1. Forces Forces can change motion.
Start movement, stop movement, or change the direction of movement
Cause an object in motion to speed up or slow down
One common misconception is that “forces cause motion.” Forces actually cause a change in motion, or more specifically, a change in velocity (an acceleration). This will be covered in more detail in the next sections, in the context of Newton’s laws.

2. Forces Contact forces Field forces
Pushes or pulls requiring physical contact between the objects
Baseball and bat
Field forces
Objects create force fields that act on other objects.
Gravity, static electricity, magnetism
Pictured is a contact force, the bat and the ball, as well as a field force, the static electric field around charged balloon exerting a force on small pieces of paper. Ask students to identify other examples of contact forces.

3. Units of Force The SI unit of force is the newton (N).
Named for Sir Isaac Newton
Defined as the force required to accelerate a 1 kg mass at a rate of 1 m/s2
Approximately 1/4 pound
Other units are shown below.
1 N = pounds (roughly 1/4 pound)
Have students determine their approximate weight in newtons to reinforce the size of the unit. When talking about problems, use both units to help them become more comfortable. For example, a N car is about a 2500 lb car.

4. The Four Fundamental Forces
Electromagnetic
Caused by interactions between protons and electrons
Produces friction
Gravitational
The weakest force
Strong nuclear force
The strongest force
Short range
Weak nuclear force

5. The Force Diagram Force Diagrams- Represent forces using vector arrows
All forces are drawn as if they act on a central point of the object
Free body diagrams show only forces acting on one object

6. Force Diagrams Forces are vectors (magnitude and direction).
Force diagram (a)
Shows all forces acting during an interaction
On the car and on the wall
Free-body diagram (b)
Shows only forces acting on the object of interest
On the car
Students often have trouble isolating the forces acting on an object to draw a free-body diagram for the object. The free-body diagram of the car is analyzed in more detail in the next slide.

7. Free-Body Diagrams Three forces are shown on the car.
Describe each force by explaining the source of the force and where it acts on the car.
Is each force a contact force or a field force?
For simplicity, all forces are shown acting on the center of the object. Remind students that, when adding vectors, they can be moved parallel without changing the results. Even though the upward force acts on each of the 4 tires, the total is shown acting on the center of the car. Even though the wall strikes the front bumper, that force can be moved to the center of the car without changing the resultant. Gravity (the pull of Earth’s field) acts on every particle in the car but is shown as a single downward force at the center.

8. Force Diagram

9. Force Diagram Step for drawing a free body diagram
Identify forces acting on the object
Tow truck exerts force on the car
Road exerts force on the car
Car is acted on by gravity
Draw a simple diagram

10. Force Diagram Add magnitude of forces to arrows
Indicate force with a vector arrow on the car by the tow truck (5800 N)
Gravitational force acting on the car (14700 N)
Road exerts an upward force on the car (13,690 N)
Interaction between the road and the tires exert a backward force of (775 N)

11. Force Diagram Practice
Draw a force diagram of a crash test dummy in a car at the moment of collision
Forces acting on the car are
19,600 N downward
17,800 N forward
25,000 N backward

12. Newton’s First Law
Experimentation led Galileo to the idea that objects maintain their state of motion or rest.
Newton developed the idea further, in what is now known as Newton’s first law of motion:
Discuss Galileo’s experiment with balls rolling down and then back up inclines. Each ball returned to its original height even if the angle of incline was changed. He theorized that the ball would roll forever if the track was horizontal because it would never reach the starting height.
A short version of this law would be as follows:
Fnet = 0 <-----> v = constant
If net force is zero, the velocity is constant and, if the velocity is constant, the net force is zero.
It sounds simple, but students have a difficult time with this law because they do not “see” the force of friction when they look at moving objects.

13. Forces acting on the car are 19,600 N downward 17,800 N forward
Draw a force diagram of a crash test dummy in a car at the moment of collision
Forces acting on the car are
19,600 N downward
17,800 N forward
25,00 N backward
Forces acting on the dummy are
585 N downward
175 N backward
585 N upward

14. Newton’s First Law Called the law of inertia Inertia
Tendency of an object to remain in its state of motion
Tendency of an object not to accelerate or decelerate
Mass is a measure of inertia
More mass produces more resistance to a change in velocity
Which object in each pair has more inertia?
A baseball at rest or a tennis ball at rest
Answer: the baseball
A tennis ball moving at 125 mi/h or a baseball at rest
Students may choose the moving tennis ball if they confuse inertia (mass) with momentum (mass times velocity). Emphasize that inertia depends only on mass, and so the baseball has a greater inertia in both cases.

