Content Benchmark P.12.B.1
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Students know laws of motion can be used to determine the effects of forces on the motion of objects. E/S

Sir Isaac Newton developed his Three Laws of Motion from centuries of thought and observation. In a letter to Robert Hook, Newton wrote “If I have seen further, it is by standing on the shoulders of giants.” In particular two “giants” that helped Newton develop his work were the famous scientists Aristotle and Galileo. To understand these two scientists, is to understand Newton and his laws of motion.

For more information about the physics of Aristotle versus Galileo, go to
http://csep10.phys.utk.edu/astr161/lect/history/aristotle_dynamics.html

Newton’s First Law of Motion (Law of Inertia)

Newton’s First Law states that an object at rest remains at rest, and an object in motion continues in motion at a constant velocity in a straight line, unless acted upon by an external force or unbalanced force. An external force or unbalanced force is crucial for students to comprehend. Below are two illustrations of forces acting on a book in a balanced and unbalanced state.

Figure 1: Forces (from http://www.physicsclassroom.com/Class/newtlaws/U2L1d.html)

For example, Marks’s car is stuck in a snowdrift, so he asks Bob sitting in the passenger seat to push him out of the snow. He agrees and starts pushing as hard as he can on the dashboard; yet the car doesn’t move. Bob, in this example, is considered the internal force. In order for the car to move, he should have stepped out of the car and pushed from there; thus becoming the external force needed to cause the car to move.

Figure 2: Newton’s 1st Law (from http://www.physicsclassroom.com/Class/newtlaws/U2L1a.html)

An object resisting a change in its “natural state of motion” (stopped or moving in a straight line) is what Newton referred to as inertia. This is why Newton’s First Law of Motion may as well be coined the Law of Inertia; the resistance an object has to a change in its state of motion.

To learn more about Newton’s First Law, go to
http://www.astronomynotes.com/gravappl/s2.htm#A1.1

Newton’s Second Law of Motion

Sir Isaac Newton wrote his three laws of motion in his book in a specific order being that each one builds upon the each other. Newton’s First Law stated that an object at rest will remain at rest, and an object in motion will continue in motion at a constant velocity in a straight line, unless acted upon by an external force or unbalanced force. Thus, the First Law describes what will occur if there is no force. However, Newton’s Second Law describes what will happen if there is an external and unbalanced force.

Newton’s Second Law states when an external, unbalanced force acts on an object,
the object will accelerate in the same direction as the force. The acceleration varies directly as the force, and inversely as the mass. This in itself may be a bit confusing for the students. So, present it to them using an equation.

When an external, unbalanced for acts on an object, the object will accelerate in the same direction as the force. For example, the object might be moving to the right, while a force is pushing it to the left causing the object to slow down. Its acceleration is in the direction of the force, which is to the left, but it is still moving to the right. The acceleration varies directly as the force, which means that if the force increases, the acceleration will also increase and vice versa if the force decreases, the acceleration will also decrease. For example, push something harder and it will accelerate more. They are directly dependent on each other. Though acceleration and force may vary directly; acceleration inversely varies with mass. This means that if the mass is larger, the acceleration is less and vice versa if the mass if less, the acceleration is more. In other words, if something has less mass, it is easier to make it move faster. They depend inversely on each other. This may be written mathematically as shown below:

a F

Figure 3: Newton’s 2nd Law (from http://www.astronomynotes.com/gravappl/s2.htm#A1.2)

Figure 4: Newton’s 2nd Law (from http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#nt3)

To learn more about Newton’s Second Law, go to
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l3a.html

Newton’s Third Law of Motion (Action-Reaction)

To review, Newton’s First Law describes what happens when there is no force. His Second Law describes what happens when there is a force. And lastly, his Third Law describes what happens when objects interacting.

Newton’s Third Law states that for every action force, there is an equal and opposite reaction force. This law is also known as the Law of Action-Reaction Pair. A force is a push or pull upon an object, which results from its interaction with another object. According to Newton, whenever object A and object B interact with each other; they exert forces upon each other both equal in magnitude and opposite in direction. For example, when sitting in a chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body. These two forces are called action-reaction pair because they always come in pairs.

