Newton’s Second and Third Laws of Motion

What do you think? If a net force acts on an object, what type of motion will be observed? Why? How would this motion be affected by the amount of force? Are there any other factors that might affect this motion? When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. Hopefully, students will follow Newton’s first law (balanced forces produce no acceleration) with the idea that unbalanced forces produce accelerations. They may posit that a greater force will produce a greater acceleration. They may also use the idea of inertia from the previous section to realize that a greater mass corresponds to a smaller acceleration. On the other hand, it may be difficult for some students to let go of the idea that a force is necessary to maintain constant motion. Revisit this misconception with examples throughout this presentation.

Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to the object’s mass

Newton’s Second Law Increasing the force will increase the acceleration. Which produces a greater acceleration on a 3-kg model airplane, a force of 5 N or a force of 7 N? Answer: the 7 N force Increasing the mass will decrease the acceleration. A force of 5 N is exerted on two model airplanes, one with a mass of 3 kg and one with a mass of 4 kg. Which has a greater acceleration? Answer: the 3 kg airplane Be sure students understand what is meant by the terms “directly proportional” and “inversely proportional.” A simulation from the Phet web site is available to help students visualize the force and the acceleration. The web address is: http://phet-web.colorado.edu/web-pages/index.html Choose the “Motion” simulations, then select “motion in 2D.” You can turn off the vectors and just allow students to observe the motion. Then ask the students to predict the acceleration vector. Which way will it point? Will it have a constant size? After predicting, show the acceleration vector. Next, have them predict the force vector’s direction and size. After predicting, show the force vector and both vectors. Then you can try the other motions described on the screen and ask them to observe the motion, describe the acceleration, and describe the forces. This exercise allows students to see that accelerations are caused by forces. We see the accelerations, but often do not see the forces.

Newton’s Second Law (Equation Form) F represents the vector sum of all forces acting on an object. F = Fnet Units for force: mass units (kg)  acceleration units (m/s2) = kg·m/s2 The units kg•m/s2 are also called newtons (N). It is often useful to write the equation as a = F/m to show students the relationship between force and acceleration and between mass and acceleration. It is easier to see that forces cause accelerations when the equation is written in this form. Even though students saw these units in section 1, they may not recall the fact that newtons are simply a short name for the SI units of kg•m/s2. When solving problems, they will need to know this equivalence in order to cancel units. Remind students of the other units for force, such as dynes (g•cm/s2) and pounds (slug•ft/s2). = m·a

Classroom Practice Problem Space-shuttle astronauts experience accelerations of about 35 m/s2 during takeoff. What force does a 75 kg astronaut experience during an acceleration of this magnitude? Answer: 2600 kg•m/s2 or 2600 N

What do you think? Two football players, Alex and Jason, collide head-on. They have the same mass and the same speed before the collision. How does the force on Alex compare to the force on Jason? Why do you think so? Sketch each player as a stick figure. Place a velocity vector above each player. Draw the force vector on each and label it (i.e. FJA is the force of Jason on Alex). When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. This question will likely produce a wide variety of responses. Some students may believe that the forces are always equal. Many will believe they are equal for the first example but not so for the second and third examples (next slide).

What do you think? Suppose Alex has twice the mass of Jason. How would the forces compare? Why do you think so? Sketch as before. Suppose Alex has twice the mass and Jason is at rest. How would the forces compare?

Newton’s Third Law Forces always exist in pairs. You push down on the chair, the chair pushes up on you Called the action force and reaction force Occur simultaneously so either force is the action force Emphasize that the action and reaction forces occur at the same time.

Newton’s Third Law If two objects interact, the magnitude of the force exerted on Object 1 by Object 2 is equal to the magnitude of the force simultaneously exerted on Object 2 by Object 1, and these two forces are opposite in direction For every action, there is an equal and opposite reaction

The forces act on different objects. Newton’s Third Law The forces act on different objects. Therefore, they do not balance or cancel each other. The motion of each object depends on the net force on that object.

Hammer Striking a Nail What are the action/reaction pairs for a hammer striking a nail into wood? Force of hammer on nail = force of nail on hammer Force of wood on nail = force of nail on wood Which of the action/reaction forces above act on the nail? Force of hammer on nail (downward) Force of wood on nail (upward) Does the nail move? If so, how? Fhammer-on-nail > Fwood-on-nail so the nail accelerates downward This example is continued on the next slide.