15. Net Force - the Sum of the Forces
This car is moving with a constant velocity.
Fforward = road pushing the tires
Fresistance = force caused by friction and air
Forces are balanced
Velocity is constant because the net force (Fnet) is zero.
Net external force can be determined by a change in motion
Ask students how to increase the speed of the car. Answer: Increase the forward force (accelerator) or decrease the resistance force (make the car more aerodynamic).
Ask students how to decrease the speed of the car. Answer: Increase the resistance force (the brakes) or decrease the forward force (accelerator).
This will provide a nice introduction to Newton’s 2nd Law.

16. Equilibrium The state in which the net force is zero.
All forces are balanced.
Object is at rest or travels with constant velocity.
In the diagram, the bob on the fishing line is in equilibrium.
The forces cancel each other.
If either force changes, acceleration will occur.
After reviewing this slide, return to the previous slide and ask students if the car is in equilibrium.

17. Net External Forces
Net external forces = vector sum of all the forces acting on the object

18. Practice Problems
A man is pulling on his dog with a force of 70.0N directed at an angle of 30.0º to the horizontal.
Find the x and y component.

19. Practice Problems
The man pulls a box with a force of 25.0N at angle of 18.0º to the horizontal.
Find the x and y component

20. Practice Problems
A crate is pulled to the right with a force of 85N, to the left with a force of 115N, upward with a force of 565 N, and downward with a force of 236N.
Find the net external force of x
Find the net external force of y
Find the magnitude and direction of the net external force on the crate

21. Classroom Practice Problem
An agricultural student is designing a support system to keep a tree upright. Two wires have been attached to the tree and placed at right angles to each other (parallel to the ground). One wire exerts a force of 30.0 N and the other exerts a force of 40.0 N. Determine where to place a third wire and how much force it should exert so that the net force on the tree is zero.
Answer: 50.0 N at 143° from the 40.0 N force
Be sure students have looked at Sample Problem B in the Student Edition before trying this problem.
Give students some time to work on this problem and then go through each step with them.
After completing this problem, show the students that any two of the three forces will be cancelled by the third force. These balanced forces produce equilibrium.

22. 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:
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.

23. 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)
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).

24. Practice Problems
The net external force on the propeller of a 0.75 kg model airplane is 17 N forward. What is the acceleration of the plane?
The net external force on a golf cart is 390 N north, if the cart has a total mass of 270 kg, what are the magnitude and direction of its acceleration?

25. Practice Problems
A car has a mass of 1500 kg. What force is required to accelerate the car at 4.5m/s2 to the east?
A 2.0 kg mass starts from rest at the top of an inclined plane 85 cm long and slides down to the bottom is 0.50s. What net external force acts on the mass along the incline?

26. 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

27. Classroom Practice Problem
The muscle responsible for closing the mouth is the strongest muscle in the human body. It can exert a force greater than that exerted by a man lifting a mass of 400 kg. Richard Hoffman of Florida recorded the force of biting at 4.33  103 N. If each force has a magnitude equal to the force of Hoffman’s bite, determine the net force. One force is along the horizontal, the second force is -90º from the horizontal, and the third force is -60 º from the horizontal.

28. Classroom Practice Problem
In 1994, Vladimir Kurlovich, from Belarus, set the record as the world’s strongest weightlifter. He did this by lifting and holding above his head a barbell whose mass was 253 kg. Kurlovich’s mass at the time was roughly 133 kg. Draw a free-body diagram showing the various forces in the problem. Calculate the normal force exerted on each of Kurlovich’s feet during the time he was holding the barbell.

29. Classroom Practice Problem
The net force exerted by a woodpecker’s head when its beak strikes a tree can be as large as 4.90 N, assuming that the bird’s head has a mass of 50.0 g. Assume that two different muscles pull the woodpecker’s head forward and downward, exerting a net force of 4.90 N. If the forces exerted by the muscles are at right angles to each other and the muscle that pulls the woodpecker’s head downward exerts a force of 1.70 N, what is the magnitude of the force exerted by the other muscle? Draw a free-body diagram showing the forces acting on the woodpecker’s head.  

30. 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).

31. 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?

32. Newton’s Third Law
When two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the force exerted on object 2 by object 1. These two forces are equal as well as opposite.
Emphasize that the action and reaction forces occur at the same time.

33. Forces always exist in pairs.
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.

34. Newton’s Third Law
For every action force there is an equal and opposite reaction force.
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.

35. 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.

36. 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.

37. 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.
Earth pulls down on the book (force of gravity).
The book pulls up on Earth.
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.

38. 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 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).

39. Field forces also act as pairs
Newton’s Third Law
Field forces also act as pairs
Emphasize that the action and reaction forces occur at the same time.

40. Practice Problems
A 6.0 kg object undergoes an acceleration of 2.0 m/s2.
What is the magnitude of the net external force acting on it?
If this same force is applied to a 4.0 kg object, what acceleration is produced?