Figure 5: Action-Reaction Pair Forces (from http://www.physicsclassroom.com/Class/newtlaws/U2L4a.html)

An important concept to illustrate when looking at action-reaction pairs is that the two forces are acting on different objects, not on the same object. For example, have the students stand on the ground and identify the action-reaction pair forces. The students are pushing on the ground with a force due to gravity (Fg down) and the ground is pushing upon them (FN up). The FN is the normal force that balances out the force due to gravity down. It is always perpendicular to the surface the object is on.

Lastly, action-reaction pair forces may either be in direct contact or action-at-a-distance force. Here are some examples of action-reaction forces that depend on the objects being in direct contact, meaning that the two objects involved are touching each other to exert forces in equal magnitudes and opposite directions.

1. The baseball forces the bat to the right (an action); the bat forces the ball to the left (the reaction).

2. Athlete pushes bar upward (an action); the bar pushes athlete downwards (the reaction).

Figure 6: Contact Forces (from http://www.physicsclassroom.com/Class/newtlaws/U2L4b.html)

Here are some examples of action-reaction pairs occurring without friction, or even without direct contact, known as action-at-a-distance force.

1. A rocket pushes out exhaust (an action); the exhaust pushes the rocket forward (the reaction).

2. The earth pulls down on a ball (an action); the ball pulls up on the earth (the reaction).

3. If I push on a lawn mower, it pushes back on me with an equal, but opposite force. Explain why we don’t both just stay still.

• The forces are acting on different bodies (and there are other forces to consider).
• It doesn’t matter to the lawn mower that there is a force on me… all that matters to the lawn mower is that there is a force on it, so it starts to move!
• Another action-reaction pair you need to consider is that I am pushing backwards on the ground, and it pushes forwards on me.

Figure 7: Action-Reaction Pair (from http://www.studyphysics.ca/newnotes/20/ unit01_kinematicsdynamics/chp05_forces/lesson17.htm)

To learn more about Newton’s Third Law, go to
http://theory.uwinnipeg.ca/mod_tech/node24.html

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Performance Benchmark P.12.B.1

Students know laws of motion can be used to determine the effects of forces on the motion of objects. E/S

Common misconceptions associated with this benchmark:

1. Students have the incorrect idea that sustaining motion requires a continued force.

Sir Isaac Newton built on Galileo’s thoughts about objects in motion. Newton’s First Law clearly states that a force is not needed to keep an object in motion. Slide a physics book across a tabletop and watch it slide to a rest position. The book in motion on the tabletop does not come to a rest position because of the absence of a force, rather the presence of a force, a force being the force of friction. The force of friction is what brings the book to a rest position. In the absence of friction, the book would continue in motion with the same speed and direction forever or at least until the end of the tabletop. Thus, a force is not required to keep any object horizontally moving in motion.

To learn more about this misconception, go to
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1b.html#Misconception

2. Students incorrectly think that if an object has a speed of zero (even instantaneously), it has no acceleration, and they also incorrectly believe that the “natural motion” for objects is to be at rest.

Aristotle said that if you stop pushing an object, it would stop moving or come to rest. He as well believed that “at rest” was the natural state for any object. Unfortunately both Galileo and Newton proved Aristotle to be incorrect. According to Newton’s First Law of Motion, also referred to as the Law of Inertia, is defined as the tendency of an object to resist changes in its state of motion. An object at rest has zero velocity and in the absence of an unbalanced force, it will remain with a zero velocity. It will not change its state of motion (velocity). Thus, inertia could be redefined as the tendency of an object to resist accelerations. For example, an object in motion with a velocity of 3 m/s, East will (in the absence of an unbalanced force) remain in motion with a velocity of 3 m/s, East. It will not change its state of motion (velocity). Thus, the “natural motion” for objects is not to be at rest but to resist changes in their velocity.

To learn more about the state of motion, go to http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1b.html

3. Students incorrectly think that acceleration always occurs in the same direction as the motion.

Newton’s Second Law describes objects experiencing a force. According to Newton, an object will only accelerate if there is a net force or unbalanced force acting upon it. The presence of an unbalanced force will accelerate an object by changing its speed, direction, or both its speed and direction. [Remember, acceleration occurs anytime an object's speed increases, speed decreases, or direction of motion changes.] Thus, the acceleration of an object as caused by a net force will be directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. In essence, the direction of acceleration is in the same direction as the net force.

