Newton’s Second Law of Motion
In the presence of a net force, an object experiences an acceleration.
F=ma
Teacher’s Guide
By: Gifford Gillette (Taylorview Junior High)
Lesson Overview: Lab designed to help students learn Newton’s second law of motion. / Subject Area: Physical ScienceNational Science Education Standards Addressed:
1. State and apply Newton’s three laws of motion
2. Define mass / Topic: Newton’s 2nd law of motion
Audience:
9th grade
Resources: students – if there is a farmer’s boy in your class they should be able to provide the ball bearings (steelies) and every boy has hot-wheels tracks to donate. / Suggested Time: 55 minutes
Materials: hot-wheels race tracks, cabinet packaging, ball bearings.
Learning Objectives:
1. Learn how net force, mass, and acceleration influence the motion of an object.
2. Provide examples of Newton’s second law of motion.
3. Describe Newton’s second law of motion mathematically.
Background:
1. Introduces students to a fundamental concept in physics.
2. The lab tests their critical thinking skills.
3. Students get hand’s-on experience with Newton’s second law by colliding objects (they like that).
4. It picks up where we left off with Newton’s 1st law (easy transition).
Assessment Strategy:
1. Quiz the students during the lab by asking find-out questions. i.e. What do you expect to happen if the target ball is bigger?
2. When they ask questions about conversions respond with a question about what is the mathematical relationship between force, mass, and acceleration and what is given in the question?
3. As them for example of Newton’s second law of motion and then use their examples to teach them the relationship.
Teaching Tips:
The lab is pretty self-explanatory but to introduce the concepts or reiterate them it may be helpful to provide an example. For example, whirl a yo-yo at the end of its string in a vertical path. Ask the students if the yo-yo is changing directions. Be prepared to explain that even though it is traveling in a continuous circle it is indeed changing directions. Only motion in a straight line is motion that is not changing its direction. Movement in a circle is actually a continuous changing of directions. Therefore, it must be undergoing an acceleration. Ask what force is acting on the yo-yo to change its direction. In an open discussion, explain to students that it is the force of your hand pulling on the string which changes the yo-yo’s direction. Explain that the yo-yo is undergoing two motions at once: It is going up and down as well as left to right.
Newton’s Second Law of Motion introduces one of the most important fundamental concepts in science: mass. The more mass an object has the more difficult it is to change its state of motion, whether it is at rest or moving in a straight line at a constant speed. Think of it this way: An elephant has more inertia than a mouse. It is much harder to push an elephant across a floor than it is a mouse, and much harder to stop the elephant once it is moving. Therefore, by definition, an elephant has more mass than a mouse.
The Second Law goes on to mathematically define the exact relationship between net force and acceleration: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. Also, the direction of the acceleration is in the direction of the net force acting on the object. More simply, and as Newton put it: F=ma, where “F” (force) and “a” (acceleration) are both vector quantities, and “m” is the object’s mass. Note that the “F” in this equation is the net force, that is, the sum of all the forces acting on the object.
In SI units (metric system), mass is measured in kilograms, acceleration is in meters per second per second, and the unit of force is the newton (N). One newton is the force required to impart an acceleration of 1 m/sec2 to a mass of 1 kg (1N = 1 kg m/sec2). By the way, the newton unit of measurement was named in honor of Sir Isaac himself.
Newton’s Second Law of Motion
Newton’s Second Law takes up where the First Law ends. The First Law describes inertia: A body will not change its existing state of motion without a net force acting on that body. In other words, without an outside force a body will remain still if still, or, if moving, keep moving in the same direction at a constant speed. The second law states that the acceleration of an object is dependent upon two variables – the net-force acting upon the object and the mass of the object.But what happens when a net force interacts with inertia? The Second Law tells us that a net force will change the velocity of an object by changing either its speed or its direction. Such a change in velocity is called an acceleration. So, we can say that a net force gives rise to acceleration. In this lab you will predict and calculate how the mass and the net force of a ball bearing will affect the acceleration of another “target” ball bearing.
