Purpose

• To elucidate the laws of motion

Objectives

• To describe the concept of inertia
• To apply net forces to motion problems
• To relate the concepts of net force, mass, and acceleration
• To compare equal and opposite forces

Materials & Resources

• Toilet paper or paper towels (and rolls)
• Block of wood (or other heavy object)
• Very thin string (such as sewing thread)
• Metal foil pie pan (a.k.a. pie tin)
• Heavy scissors
• Marble (or another solid, dense ball)
• Various small objects that can be tied to string
• Small ball (baseball, softball, tennis ball etc. will do)

Introduction

Up until this point, we have studied kinematics, the description of motion. Now we turn our attention to dynamics, the causes of motion.

While Isaac Newton did not discover all the laws of motion by himself, he recognized they comprise a complete set of statements that cover all of mechanics. They are often thus labeled Newton’s Laws as a consequence.

We introduce several important concepts here. First, it is acceleration, not displacement or velocity, which is the key quantity needed when linking kinematics to dynamics. Second, we analyze the concept of inertia and its relationship to mass. Finally, we describe the notion of force, and show how the net, or total, force is what matters most.

We will perform some observational experiments with household items to illustrate the laws of motion. We will also use simulations to solidify our results.

Part #1: Inertia

Let’s begin with perhaps the simplest of physics experimental equipment – toilet paper.

(A roll of paper towels could also work, but it’s more difficult to use)

You will need a full, or near-full, roll for this experiment. It needs to be on its usual holder, so that it can roll freely (Figure 4-1).

1. Grasp a square of toilet paper and give it a sharp, sudden tug. What happens?
• Now grasp another square of toilet paper and slowly pull it. What happens?
• Grasp the bottom string and slowly pull until one of the strings breaks.               Which string breaks?
• Fix the apparatus. This time, grasp the bottom string and pull                         suddenly. Which string breaks?

Figure 4-3. A metal foil pie pan (left). A pie pan with a wedge cut out of it (right). A marble is rolled along the inside of the pan so that it rolls off the pan. Which path will it take?

For our third mini-experiment, we need a pie pan made of thin metal foil (Figure 4-3). Using a heavy scissors, cut a wedge out of the pan – it is not vital that it be exactly ¼ of the pan, but it should be close.

• You will roll a marble (or other small, dense sphere) along the inside of the pie pan. But before you try this, predict the path is will make as it exits the pan – will it continue to curve in the same direction as the pan (to the left), will it go straight, or will it curve to the right? (No points will be taken off, regardless of your answer, but you do need to make a prediction to earn points)
• Perform this mini-experiment. What does happen to the marble when it exits the pie pan? (Did it agree with your prediction?)

Finally, tie a piece of string to a small, but relatively heavy object, and hold it so that it hangs straight down (Figure 4-4). Then walk with it as instructed, watching carefully for the response of the object. You may want to do the following mini-experiments in an open space. Note that the longer the string, the more obvious the effects.

• Hold the string while standing still. Then start walking forward suddenly. What happens to the object on the string? Specifically, does it immediately start forward as well? If not, what does it do?
• Walk forward holding the string. Then come to a sudden stop.                               What happens to the object on the string?
• While walking at a constant pace in a straight line, what happens to the object on the string?
1. While walking at a constant pace, turn suddenly to the left. What happens to the object on the string?
1. Repeat the above, but this time turn to the right. What happens to the object on the string?
1. Which mini-experiments showed how an object at rest had a tendency to remain at rest?
1. Which mini-experiments showed how an object in motion had a tendency to remain in motion?
1. Which quantity (displacement, velocity, or acceleration) is meant when we used the word “motion” above?
1. The word “inertia” in everyday life references the idea of resistance to change. What are we resisting a change of here?

Part #2: Force

For this activity, go to the web site http://phet.colorado.edu. In succession, click on the links for “Play with Simulations”, “physics”, and “motion”, then look for the “Forces and Motion: Basics” simulation. Start with the “Acceleration” window. Once there, set the friction to zero.