To learn more about acceleration and its state of motion, go to: http://www.hypertextbook.com/physics/mechanics/acceleration/

4. Students incorrectly think that large objects exert a greater force
than smaller objects.

Force is directly proportional to mass and acceleration, according to Newton’s Second Law of Motion. For example, imagine a ball of certain mass moving at a certain acceleration. This ball has a certain force. Now imagine the ball becomes twice as big (double the mass) but keep the acceleration the constant. Newton’s Second Law equation, F=ma, says that this new ball will have twice the force of the original ball. Now imagine the original ball moving at twice the original acceleration. Newton’s Second Law equation, F=ma, says that this new ball will have twice the force of the original ball at its original acceleration. In other words, if you double the mass, you double the force. If you double the acceleration, you double the force as well. The force of an object is derived from both its mass and acceleration. For example, something very massive (high mass) that is changing speed very slowly (low acceleration), like a glacier, can still have a great force. On the other hand, something very small (low mass) that is changing speed very quickly (high acceleration), like a bullet, can still have a great force. In addition, something very small, changing speed very slowly will have a weak force.

To learn more about this misconception and others related to force, go to http://modeling.asu.edu/R&E/FCI.PDF

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Content Benchmark P.12.B.1

Students know laws of motion can be used to determine the effects of forces on the motion of objects. E/S

Sample Test Questions

1^st Item Specification: Apply Newton’s three laws of motion to physical situations (knowing the number of each law is not core knowledge).

Depth of Knowledge Level 1

1. Which of the following would supply the greatest acceleration when applied to a 10 kg mass?
1. 5N
2. 10N
3. 15N
4. 20N

2. What is inertia?
1. The force required to change the motion of an object.
2. The energy required to change the motion of an object.
3. The resistance to changes in motion of an object.
4. The momentum of an object in motion.

Depth of Knowledge Level 2

3. Which of the following would require the least amount of force,
   if applied to the same ball?
1. Stopping the ball that is rolling on a flat and smooth surface.
2. Changing the direction of a ball that is rolling on a flat and smooth surface.
3. Starting the ball in motion on a flat and smooth surface.
4. Keeping the ball moving at a constant speed on a flat and smooth surface.

4. A hammer strikes a nail and drives the nail into a block of wood. If the action force is the hammer striking the nail, the reaction force is
1. the nail striking the wood with an equal and opposite force.
2. the nail striking the hammer with an equal and opposite force.
3. the wood striking the hammer with an equal and opposite force.
4. the wood striking the nail with an equal and opposite force.

2^nd Item Specification: Describe how the strength of the net force and mass of an object determine the amount of change in an object’s motion (includes the effects of the force of gravity on objects).

Depth of Knowledge Level 1

5. Which of the following boxes would have the greatest acceleration?
1. A 10 kg box pushed with 5N of force.
2. A 10 kg box pushed with 10N of force.
3. A 20 kg box pushed with 5N of force.
4. A 20 kg box pushed with 10N of force.

6. A 10 kg toy truck is traveling to the right and is applying a constant force of 20 Newtons to continue its forward motion. A constant frictional force of 7 N is acting against motion of the truck. Calculate the acceleration of the truck.
1. 0.77 m/s²
2. 1.0 m/s²
3. 1.3 m/s²
4. 3.0 m/s²

7. A person pulls on a rope attached to a wall with 300 N of force. Then the same person pulls with 300 N of force in a tug-a-war against another person.
   The person is pulling
1. with an equal amount of force in both cases.
2. with less force when the rope is attached to the wall.
3. with more force when the rope is attached to the wall.
4. with more force during the tug-a-war.

Depth of Knowledge Level 2

8. A student parachutes from a plane. After the parachute opens, the person is traveling down at a constant velocity of 3 m/s. Which of the following forces are acting on the student?
1. Gravity only
2. Air resistance only
3. Gravity and air resistance
4. A downward net force

9. Below is a diagram of a cart on a flat surface being acted upon by a force to the right. Assume that friction is negligible. Use the diagram to answer the following question.

If the mass of the cart was increased to 20 kg, what would happen to the acceleration? The acceleration would

1. increase.
2. decrease.
3. remain constant.
4. be unable to be determined.

3^rd Item Specification: Explain how friction affects the motion of an object.

