• During the lesson, use the following checklist to monitor students’ understanding and ensure students master targeted learning goals within the time frame:

• Student understands that a change of movement is generated by the application of force. It is not a product of some characteristic of the object itself.

• Student understands that when forces are balanced, there is no change of motion.

• Student understands that when the forces are out of balance, change of motion is generated.

• Student understands that force vectors are independent of each other, so that action along one vector has no influence on any other vector.

1. Open the lesson with the following narrative:

“In April 1970, the lunar mission Apollo 13 suffered an explosion while on the way to the moon. It had to loop around the moon and coast a quarter-million miles back to Earth largely without power. As it neared the Earth it was found to have drifted off its expected flight path so much that re-entry into the atmosphere had become impossible. The spacecraft would have skipped off the atmosphere like a flat stone off water and been lost in space. A tiny leak somewhere in its damaged plumbing had gradually exerted enough force to drive the spacecraft off course. Yet the force generated by the leak was too small to be noticed by the astronauts. The trajectory of Apollo 13 was corrected with difficulty, as the astronauts had to fire their spacecraft’s engine while most of its navigation systems were turned off. In the end they landed safely.

Show the following video featuring highlights from the 1972 NASA film “Apollo 13: Houston, We’ve Got A Problem.”

http://dsc.discovery.com/videos/classic-nasa-film-apollo-13-1.html

“This lesson will explore the relationship between force and movement, and demonstrate that movement is the product of unbalanced forces. The forces we will deal with will not be as big as those involved in the Apollo 13 mission, with no potential for disaster. But the forces are the same, differing only in scale.

“In theory the relationship between force and motion is simple, as movement is the product of force. Newton’s first law of motion tells us that a body in motion will remain in motion until acted on by an unbalanced force. This implies that everything will continue moving in a straight line until it hits something. In the real world that hardly ever happens. That’s not because Newton was wrong, but because in the real world all objects are subject to multiple forces. Their actual motion depends on the net force exerted on them at a given moment. These forces can be complex and difficult to gauge, but we will examine a situation where it is simple and straightforward.

“The force exerted on an object is expressed as a vector. There are any number of force vectors acting on a body, but they are typically summed up by one for each of the three dimensions (X, Y, and Z, or up-down, right-left, and back-forward.)”

2. Review with students what a vector represents: force with a direction. There must be two components: the magnitude of the force and the direction.

Review what force is: action that accelerates an object. Acceleration, meanwhile, is the rate of change of velocity of an object over time. Keep applying force, and you keep accelerating an object, speeding it up or slowing it down depending on the direction. A constant force produces a constant speed.

Point out that, on the surface of the Earth, the relation between force and motion is not obvious, since friction (especially air resistance) increases as velocity increases. Therefore, you eventually reach terminal velocity, where the available force can maintain the object’s velocity against the friction, but not increase it.

3. Mark a point one meter above the floor or a table top, drop a table tennis ball from that point, and mark were it lands.

“Before I dropped the ball, the forces acting on the ball were gravity, and the force of my fingers holding it against gravity. Those forces were in balance. Since there was no net force exerted on the ball, it remained at rest. According to Newtonian physics, the object at rest is the same as when the velocity of the object is zero.

“After I dropped the ball, the force acting on the ball was gravity and air resistance. Gravity is well-known to be a vector toward the center of the Earth of 9.8 meters per second squared. Air resistance is not trivial, and increases as the velocity of the falling object increases. In this case, gravity was stronger than air resistance, and so the ball fell.

“At some point air resistance (also called drag) will equal the opposite acceleration due to gravity, and the object will at that point have reached its terminal velocity. It will continue falling at a continuous velocity, rather than an increasing velocity. But in this demonstration the air resistance will be disregarded.”

4. Turn on the electric fan so that it blows from one side. Drop the ball again and mark where it lands. Measure the distance between the point of the first landing and the second.

“The ball moved sideways this time, as well as down, because an additional unbalanced force acted upon it. The wind generated by the fan pushed against it from one side and was not balanced by any force on the other side, except for the usual air resistance. Combined with gravity, the net force was diagonal.”

How much was the force? The distance that the ball moved sideways, in centimeters, is X percentage of the 100 centimeters that the ball fell downward during the same interval. Therefore, the force imparted by the fan was X percent of the force imparted by gravity. If the ball moved 13 centimeters, then the force moving it in that direction—the vector—was .13 x 9.8 meters per second squared, or 1.274 meters per second squared.

“The ratio is reliable because the movement of the ball to one side had no impact on its downward motion. Vectors from different directions are independent of each other. The fact that the ball was moving to one side did not speed up or slow down the fall of the object, as the unbalanced force that caused it to fall (the force of gravity) was not affected. (Of course, thanks to air resistance, had it been a parachute or wing rather than a ball, its speed of fall could have been slowed considerably.) The independence of vectors is very important when talking about things like ballistics. If you fire a bullet horizontally, how far it will go basically depends on how long it takes to fall to the ground. The fact that it is moving fast horizontally does not change the fact that it is falling.

To further illustrate this, show the following videos:

• Short demonstration of gravity’s effect on horizontal movement: https://www.youtube.com/watch?v=77GSO3NCWwg

• Mythbusters Bullet Fired Dropped #1:

  http://dsc.discovery.com/videos/mythbusters-dropped-vs-fired-bullet.html

• Mythbusters Bullet Fired Dropped #2:

  https://www.youtube.com/watch?v=D9wQVIEdKh8

“Likewise, in our experiment, the ball moved diagonally in the second case rather than straight down. But this movement was a product of the two vectors of motion, and did not change either vector.”

5. Using graph paper (S-7-1_Graph Paper.doc), students will use the data that has been gathered to graph the two force vectors that were affecting the ball in the second case. The vertical vector would be 100 units, and the horizontal vector would be the sideways displacement shown by the falling ball, of X units.

Students should label the vectors with the force that was imparted (9.8 meters per second squared downward, and X percent of 9.8 meters per second squared sideways.)

They should draw the diagonal path of the ball, between the top of the graph to the end of the sideways vector, showing the actual path of the ball.

In a case where X is 13 units, the graph would look like this:

 

6. Students can then break into small groups, each of which will then perform its own version of the experiment and graph the results. However, each group should have a different variable, such as a ball of a different size or weight, or the fan in a different position.

7. After finishing the graphs, have groups compare their results and discuss the differences and their likely causes.

Extension:

• Part 1: Students who need to be challenged can additionally figure how far the ball traveled in its diagonal path, using the Pythagorean theorem (A²+B²=C², where the two vectors are A and B and the diagonal path is C.) In our example, the path would equal 100.841 centimeters.

Students can figure the actual velocity in each vector and on the diagonal path of actual travel, given that the time it takes to fall one meter averages .45 seconds. (In our example it traveled downward at a rate of 2.22 meters per second or about 8 kilometers per hour, and sideways at .289 meters per second, or about 1 kilometer per hour.)

• Part 2: Students can raise the height to 2 meters and compare the results. The average time to fall 2 meters is .64 seconds.

Point out that acceleration is continuous and cumulative over time, until terminal velocity is reached. That is why the difference between 1 meter and 2 meters is not linear.