Force Causes Acceleration
Friction
Mass and Weight
Mass Resists Acceleration
When Acceleration Is g—Free Fall
When Acceleration Is Less Than g—Nonfree Fall
Inertia, acceleration, and falling objects as introduced in Chapters 2 and 3, and are further developed in this chapter. Here we distinguish between mass and weight without making a big deal about their units of measurement (because I think time is better spent on physics concepts.) A brief treatment of units and systems of measurement is provided in Appendix A.
It is useful to represent magnitudes with numerical quantities from time to time. An option that sometimes better makes the point is the exaggerated symbol technique that is shown in the textbook.
This chapter is reinforced with 8 lessons in the student workbook, Practicing Physics. You may or may not be interested in the Force-Vector Diagrams sheet, but it’s a must if you treat problem solving.
There is one OHT for this chapter, Figure 4.11.
In the Practicing Physics book:
• Mass and Weight • Cart
• Converting Mass to Weight • Force and Acceleration
• A Day at the Races with a = F/m • Friction
• Dropping Masses and Accelerating • Falling and Air Resistance
In the Next-Time Questions book:
• Skidding Truck • Book Push Against the Wall
• Spool Pull • Acceleration at the Top
• Falling Balls • Net Force Half-Way Up
• Skydiver • Acceleration on the Way Up
• Truck and Car Collision • Balanced Scale
• Block Pull • Galileo
SUGGESTED LECTURE PRESENTATION
In Chapter 2 the concept of inertia was introduced—the notion that once an object is in motion, it will continue in motion if no forces are exerted on it. Moving things tend to remain moving at constant velocity. In the previous chapter we learned about acceleration—the change in velocity that objects experience when a force is exerted. In this chapter we’ll treat the relationship between force and acceleration.
Friction: Drag a block at constant velocity across your lecture table. Acknowledge the force of friction, and how it must exactly counter your pulling force. Show that pulling force with a spring balance. Now since the block moves without accelerating, ask for the magnitude of the friction force. It must be equal and opposite to your scale reading. Then the net force is zero. While sliding the block is in dynamic equilibrium. That is, SF = 0.
CHECK QUESTION: (similar to one in the text). Suppose in a high-flying airplane the captain announces over the cabin public address system that the plane is flying at a constant 900 km/h and the thrust of the engines is a constant 80,000 newtons. What is the acceleration of the airplane? [Answer: Zero, because velocity is constant.] What is the combined force of air resistance that acts all over the plane’s outside surface? [Answer: 80,000 N. If it were less, the plane would speed up; if it were more, the plane would slow down.]
Continue your activity of pulling the block across the table with a spring balance. Show what happens when you pull harder. Your students see that when the pulling force is greater than the friction force, there is a net force greater than zero, as evidenced by the observed acceleration. Show different constant speeds across the table with the same applied force, which shows that friction is not dependent on speed. Distinguish between static and sliding friction, and show how a greater force is needed to get the block moving from a rest position. Show all this as you discuss these ideas. Cite the example in the book about skidding with locked brakes in a car [where the distance of skid for sliding friction is greater than static friction, where lower braking application results in nonsliding tires and shorter sliding distance]. Discuss the new automatic braking systems (ABS) now available on cars.
Page 19 of Practicing Physics treats friction in some detail.
After you have adequately discussed friction and net force, pose the following (Be careful that your class may not be ready for this, in which case you may confuse rather than enlighten.):Mass and Weight: To distinguish between mass and weight compare the efforts of pushing horizontally on a block of slippery ice on a frozen pond versus lifting it. Or consider the weightlessness of a massive anvil in outer space and how it would be difficult to shake, weight or no weight. And if moving toward you, it would be harmful to be in its way because of its great tendency to remain in motion. The following demo (often used to illustrate impulse and momentum) makes the distinction nicely:
DEMONSTRATION: Hang a massive ball by a string and show that the top string breaks when the bottom is pulled with gradually more force, but the bottom string breaks when the string is jerked. Ask which of these cases illustrates weight. [Interestingly enough, it’s the weight of the ball that makes for the greater tension in the top string.] Then ask which of these cases illustrates inertia. [When jerked, the tendency of the ball to resist the sudden downward acceleration, its inertia, is responsible for the lower string breaking.] This is the best demo I know of for showing the different effects of weight and mass.
Mass Resists Acceleration: The property of massive objects to resist changes is nicely shown with this follow-up demonstration.
DEMONSTRATION: Lie on your back and have an assistant place a blacksmith’s anvil on your stomach. Have the assistant strike the anvil rather hard with a sledge hammer. The principles here are the same as the ball and string demo. Both the inertia of the ball and the inertia of the anvil resist the changes in motion they would otherwise undergo. So the string doesn’t break, and your body is not squashed. (Be sure that your assistant is good with the hammer. When I began teaching I used to trust students to the task. In my fourth year the student who volunteered was extra nervous in front of the class and missed the anvil entirely—but not me. The hammer smashed into my hand breaking two fingers. I was lucky I was not harmed more.)