Depth of Knowledge Level 1

10. Which of the following boxes would have the most friction acting upon it?
1. A smooth metal box being pushed across a smooth wooden floor.
2. A smooth metal box being pushed across a rough carpeted floor.
3. A rough cardboard box being pushed across a smooth wooden floor.
4. A rough cardboard box being pushed across a rough carpeted floor.

11. Use the diagram to answer the question below.

A cart is being pulled North across a carpeted floor. Which direction is the force of friction acting?

1. North
2. South
3. East
4. West

Depth of Knowledge Level 2

12. Which of the following surfaces is easiest to roll a marble on and why?
1. A sheet of ice because there is very little friction between
   the ice and the marble.
2. A sheet of sand paper because there is very little friction between
   the sand paper and the marble.
3. A piece of wood because there is very little friction between
   the wood and the marble.
4. A piece of carpet because there is very little friction between
   the carpet and the marble.

13. You have created a track out of cardboard for a marble to travel down. In order for the marble to complete the track, why does the first hill have to be the highest?
1. The friction caused by the track resists the motion of the marble.
2. The friction caused by the track increases the motion of the marble.
3. Gravity is pulling down on the marble causing it to slow down.
4. Gravity is pulling down on the marble causing it to speed up.

4^th Item Specification: Given the distance vs. time and velocity vs. time plots, interpret and predict different types of motion.

Depth of Knowledge Level 1

14. Below are four distance vs. time graphs. Use these four graphs to answer the following question.

Which graph illustrates a car that is continuously accelerating?

1. Graph 1
2. Graph 2
3. Graph 3
4. Graph 4

15. Below is a distance vs. time graph showing the action of a person over time.
    Use this graph to answer the following question.

Which of the following statements is the BEST description
of the person’s action?

1. The person is walking up a large hill.
2. The person is walking faster as time increases.
3. The person is walking at a slowing speed up a hill.
4. The person is walking at a constant speed.

Depth of Knowledge Level 2

16. Below is a velocity vs. time graph showing the movement of a train over time.
    Use this graph to answer the following question.

Which of the following statements is the BEST description of
the train’s motion?

1. The train is not moving in any direction.
2. The train is continuously accelerating.
3. The train is moving with a constant velocity.
4. The train is accelerating slowly.

17. Below is a velocity vs. time graph showing the movement of a bike over time.
    Use this graph to answer the following question.

Which of the following statements is the BEST description of
the bike’s motion?

1. The bike is traveling up a hill.
2. The bike is traveling at a constant velocity.
3. The bike is accelerating at a constant rate.
4. The bike is accelerating at an increasing rate.

5^th Item Specification: Identify how an example may illustrate a change and/or redirection of force where the amount of work remains unchanged.

Depth of Knowledge Level 1

18. What is the definition of work?
1. Multiplying an object’s force times mass.
2. Multiplying an objects force times displacement.
3. An object moving in the same direction at a constant speed.
4. Picking up and returning an object to the same location.

19. Which of the following describes when the MOST work is done?
1. Moving a book from the table to the floor.
2. Pushing against a wall for 5 minutes.
3. Running one complete lap around a track.
4. Sitting still on a chair for 5 minutes.

Depth of Knowledge Level 2

20. In which of the following situations is the MOST work done?
1. Lifting a 50 N box up 2 meters.
2. Lifting a 50 N box up 2 meters and then down 2 meters.
3. Lifting a 75 N box up 1 meter.
4. Lifting a 75 N box up 1 meter and then down 1 meter.

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Content Benchmark P.12.B.1

Students know laws of motion can be used to determine the effects of forces on the motion of objects. E/S

Answers to Sample Test Questions

1. D, DOK Level 1
2. C, DOK Level 1
3. D, DOK Level 2
4. B, DOK Level 2
5. B, DOK Level 1
6. C, DOK Level 2
7. A, DOK Level 1
8. C, DOK Level 1
9. B, DOK Level 2
10. D, DOK Level 1
11. B, DOK Level 1
12. A, DOK Level 2
13. A, DOK Level 2
14. B, DOK Level 1
15. D, DOK Level 1
16. C, DOK Level 2
17. C, DOK Level 2
18. B, DOK Level 1
19. A, DOK Level 1
20. A, DOK Level 2

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Content Benchmark P.12.B.1

Students know laws of motion can be used to determine the effects of forces on the motion of objects. E/S

Intervention Strategies and Resources

The following is a list of intervention strategies and resources that will facilitate student understanding of this benchmark.

