Rev. 11/14/2005
Science Concepts:
Newton’s Second Law tells us that a net force will change the velocity of an object by changing either its speed or its direction.
Duration:
1 hour
Essential Questions:
What are the relationships between force, mass, and acceleration?
Introduction:
This material examines Newton’s Second Law of Motion in a way that will help you teach the law to your students. The photocopy-ready Student Activities pages will give students the opportunity to learn aspects of the Second Law in a way that they will find interesting and fun. The activity can be tailored for the level of your students, and can be completed individually or in groups. In addition, students will create a logbook, called Newton’s Lawbook, in which they can take notes and track their findings from the scientific experiments offered in the Student Activity page.
Background information:
Newton’s Second Law of Motion introduces one of the most important fundamental concepts in science: mass. Sir Isaac Newton used the word “mass” as a synonym for “quantity of matter.” Today, we more precisely define mass as a “measure of the inertia of a body.” 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.
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.
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.
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.
The Swift Satellite
Swift is a space-based multiwavelength observatory dedicated to the study of gamma-ray bursts. Its purpose is to determine the origin and nature of these powerful cosmic explosions; determine how the blastwaves from the bursts evolve and interact with their surroundings; and determine if these bursts can be used as effective probes of the early Universe. Launched on November 20th, 2004, Swift is a collaboration between the United States, the United Kingdom, and Italy.
Newton’s Second Law and the Swift Satellite
Swift has a mass of about 1,400 kilograms, which is about the same mass as 30 ten-year-olds in a bag! In order to get the Swift satellite into orbit, it was launched from a Boeing Delta rocket with a mass of about 231,800 kg. With Swift inside the rocket, the combined mass of the two was 233,300 kg!
The Earth’s gravity pulls the rocket (with Swift inside) down with a force of about 2,285,000 newtons. But the rocket’s boosters can exert an upward force of about 2,722,000 newtons. This means that the upward force is stronger than the downward force by about 437,000 newtons. As the rocket lifts off, it has a net upward force of 437,000 newtons exerted on it. With a total mass of 233,300 kg, the rocket accelerated upward at a rate of 1.8 meters per second per second (acceleration = force / mass). In other words, for every second of travel time the rocket will increase its velocity by almost 2 meters per second. As Newton’s Second Law explains it: In the presence of a net force, an object experiences an acceleration (F=ma).
Materials: [lay this out to be like the other activities, in a bulleted list for each thing]
• two identical ball bearings
• two marbles 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
Objectives: Students will…
Find the average speed of the masses rolling down the incline.
Find that the balls with a larger mass will cause the target ball to travel the 100 cm distance in less time.
See the relationship between force, mass, and acceleration.
Procedure: (You should read the instructions below as well as those in the student handout, this handout contains more details.)
1. Pre-class: Demos and Thought Problems
Use the following demonstrations to introduce Newton’s Second Law to your class.
Place an empty cardboard box and two or three bricks or heavy books on a table (or the floor). Push the empty box across the table. Note how much force was required to perform the task. Now put one of the bricks or books in the box. Again, push it across the table. Was more, less, or the same amount of force required to accomplish the task? Add another brick or book to the box and push it across the table again. Was more, less, or the same amount of force required this time to accomplish the task? Explain the experiment using the proper physics vocabulary of force, mass, acceleration, velocity, distance, time, etc.
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. Discuss other examples of objects which undergo two motions at once. Examples may include an airplane lifting off from the runway, a skier going down a hill, or a baseball hit by a batter. To undergo two motions at once requires the existence of more than one force – one force may get the object moving while the other changes its direction. For example, the bat may provide the force to move the ball forward and up into the air, but it is gravity providing the force which causes it to arc toward the ground again. You can demonstrate this by throwing or kicking a ball.
In-class
Activity: Collision on the Tracks
Part 1 – Colliding Spheres
See student handout for detailed procedure.