Materials
You will need the following items for this experiment:
• two identical ball bearings
• two ball bearings with different masses (similar sizes), each with less mass than the ball bearings
• two tracks, 1 meter each
• a ruler
• a stopwatch
• a balance or scale
Procedure
1. Set up a ramp, 1 meter in length. Use books or a board to incline the ramp at an angle of 5 to 10 degrees.
3.Starting from the top of the ramp, put marks along the track at 40 and 70 centimeters.
4. Place the other track at the end of the incline. Make sure there’s a smooth transition where the tracks are joined. Put a book at the end of the last track.
5. Put one of the ball bearings at the bottom of the inclined track, where it becomes level.
Part 1
1. Put the ball bearing with the smallest mass at the top of the inclined track. Use a ruler to hold the ball steady.
2. Before you release the ball bearing, predict what will happen when it hits the heaviest ball bearing.
3. Remove the ruler and let the ball bearing roll down the track. Observe what happens when it hits the heavy ball bearing. Was it what you expected? Why or why not?
4. Repeat the experiment, using a stopwatch to measure how long it takes the light ball bearing to roll down the track and hit the target ball bearing. Use this information, along with your
calculations of the ball bearing’s mass, to calculate the acceleration of the ball bearing. Enter your data and calculations in the Table below.
5. Repeat the experiment twice more. First, start the ball bearing at the 70 cm mark. Second, start it at the 40 cm mark. Record your data and calculate the acceleration of the ball bearing in the Table below.
Average Time
(sec) / Distance Covered
(cm) / Initial Speed
(cm/sec) / Average Speed
(cm/sec) / Acceleration
(cm/sec/sec)
70 / 0
40 / 0
6. Replace the small ball bearing with the medium-sized one. Place it at the top of the ramp. Predict what will happen when this ball bearing hits the target ball bearing.
Let the ball bearing roll and observe what happens. Were your predictions right? Why or why not?
7. Finally, roll the last, large ball bearing down the ramp. What will happen this time when it strikes the other ball bearing?
Part 2
1. In this experiment you will investigate what happens to the target ball bearing after it is struck by the smaller ball bearings. Roll the lightest ball bearing from the 70 cm mark on the incline, letting it hit the target. Use a stopwatch to record the time it takes the target ball to travel 50 cm to the book. Perform the experiment three times and determine the average time. Record
your results in the Table below.
2. Repeat the above procedure with the more massive ball bearing. Enter your data and results in the Table below.
Time 1 (sec) / Time 2 (sec) / Time 3 (sec) / Average Time (sec)
Small B-B
Medium B-B
Large B-B
3. What was the reaction of the target ball bearing after the impacts from each of the three balls? Relate your observations to Newton’s Second Law of Motion.
4. Now calculate the results for the target ball in the Table below.
Think About It
Average
Target Ball
Roll Time
(sec) / Distance
Target Ball
Moved
(cm) / Initial
Speed of
Target Ball
(cm/sec) / Final Average
Speed
of Target Ball
(cm/sec) / Acceleration
of Target Ball
(cm/sec/sec)
Small B-B / 70 / 0
Medium B-B / 70 / 0
Large B-B / 70 / 0
Now let’s put it all together. Look at the force applied by the rolling ball (Fi = miai) and the acceleration of the target ball (at = Fi/mt). Note that “i” represents impact, and “t” equals target.
1. What happened to the motion (acceleration) of the target ball as the force from the rolling balls increased (due to the larger masses)?
2. Using mathematical language, explain the relationship between force and acceleration.
Calculation Friday!!!
1. What acceleration will result when a 12-N net force applied to a 3-g object? A 6-g object?
2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass.
3. An object is accelerating at 2 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration?
4. An object is accelerating at 2 m/s2. If the net force is tripled and the mass is halved, then what is the new acceleration?
5. According to Newton’s 2nd Law, what force is necessary to accelerate a
5 kg rock to 8m/s2? (p. 70)
6. Define friction and what kind of energy does it always produce?(p.70)
7. What are some ways to reduce friction?
8. What does the Law of Gravitation state? (p. 75)
8. What is the range of gravity? (p. 76)
9. How are weight and mass different? (p. 78)
10. What does Newton’s 3rd Law state? (p. 83)
11. . Use Newton’s 3rd Law to identify the reaction forces:
A) tire pushes road
B) rocket pushes gas
C) foot pushes soccer ball
11. If forces are equal and opposite, how come objects behave so differently?