Physics Review

Newton's Laws Concepts and Problems

Success is not achieved through photographic regurgitation of the words written below. You must take the concepts reviewed below and recall how we applied them. After using this packet to clear up any weaknesses, you must apply what you learned to other problems: the tutorials, the book problems, anything I’ve given you. You will be tested on applying the concepts, not on reciting the words used to describe them.

Before you can use Newton's Laws, you must make sure that you understand the following fundamentals:

The difference between velocity and acceleration. Know what velocity represents physically. Know what acceleration represents physically (If you think it means how fast something is moving, then you are not thinking enough.) Use specific language when speaking of velocity and acceleration. It is not enough to say "the car is going east?" What do you mean by that? Do you mean that the car is moving eastward or that the car's acceleration is eastward? These are two completely different ideas, and you must understand why.

How to describe acceleration in numbers and/or words with proper units. This depends on understanding what acceleration means.

How to state a spatial direction for any acceleration. In other words, how to tell if an acceleration is up, down, left, right, east, west or whatever. Notice this says direction of ACCELERATION, not MOTION.

The difference between mass and weight. They each mean something different. For example, weight is a force. What is causing this force? Which way does this force point? What is mass? On earth, how can you calculate weight if you know mass?

How to draw a complete free body diagram (fbd) of an object. The diagram must contain vector arrows for forces only. To avoid confusion, do not put arrows that show velocity or acceleration in the force diagram.

Net force: what is it, how do you find it.

First Law–A greatly misunderstood law in physics? It’s words are written in Chapter 4. You need to be able not only to state this, but be able to apply it to motion or no-motion situations. To help in this effort, you must always remember the significance of the phrases:

"net Force"

"at a constant velocity"

"zero acceleration"

"at a constant speed in a straight line"

Exercise 1: Review how the phrases above enter into the 1st Law.

Exercise 2: Can an object with forces acting on it remain at rest?

Exercise 3: Can an object with only one force acting on it remain at rest?

Exercise 4: I push a cart across the level floor. Ignore friction. Once the cart leaves my hand, do any horizontal forces act on it? What would the cart's fbd look like while it is in motion?

Exercise 5: A moving object has only one unbalanced force acting on it. Could it possibly be at rest a little bit later? Could it possibly come to rest and remain at rest later on? (Remember, the force is there whole time - like gravity during free-fall.)

Second Law - Anyone can state the 2nd Law. It is the easiest formula in science. But can you visualize what it is telling you and can you apply it?

Exercise 6: Through friction/tires etc., suppose the road can exert a net force on a small car. Suppose the same net force can be exerted on a car that is twice as massive. What can you tell me about the acceleration produced in the more massive car? If I told you that the little car can get up to 80 miles per hour with that engine in it, would it be correct to say that the big car could not get up to 80 mph with that engine in it?

Exercise 7: What information does the 1st Law tell you that the 2nd Law does not already tell you?

Exercise 8: What information does the 2nd Law tell you that the 1st Law does not?

Note: You should be drawing free body diagrams and using them to apply the second law even when the problem does not say specifically to do so. Once you get in the habit of this, you have the power to solve just about any force problem. See problem set.

Third Law–A person really can’t understand forces without understanding Newton’s 3rd. The problem set at the end of the packet seems more devoted to the 2nd and 1st Laws and less to the 3rd Law, but here is what is going on: Problems that are solved using the 2nd and 1st Laws are best done by applying perfect Free-body Diagrams (FBD’s). You have seen me make a big deal about those in class. If you want to master this, you will do perfect FBD’s and use your FBD to MAKE YOUR OWN equations. It turns out that you can’t understand how to make FBD’s without understanding Newton’s 3rd Law.

Consider the following:

Exercise 9: If Stephan Ur-kel pushes on an enormously massive Zamboni machine (the machine that re-smoothes ice rink surfaces), the Z. pushes back on him. Ignoring friction with the ice, is the net force on Urkel zero?

Exercise 10: The previous answer is No. What is causing the force?

Exercise 11: Is the net force on the Z. zero?

Exercise 12: Will the Z. accelerate, assuming there is not friction?

Exercise 13: Will Urkel accelerate?

Exercise 14: The previous two answers are Yes. Why? Use two free-body diagrams and Newton's 2nd Law to prove who accelerates more, Stephan or the Z.

Exercise 15: Who feels a bigger force in this battle, Stephan or the Z? Think carefully!