1. Briefly describe the appearance of the simulation. What kind of object is it using?
• Set the applied force (you can click on the arrows or use the slide bar) to 100 N. Run the sim and watch carefully how the object behaves and briefly describe what happens.
• Next, set the applied force to 200 N and run the sim. Does the object move faster, slower, or at the same rate compared to when the applied force was 100 N? Does it move in a different direction or the same direction?
• Next, reset the sim and set the applied force to – 100 N. Run the sim. Does the object move faster, slower, or at the same rate compared to when the applied force was + 100 N? Does it move in a different direction or the same direction?
• Briefly summarize: How does the acceleration of an object depend on the applied force (both magnitude and direction)?
• Next, let’s play with mass. Reset the sim. What is the mass of the default object (the crate)?
• Change to a refrigerator (note the small window at left). What is its mass? How does it compare to the mass of the crate?
• Set the applied force to 100 N and run the sim. How does the motion of the refrigerator compare to the motion of the crate when using the same applied force?
• Next, try the “unknown” object (it has a question mark). Set the applied force to 100 N and run the sim. Is the unknown more massive, less massive, or the same mass as the crate? And how did you determine that?
1. Assuming the force is the same, how does the acceleration of an object depend on the mass of the object?
1. Assuming the mass is the same, how does the acceleration of an object depend on the force exerted on the object?
1. Which concept (force, mass, or acceleration) is related to the concept of inertia described in Part #1?

Part #3: Action-Reaction

So far, our studies have only considered the motion of one object. Our last exploration regarding the laws of motion relates objects to each other. For simplicity, physicists look at how just two objects affect each other; we can extrapolate how three or more objects interact from putting together various pairs of objects.

1. Hold a small ball at rest. Then drop the ball. What happens to the ball? (This is not a trick question!)
• Place the ball on a horizontal surface (like a table or countertop). Why doesn’t it fall the floor? (Again, not a trick question)
• The ball exerts force on the table (or countertop etc.). In which direction is this force? How do you know this?
• The table exerts force on the ball. In which direction is this force? How do you know this?
• How does the amount of force from the ball (acting on the table) compare to the amount of force from the table (acting on the ball)?
• Replace the ball with a heavier object and repeat the above actions. Then answer the following questions:
• How does the amount of force exerted by the heavier object on the table compare to the amount of force exerted by the ball?
• How does this change the amount of force exerted by the table?
• How do the forces from the heavier object and table compare to each other?  How does this statement compare to the prior result with the ball (Question #5 above)?
• In general, how do the amounts of forces between two objects compare to each other?
• In general, how do the directions of forces between two objects compare to each other?

Summary

Here is a summary of the 3 laws of motion:

• 1st law of motion: An object at rest tends to stay at rest; an object in motion tends to stay in motion.
• 2nd law of motion: The acceleration of an object is directly proportional to the net force acting upon it, and inversely proportional to the mass of the object. Or, in equation form,

SF = ma

• 3rd law of motion: When an object exerts a force, it feels an equal and opposite force in return.

1. A child kicks a soccer ball in a field of grass.
• What happens to the velocity of the ball after it leaves the child’s foot?
• What would happen to the soccer ball without the grass? (For example, imagine kicking the soccer ball on a smooth surface like a parking lot)
• Astronauts in space (aboard the International Space Station, for instance) are effectively weightless. Suppose an astronaut gently throws a tool to a companion. What type of path (a circle, parabola, straight line, zigzag etc.) will the tool follow? Once let go, which of the three laws is the tool explicitly obeying?
• Hold a ball still – how does the force exerted by the ball on your hand compare to the force exerted by your hand on the ball (both magnitude and direction)?
• Drop the ball. While the ball is in free-fall (and ignoring air drag or wind), how does the force exerted by the ball on the planet Earth compare to the force exerted by the Earth on the ball (both magnitude and direction)?
• Given your answer immediately above, why is it that the ball falls down whereas the Earth doesn’t move? (Hint: to fully understand physics situations, we really need to apply all three laws of motion, not just one)

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