Relate the ideas of tightening a hammer head by slamming the opposite end of the handle on a firm surface, with the bones of the human spine after jogging or even walking around Interestingly, we are similarly a bit shorter at night. Ask your students to find a place in their homes that they can’t quite reach before going to bed—a place that is one or two centimeters higher than their reach. Then tell them to try again when they awake the next morning. Unforgettable, for you are likely instructing them to discover something about themselves they were not aware of!
Briefly review the idea of acceleration and its definition, and state that it is produced by an imposed force. Write this as a ~ F and give examples of doubling the force and the resulting doubling of the acceleration, etc. Introduce the ideas of net force, with appropriate examples—like applying twice the force to a stalled car gives it twice as much acceleration—three times the force, three times the acceleration.
CHECK QUESTION: If one were able to produce and maintain a constant net force of only 1 newton on the Queen Mary ocean liner, what would be its maximum speed? [Give multiple choices for an answer: a) 0 m/s; b) 1 m/s; c) less than 1 m/s; d) about 10 m/s; e) almost the speed of light!] In the following discussion, the key concept is net force. Point out the enormous applied forces necessary to overcome the enormous water resistance at high speeds, to yield a net force of 1 newton; and the meaning of acceleration—that every succeeding second the ship moves a bit faster than the second before. This would go on seemingly without limit, except for relativistic effects which result in e) being the correct answer.
Falling Objects: Point out that although Galileo introduced the idea of inertia, discussed the role of forces, and defined acceleration, he never tied these ideas together as Newton Newton
SKIT: Hold a heavy object like a kilogram weight and a piece of chalk with outstretched hands, ready to drop them. Ask your class which will strike the ground first if you drop them simultaneously. They know. Ask them to imagine you ask the same of a bright youngster, who responds by asking to handle the two objects before giving an answer. Pretend you are the kid judging the lifting of the two objects. “The metal object is heavier than chalk, which means there is more gravity force acting on it, which means it will accelerate to the ground before the chalk does. “Write the kids argument in symbol notation on the board. a ~ F. Then go through the motions of asking the same of another child, who responds with a good argument that takes inertia rather than weight into account. This kid says, after shaking the metal and chalk back and forth in his or her hands, “The piece of metal is more massive than the chalk, which means it has more inertia, than the chalk, which means it will be harder to get moving than the chalk. So the chalk will race to the ground first, while the inertia of the metal causes it to lag behind. “Write this kid’s argument with, a ~ 1/m. State that a beauty of science is that such speculations can be ascertained by experiment. Drop the weight and the chalk to show that however sound each child’s argument seemed to be, the results do not support either. Then bring both arguments together with a ~ F/m, Newton
Relate your skit to the case of falling bricks, Figure 4.12, and the falling boulder and feather, Figure 4.13. Once these concepts are clear, ask how the bricks would slide on a frictionless inclined plane, then illustrate with examples such as the time required for a fully loaded roller coaster and an empty roller coaster to make a complete run. In the absence of friction effects, the times are the same. Cite the case of a Cadillac limousine and Volkswagen moving down a hill in the absence of friction. By now you are fielding questions having to do with air resistance and friction. (Avoid getting into the buoyancy of falling objects—information overload.)
DEMONSTRATION: After you have made clear the cases with no friction, then make a transition to practical examples that involve friction—leading off with the dropping of sheets of paper, one crumpled and one flat. Point out that the masses and weights are the same, and the only variable is air resistance. Bring in the idea of net force again, asking what the net force is when the paper falls at constant speed. (If you left the Chapter 3 demo of the falling book and paper on top of it unexplained, reintroduce it here.)
CHECK QUESTIONS: What is the acceleration of a feather that “floats” slowly to the ground? The net force acting on the feather? If the feather weighs 0.0 N, how much air drag acts upward against it? [Acceleration is zero at terminal speed, and air drag = weight of object.]
These questions lead into a discussion of the parachutists in Figure 4.15. When the decrease of acceleration that builds up to terminal velocity is clear, return to the point earlier about the Cadillac and Volkswagen moving down an incline, only this time in the presence of air resistance. Then ask whether or not it would be advantageous to have a heavy cart or a light cart in a soap-box-derby race. Ask which would reach the finish line first if they were dropped through the air from a high-flying balloon. Then consider the carts on an inclined plane.
For your information, the terminal velocity of a falling baseball is about 150 km/h (95 mi/h), and for a falling Ping-Pong ball about 32 km/h (20 mi/h).
So far we have regarded a force as a push or a pull. We will consider a deeper definition of force in the next chapter. Onward!
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