So far this packet has not said what the 3rd Law says. (But all students in class were required to read it from Chapter 4.) The 3rd Law says that all forces come in pairs (no exceptions!). In fact, the force that Urkel feels and the force that the Zamboni feels are not two separate forces; they are like two sides of the same coin. You cannot have one without the other. Since the forces are essentially the same force, the force that Urkel feels is equal to the force that the Zamboni feels. This is all that the Third Law says. Do not make more of it than this. Also note that what it does not say:

  1. It does not say that Urkel and the Z. will accelerate equally. See exercise 14 to explain why.
  2. It does not nullify Newton's Second Law or Newton's First Law. Don't try to make the 3rd Law say things that are not true. To see why this is a concern, consider Exercise 16.

Exercise 16: You push a crate across a floor that provides a lot of friction. Here is the fbd:

FfricYou Pushing = Fpush

Is there any physical reason why Ffric has to be equal to Fpush? (No.) So are Fpush and Ffric flip sides of the same force coin? Does the 3rd Law say that Fpush and Ffric have to be equal to each other? Will the box above accelerate?

Exercise 17: You should have seen that analyzing the previous problem has nothing to do with the 3rd Law. It is really a 2nd Law problem. But the 3rd Law is true. There are not exceptions to it. So what then is the 3rd Law reaction force that is equal to Fpush? Where is the flip side to the Fpush coin? Describe it in words. (Think physically, not mathematically.) Do you find the answer in the picture above?

Problem Set - Use force diagrams (fbd's) whenever possible to solve problems.

  1. A truck with mass M has an engine that always supplies the same force. The car's acceleration is 2 m/s2 forward with the engine running. A bunch of sand is then dumped into the truck to make its mass 5M. A) With the same engine, what is the car's acceleration now? B) The truck is still full of sand but is given a new engine that can supply double the original force. What is the acceleration now? C) With the new engine still in, the sand is removed from the truck again. What is the acceleration now?
  2. A car is traveling on a typical earth day at a constant velocity of 5 m/s on level ground. The car's mass is 100 kg. The engine pushes the car forward with a force of 100 N. Draw and label all of the forces that act on the car. Solve numerically for each force in the diagram.
  3. Look at your diagram for the previous problem. Using this diagram, what is the net force on the car equal to? If a = Fnet/m, then use this equation to solve for a. Is this acceleration consistent with the fact that the car moved at constant velocity? Do you need to rethink the last problem? (You do, if you don't have consistency. Dealing with such inconsistencies and not ignoring them is the mark of a good physics student.)
  4. Tell me the weight, force due to gravity, of the following objects: A) a 2 kg hamster, B) a 60 kg person, C) A 40 N barbell, D) a 10 lb watermelon.
  5. Tell me A) the mass of a 40 N barbell on earth, B) the force due to gravity (weight) of this same barbell if it were on the moon, and C) the mass of this same barbell if it were on the moon.
  6. Sketch the free-body diagram of a rock that is in free-all. You may make up the mass. Have your friend make up a different mass. A) Use your fbd and Newton's 2nd Law correctly to solve for the acceleration of the rock in free-fall. B) Compare your acceleration to your friend, who used a different mass. Are your answers different? C) Does your answer for acceleration depend on which direction the rock might have been moving? Could this answer have been true for a rock momentarily at rest during the free-fall?
  7. This is a good computer simulation problem. Try to answer it on paper first. Luke Duke travels in a space-ship with an open window on the side. His cousin Daisy travels in a space ship next to him with a window open towards Luke. Both ships travel at the same constant velocity. While they are moving, Daisy sends a basketball directly out the window, aiming it at Luke. Will the ball travel to Luke, in front of Luke's window, or behind Luke's window. Explain. B) Does the ball have any net force acting on it as it travels between the spaceships? Does it accelerate as it travels? C) If Boss Hogg observes all of this from a stationary point above them, does he see the ball take a sideways path or a diagonal path as it travels between the spacehips? C) Suppose Daisy wants the ball to travel not to Luke, but to Uncle Jesse in the window just behind Luke. Realizing the she is not allowed to throw the ball out the window at an angle, what does she need the pilot of Luke's spaceship to do?
  8. A cardboard ball has a mass of 0.1 kg. A sheet of identical cardboard has the same mass, 0.1 kg. The two pieces of cardboard are allowed to fall. A) One of them feels an air resistance force of 0.5 N. The other feels an air resistance force of 0.1 N. Which force goes with which object? B) Which object has a greater acceleration while falling. (Try to answer this without doing any math. Then do the problem like a robot to check your thinking.)
  9. You have a mass of 70 kg. Normally, the ground pushes up on you with a force of 700 N. A) Prove this. B) At one instant, you notice that the ground is only pushing up on you with 200 Newtons of force. What is happening to you (and the ground) at that instant? (Confused about how to answer this? Draw a force diagram and apply Newton's Second Law and you will find the question answers itself.)
  10. You are pushing your sled on frictionless ice with an acceleration of 5 m/s2. The sled has a mass of 40 kg. How strong is the force that you exert on the sled?
  11. You slap a 2 kg hockey puck with a force of 40 N. While you are slapping it, friction opposess the motion with a force of 32 N. A) What is the acceleration of the puck while you are slapping it? B) After you have stopped touching it, the puck moves forward and friction still exerts a 32 N force. What is the puck's acceleration now? C) Describe the direction of the puck's acceleration in words.
  12. The data below shows the velocity of a 4 kg ball traveling vertically. Up is positive.