41. Practice Problems
A child pulls a wagon with a horizontal force, causing it to accelerate. Newton’s third law say that the wagon exerts an equal and opposite force on the child. How can the wagon accelerate?

42. Practice Problems
Identify the action-reaction pairs in the following situations:
A person takes a step
A baseball player catches a ball
A snowball hits someone in the back
A gust of wind strikes a window

43. Practice Problems
The forces acting on a sailboat are 390N north and 180N east. If the magnitude (including the crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?

44. Practice Problems
The forces acting on a sailboat are 390N north and 180N east. If the magnitude (including the crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?

45. Practice Problems
David Purley, a racing driver, survived deceleration from 173 km/h to 0 km/h over a distance of m when his car crashed. Assume that Purley’s mass is 70.0 kg. What is the average force acting on him during the crash? Compare this force to Purley’s weight. (Hint: Calculate the average acceleration first.)

46. Practice Problems
A giant crane in Washington, D. C. was tested by lifting a  106 kg load.
a. Find the magnitude of the force needed to lift the load with a net acceleration of 0 m/s2.
b. If the same force is applied to pull the load up a smooth slope that makes a 30.0 angle with the horizontal, what would be the acceleration?

47. Practice Problems
In 1991, a lobster with a mass of 20.0 kg was caught off the coast of Nova Scotia, Canada. Imagine this lobster involved in a friendly tug of war with several smaller lobsters on a horizontal plane at the bottom of the sea. Suppose the smaller lobsters are able to drag the large lobster, so that after the large lobster has been moved 1.55 m its speed is m/s. If the lobster is initially at rest, what is the magnitude of the net force applied to it by the smaller lobsters? Assume that friction and resistance due to moving through water are negligible.

48. What do you think?
How do the quantities weight and mass differ from each other?
Which of the following terms is most closely related to the term friction?
Heat, energy, force, velocity
Explain the relationship.
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.
Weight and mass are often confused. Students learned earlier that mass was the amount of matter in an object and weight was the force of gravity, but they often still confuse the issue. When eliciting their responses, ask them to discuss appropriate units for each. You might discuss “weightlessness” and ask if objects can be massless as well.
Friction is often confused with heat or thermal energy. Students likely will think of friction as being related to many of the quantities listed above.

49. Weight and Mass Mass is the amount of matter in an object.
Kilograms, slugs
Weight is a measure of the gravitational force on an object.
Newtons, pounds
Depends on the acceleration of gravity
Weight = mass  acceleration of gravity
W = mag where ag = 9.81 m/s2 on Earth
Depends on location
ag varies slightly with location on Earth.
ag is different on other planets.
Mention that weight is less on the moon because ag on the moon is 1.6 m/s2 .
Reinforce that converting between mass and weight is simple, just multiply or divide by 9.81 m/s2 .
Point out that each kg has a weight of 9.81 N on Earth.

50. Normal Force Force on an object perpendicular to the surface (Fn)
It may equal the weight (Fg), as it does here.
It does not always equal the weight (Fg), as in the second example.
Fn = mg cos 
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

51. Normal Force
An object placed on a tilted surface will often slide down the surface.
The rate at which the object slides down the surface is dependent upon how tilted the surface is; the greater the tilt of the surface, the faster the rate at which the object will slide down it.
In physics, a tilted surface is called an inclined plane.
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

52. Normal Force
As shown in the diagram, there are always at least two forces acting upon any object that is positioned on an inclined plane - the force of gravity and the normal force.
The force of gravity (also known as weight) acts in a downward direction
The normal force acts in a direction perpendicular to the surface (in fact, normal means "perpendicular").
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

53. Normal Force
Up to this point in the course, we have always seen normal forces acting in an upward direction, opposite the direction of the force of gravity.
But this is only because the objects were always on horizontal surfaces and never upon inclined planes.
The normal forces is not always upwards, but rather that it is directed perpendicular to the surface that the object is on.
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

54. Normal Force
The force of gravity will be resolved into two components of force - one directed parallel to the inclined surface and the other directed perpendicular to the inclined surface.
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

55. Normal Force
The perpendicular component of the force of gravity is directed opposite the normal force and as such balances the normal force
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

56. Normal Force
The parallel component of the force of gravity is not balanced by any other force. This object will subsequently accelerate down the inclined plane due to the presence of an unbalanced force
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

57. Normal Force
It is the parallel component of the force of gravity that causes this acceleration. The parallel component of the force of gravity is the net force.
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

58. Normal Force
The task of determining the magnitude of the two components of the force of gravity is a mere manner of using the equations. The equations for the parallel and perpendicular components are: .
Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.