1. Part II: Forces and Newton’s Second Law PhysicsQuest
The PhysicsQuest for Part II: Forces and Newton’s Second Law PhysicsQuest
is an interactive website that is maintained by Dolores Gende in which provides the students opportunities to learn about weight, mass, and net force (vector sum of all forces) by finding the value of individual forces of acceleration using Newton’s Second Law equation.

You can access this interactive site at http://physicsquest.homestead.com/quest4B.html

2. Newton’s Challenge
Newton’s Challenge consists of three simple laboratory experiments, one for each law, which allows the students to obtain and comprehend a better understanding of the three laws of motion. Trimpe creates the experiment “pull the table cloth” trick for Newton’s First Law, hot wheelers carrying various masses down a ramp to represent Newton’s Second Law, and the use of straws and balloons to investigate Newton's Third Law by experimenting with several variations (angles), allowing the students to construct their own understanding of this law.

The challenges can be accessed at http://sciencespot.net/Pages/classphys.html#Anchor9

And the worksheets for these activities are at http://sciencespot.net/Media/newtonlab.pdf

3. Mulitmedia Physics Studio – Newton’s Laws of Motion
This site was created by Physicsclassroom.com which provides several illustrations via multimedia animations in order to help the students to visualize and understand Newton’s three laws of motion.

• The Car and the Wall –
http://www.physicsclassroom.com/mmedia/newtlaws/cci.html
• The Motorcyclist -
http://www.physicsclassroom.com/mmedia/newtlaws/mb.html
• The Truck and the Ladder -
http://www.physicsclassroom.com/mmedia/newtlaws/il.html
• The Elephant and the Feather – Free Fall
http://www.physicsclassroom.com/mmedia/newtlaws/efff.html
• The Elephant and the Feather – Air Resistance
http://www.physicsclassroom.com/mmedia/newtlaws/efar.html
• Skydiving
http://www.physicsclassroom.com/mmedia/newtlaws/sd.html

4. Mass, Force, and Acceleration
If you have access to an Internet Lab, Harcourt School Publishers created an interactive game for students to utilize towards their comprehension between mass, force, and acceleration. Students will fill out the chart to observe how mass, force, and acceleration are related. When they are done, allow the students the opportunity to write a rule.

To access the interactive activity, go to
http://www.harcourtschool.com/activity/newton/index.html

5. The Ramp Simulation
Physics Education Technology has developed a java applet for students to gain a better understanding regarding Newton’s Laws of Motion. Students will be able to explore forces, energy and work as they push household objects up and down a ramp. They will lower and raise the ramp to see how the angle of inclination affects the parallel forces acting on the file cabinet. Graphs will show forces, energy and work.

To get to this applet, go to http://phet.colorado.edu/web-pages/simulations-base.html. Once on the site, click on “Motion” in the left-hand toolbar, and then click “The Ramp.”

6. Forces in 1 Dimension
Physics Education Technology has developed a java applet for students to gain a better understanding regarding Newton’s laws of motion. Students will be able to explore forces at work as they push a filing cabinet. They will create an applied force and observe the resulting friction force and net force acting on the cabinet. Charts will show forces, position, velocity, and acceleration versus time. They will be able to apply their knowledge of Newton’s three laws of motion via free body diagrams.

To get to this applet, go to http://phet.colorado.edu/web-pages/simulations-base.html. Once on the site, click on “Motion” in the left-hand toolbar, and then click on “Forces in 1 Dimension”

7. Newton’s Law Booklet
This site developed by NASA’s Swift Mission Education and Public Outreach Web site, which examines Newton’s First Law by having the students complete the following links and create an activity booklet called Newton’s Law book. The students will be able to take notes and track their findings from the scientific experiments offered. Specifically, the following activities deal with the Law of Inertia:

• Activity #1: Inertia – A Body at Rest
http://swift.sonoma.edu/education/newton/newton_1/html/newton1.html
• Activity #2: Inertia – A Body in Motion
http://swift.sonoma.edu/education/newton/newton_1/html/newton1.html
• Activity #3: And They’re Off
http://swift.sonoma.edu/education/newton/newton_1/html/newton1.html

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