Time (sec) / Velocity (m/s)
0
0.5
1.0
1.1
1.2
1.7
2.0
2.1
2.2
2.3
2.4
2.5 / 16.5
9
1.5
0
-1.5
-9
-9
-9
-9
-9
-9
-9

A)Compare the velocity between the time 1.0 second and the time 1.2 second. Are these velocities very different or very similar? Defend your answer.

B)Find the difference in velocity between 1.0 second and 1.2 second.

C)Using the previous answer, the velocity ______by _____ m/s in 0.2 seconds.

D)Use the times 0 and 0.5 seconds to fill in the following: the velocity ______by ____ m/s in one-half a second. Therefore, the velocity ______by ____ m/s in one second.

E)From part C, how much would the velocity decrease by in 0.1 second.

F)For the times 0 to 1.7 seconds, express the acceleration as a number in m/s/s. a = _____ m/s/s

G)Comment on what the data and analysis tell you about net force in the first 1.7 seconds. Does it change with time? What could be responsible for this force? Do you think it could be gravity alone?

H)Consider the entire time shown, 0 to 2.5 seconds. Is there ever a point during the motion that the ball is not moving, but still accelerating? When? Do you see any evidence of times when the ball is moving but not accelerating.

I)Is the ball moving after 2 seconds?

J)What is the value of the resistance force on the ball after 2 seconds?

K)In the first 1.7 seconds, there was a jet of air pushing downward on the ball. How many Newtons did this jet of air exert on the ball? It took place on Earth.

  1. The block below accelerates to the right. The arrows are force vectors

2 Newtons6 Newtons

Add the correct length force arrow below, so that the block below will have a rightward acceleration half as much as the acceleration shown above. Assume equal mass.

6 Newtons

Conceptual Physics Final Review

Newton’s Law Answers

E2. Yes

E3. No

E4. No

E5. Yes; no

E6. Half the acceleration; It could get up to 80 mph, but in twice the time.

E7. Nothing

E8. It tells you how the mass of the object being accelerated affects acceleration.

E10.The Z. pushes on Urkel as Urkel pushes on the Z..

E11. No.

E14. Use a = F/M for the Z, a = F/M for Urkel. Which a is bigger and why?

E15. The forces, F, are the same. (They are not just equal; they are two sides of a coin.)

E16. No; Fpush and Ffric are not an action/reaction pair; no; will accelerate

E17. Reaction: the block is pushing on you. Never find the reaction in that diagram. Answer the following: Describe the reaction force to the friction. If you can’t do this, you still don’t fully understand the definition of force.

Problems

  1. A) 2/5 m/s/s; B) 4/5 m/s/s; C) 4 m/s/s
  2. Ffric = 100 N backward; W = 1000 N down; Fground = 1000 N up
  3. Hi.
  4. A) 20 N; B) 600 N; C) 40 N; D) 10 lb.
  5. A) 4 kg; B) 40/6 N; C) 4 kg
  6. a = 10 m/s/s; same acceleration during the whole time in free-fall including the top.
  7. A) to Luke; B) No force, a = 0; C) diagonal; D) speed up
  8. A) Crumpled: 0.1 N force; B) Crumpled: greater acceleration
  9. B) You and the ground are accelerating downward (a = 7.1 m/s2 downward.)
  10. 200 N
  11. A) 4 m/s2 forward; B) 16 m/s2 backward; C) see words in A and B.
  12. –

A) very different: one is up, the other is down

B) -3.0 m/s

C) decreases by 3 m/s in 0.2 seconds

D) decreases by 7.5 m/s in ½ sec; so it decreases by 15 m/s in one sec.

E) 1.5 m/s

F) a = -15 m/s/s or a = -15 m/s2

G) Net force is constant. Net force is downward. Net force is stronger than gravity.

H) Not moving, but still accelerating at 1.1 sec; 1.7 to 2 sec is motion with a = 0.

I) Yes.

J) 40 N; maybe it is falling through water or pudding or something or even air.

K) 20 N

13. Should be a left-pointing arrow 4 Newtons long. It should be drawn this way, twice as long as the 2 Newton arrow that is given, but still shorter than the 6 Newton arrow.