equation relating the net force to the mass and acceleration.
Usually, the net force will be either horizontal or vertical. There may be forces in the other plane, but they'll cancel (add to zero).
Horizontal forces
Horizontal forces include pushes and pulls by ropes, wind, etc., and friction (working with or against the motion).
Vertical forces
Vertical forces include the object's weight, pulls by ropes, and air resistance.
We'll look at both of these in class, but first let's have another visit to NASA for an interesting example of how the 2nd law is used in current science. Pay particular attention to the discussion of air resistance. We will be looking at that soon.