Part 2 –Colliding Spheres and Beyond
Use this experiment to explain the following concepts to your students:
a) In accordance with Newton’s First Law of Motion, the target ball remained at rest until it was acted on by the force of the impact of the ball that was rolled down the incline. This force varied depending on the mass of the impact ball.
b) The force imparted to the target ball is found by multiplying the mass times the acceleration of the impact ball. The impact balls all had (about) the same acceleration, but different masses.
c) The larger the force imparted to the target ball, the larger its acceleration. Students should understand that the rate of acceleration of the target ball depends on the mass (and therefore, force) of the rolling ball. This is Newton’s Second Law. Mathematically, this represents a direct relationship. As one variable goes up, the other variable goes up proportionally. In other words, if the mass is constant, the force and acceleration are directly proportional.
Extension Activity:
Have the students think about cars accelerating and the collisions that occur. What happens when a larger car hits a smaller car? Which cars apply the greater force (assuming they had the same deceleration or negative acceleration)?
Assessment:
Points /Part 1: Colliding Spheres
/ Part 2: Colliding Spheres and Beyond4 / Performed all suggested steps in the procedure, included observations, filling out table, and thoughtful answers to questions. / Performed all suggested steps in the procedure, included observations, filling out table, and thoughtful answers to questions.
3 / Performed all suggested steps in the procedure, included observations, partially filled out table, and answered 2 or 3 questions. / Performed all suggested steps in the procedure, included observations, partially filled out table, and answered 2 or 3 questions.
2 / Performed all suggested steps in the procedure, included observations, partially filled out table, and answered 1 or 2 questions. / Performed all suggested steps in the procedure, included observations, partially filled out table, and answered 1 or 2 questions.
1 / Described some observations from the experiment, but observations where sloppy and or incomplete. / Described some observations from the experiment, but observations where sloppy and or incomplete.
0 / Nothing turned in / Nothing turned in
Answers:
Answers will vary depending on measurements.
Part 1:
Students can calculate the acceleration of the rolling ball by figuring out the ball’s mass and the amount of time it took to roll down the ramp. The average speed can then be calculated by figuring out the distance rolled and the time it took to hit the target. The average speed must be determined in order to calculate the ball’s speed at the bottom of the ramp. Since the ball is undergoing uniform acceleration, its velocity will change linearly – from its initial velocity to its final velocity. Thus, the average velocity is simply:
However, since vo = 0, then vf = 2vavg.
To calculate the acceleration of the ball at the time of impact, subtract the ball’s initial speed (which is zero) from its final speed and divide by the time it took to hit the target. In this exercise acceleration is independent of mass, but it does depend on diameter (since the balls are rolling, not sliding or free-falling) so choose the balls to be as close to the same size as possible, and don’t use any hollow balls. The acceleration for the balls of different masses should then be the same.
Part 2:
Students will find that the balls with a larger mass will cause the target ball to travel the 100 cm distance in less time. Point out that although the mass of the impactor ball changes, the mass of the target ball remains constant.
7
Rev. 11/14/2005
Student Handout:
Newton’s Second Law: Collision on the Tracks
This activity will help you learn all about Newton’s Second Law of Motion. Use the notebook, which you have designated as your Newton’s Lawbook, to take notes, track your progress, and evaluate findings from the experiments you will conduct. Start by writing down Newton’s Second Law of Motion.
In this experiment you will examine Newton’s Second Law of Motion by investigating the relationships between force, mass, and acceleration.
Materials
• two identical ball bearings
• two marbles 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
Experiment Setup –
1. Determine the mass of each ball bearing and marble. Record the masses in the Table below.
2. 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 30 and 60 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 – Colliding Spheres
1. Put the marble with the smallest mass at the top of the inclined track. Use a ruler to hold the ball steady.
2. Before you release the marble, predict what will happen when the marble hits the ball bearing.
3. Remove the ruler and let the marble roll down the track. Observe what happens when the marble hits the ball bearing. Was it what you expected? Why or why not? Record your notes in your Newton’s Lawbook.
4. Repeat the experiment, using a stopwatch to measure how long it takes the marble to roll down the track and hit the target ball bearing. Use this information, along with your calculations of the marble’s mass, to calculate the acceleration of the marble. Enter your data and calculations in the Table below.