Performance 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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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

Sample Test Questions

1. A student hits a hockey puck which slides across a frozen lake. The force required to keep the puck sliding at constant velocity across the ice is:
a. zero Newtons.
b. equal to the weight of the puck.
c. the weight of the puck divided by the mass of the puck.
d. the mass of the puck multiplied by the weight of the puck.

2. If a hockey puck with twice the mass were substituted in #1. above, and hit with the same impulse, the puck's speed would be:
a. twice as great.
b. half as great.
c. the same.
d. at rest.

3. Identify which of the following accurately describe Newton’s Second Law of Motion.
I.. Big masses are hard to accelerate. Big masses require big forces to change speed.
II. Small masses are hard to accelerate. Small masses require large forces to change speed.
III. Big masses are easy to accelerate. Big masses require small forces to change speed.
IV. Small masses are easy to accelerate. Small masses require small forces to change speed.

a. II and III
b. I only
c. I and IV
d. IV only

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 pair is
a. The nail striking the wood with an equal and opposite force.
b. The nail striking the hammer with an equal and opposite force.
c. The wood striking the hammer with an equal and opposite force.
d. The wood striking the nail with an equal and opposite force.

5. A 10 kilograms truck traveling to the right experiences a constant force of 20 Newtons. A constant frictional force of 7 Newtons acts to the left. What is the acceleration of the truck?
a. 1.0 m/s2
b. 1.3 m/s2
c. 0.77 m/s2
d. 3.0 m/s2

6. In the top picture, a physics student is pulling upon a rope which is attached to a wall. In the bottom picture, the physics student is pulling upon a rope which is held by the Strongman. In each case, the force scale reads 500 Newton’s. The physics student is pulling:

a. with more force when the rope is attached to the wall.
b. with more force when the rope is attached to the Strongman.
c. with less force when the rope is attached to the wall.
d. the same force in each case.

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. (a)
2. (b)
3. (c)
4. (b)
5. (b)
6. (d)

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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

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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