Hammer Striking a Nail What forces act on the hammer? Force of nail on hammer (upward) Force of hand on hammer (downward) Does the hammer move? If so, how? Fnail-on-hammer > Fhand-on-hammer so the hammer accelerates upward or slows down The hammer and nail accelerate in opposite directions. Use this example to stress the fact that the action and reaction forces do not cancel each other because they act on different objects. The best way to handle this is by drawing free body diagrams of each object next to each other. The free-body diagram for the nail is show on the previous slide. Ask students to draw the free-body diagram for the hammer. Then students can visualize the action-reaction forces and see that they do not balance each other. Each object accelerates or maintains constant motion based on the forces acting on that object.

Action-Reaction: A Book on a Desk Action Force The desk pushes up on the book. Reaction Force The book pushes down on the desk. The book pulls up on Earth. Earth pulls down on the book (force of gravity). Have students observe a book sitting on a desk for this slide. After students see the action force on the slide, they should be able to state the reaction force before you show it to them. Often students think the reaction force for the desk pushing up on the book is Earth pulling down on the book. Remind them that these forces act on the same object, the book, so they are not an action-reaction pair.

Action-Reaction: A Falling Book The book pulls up on Earth. What is the result of the reaction force? Unbalanced force produces a very small upward acceleration (because the mass of Earth is so large). Action Earth pulls down on the book (force of gravity). What is the result of the action force (if this is the only force on the book)? Unbalanced force produces an acceleration of -9.81 m/s2. Now, remove the book from the desk and allow it to fall to the floor. Ask students if the forces on the book are still balanced. What is the result of this unbalanced force? Acceleration. Have students calculate the acceleration of Earth. Assume the book’s mass is 2.0 kg, so the force on the book is (2.0 kg)(-9.8 m/s2) or 19.6 N downward. Therefore, the upward force on Earth is also 19.6 N. The mass of Earth is about 6 x 1024 kg, so students can calculate the upward acceleration and see how small it will be. You could also choose a falling distance and have students calculate the time required to fall the distance Earth would move upward during that time (using the equations from Chapter 2).

Show only the forces acting on the body of interest Free Body Diagrams Show only the forces acting on the body of interest Do not show the forces acting on the reaction body

Free Body Diagram FWN FAH FNH FHN Nail accelerates downward Hammer accelerates upward

Newton’s Law Problem Process Draw a sketch Identify a coordinate system Choose x- or y-axis along direction of motion Rotate the axes, if necessary Identify relative directions of net forces Consider both x- and y-axes

Newton’s Law Problem Process Draw a free-body diagram Not the same as a sketch! Identify all forces, even if some are not needed for the final solution Apply the Newton’s law equation to each axis Fnet, x = m·ax Fnet, y = m·ay

Determining Fnet If body is at rest or moving at constant velocity: If body is accelerating: Fdirection of motion  Fopposite motion = m·a Watch your sign values!

Car moving at constant velocity on road Fnet,y = 0 W Fnormal Ffwd Fopp Fnormal + W = 0 Fnormal = W Fnet,x = 0 Ffwd + Fopp = 0 Ffwd = Fopp *** Fopp has  sign!

Crate pulled along level surface  Fnet,y = 0 (Fnormal+ Fapp, y) + W = 0 Fnormal + Fapp, y = W Fnormal Fapp Fopp W Fnormal + Fappsin = W Fnet,x = ma Fapp, x + Fopp) = max Fappcos + Fopp = max *** Fopp has  sign!

Watch out for your signs!!! Block pulled up a ramp  Fnet,y = 0 Fnormal+ W, y = 0 Fnormal = W, y Fnormal = Wcos W Fapp Fnorm Fopp  Fnet,x = max Fapp+ (Wx + Fopp) = max Fapp + (Wsin + Fopp) = ma Watch out for your signs!!!

Watch out for your signs!!! Elevator going down Fnet,y = may (T + Fk) + W = may (T + Fk) + (mg) = may T Fnet,x = 0 Fk W Watch out for your signs!!!

Now what do you think? If a net force acts on an object, what type of motion will be observed? Why? How would this motion be affected by the amount of force? Are there any other factors that might affect this motion? Acceleration or a changing velocity will result. Increase the force will increase the acceleration. Increasing the mass will decrease the acceleration.

Now what do you think? Two football players, Alex and Jason, collide head-on. For each scenario below, do the following: Sketch each player as a stick figure. Place a velocity vector above each player. Draw the force vector on each and label it. Draw the acceleration vector above each player. Scenario 1: Alex and Jason have the same mass and the same speed before the collision. Scenario 2: Alex has twice the mass of Jason, and they both have the same speed before the collision. Scenario 3: Alex has twice the mass and Jason is at rest. The forces are equal in all three scenarios. In this first case, the accelerations will also be the same because the forces are equal and the masses are equal. In the other two cases, the accelerations will differ because the masses are not the same.