Exploration Guide: Uniform Circular Motion
Name: ______
Scientists at NASA's Jet Propulsion Laboratory use their knowledge of circular motion when they launch spacecrafts. By timing the launch to take advantage of the circular motion of Earth rotating on its axis, scientists can control the speed with which the craft will travel around the Sun.
If the spacecraft travels around the Sun at a slightly higher speed than Earth does, the radius of its orbit will slowly increase, and it will move outward through the Solar System. This way, the craft could intersect with the orbits of Mars, Jupiter, Saturn, Uranus, Neptune, or Pluto.
If the spacecraft travels around the Sun at a slightly lower speed than the Earth does, the radius of its orbit will slowly decrease, and it will move inward toward the Sun. This could bring the probe near the inner planets, Venus and Mercury.
Part A: Acceleration of an Object in Uniform Circular Motion
In this activity, you will explore the acceleration of an object that travels a circular path at constant speed. Motion of this kind is called uniform circular motion.
A. The Gizmotm shows both a top view and a side view of a puck constrained by a string, traveling a circular path on an air table. Be sure the Gizmo has these settings: radius 8 m, mass 5 kg, and velocity 8 m/s. Then click Play and observe the motion of the puck.
1. The puck in the Gizmo is traveling at a constant speed, but it is NOT traveling at a constant velocity. Explain why.
______
(Hint: Velocity is a vector quantity that includes both a magnitude and a direction.)
2. Because the velocity of the puck is changing (because its direction is changing), the puck must be experiencing an acceleration. Click BAR CHART and choose Acceleration from the dropdown menu. Check Show numerical values. The leftmost bar shows the magnitude of the acceleration, or |a|. (The other two bars show the x- and y-components of the acceleration, ax and ay.) What is the value of |a|?
Jot this value down, along with radius = 8 m, in the table below.
3. Keeping velocity set to 8 m/s, set radius to 4 m. (To quickly set a slider to a value, typing the number in the field to the right of the slider and press Enter.) What is the new magnitude of the acceleration, |a|?Jot down this new value along, with radius = 4 m, with your previous data, in the table below.
4. Now set the radius to 2 m. What is the resulting value for |a|?
5. Record these values along with the others, in the table below.
Radius / Acceleration8m
4m
2m
6. Examine the corresponding pairs of values for the radius and the magnitude of the acceleration, |a|. How does |a| change when the radius is divided by 2?
______
7. How do you think |a| changes when the radius is multiplied by 2?
______
8. Multiplied by 3?
______
9. Choose your own values for the radius to test your answers in the Gizmo. What were your results?
______
10. You should have found that, in general, when the radius is multiplied by a number, |a|is divided by that same number. Also, when the radius is divided by a number, |a| is multiplied by the same number. One way to say this is, the magnitude of acceleration is inversely proportional to the radius.
B. Click Reset (). Set radius to 8 m, mass to 5 kg and velocity to 2 m/s. Click Play ().
1. Display the BAR CHART pane and be sure that Acceleration is selected. Check Show numerical values to display the magnitude of the acceleration. What is |a|?
______
2. Jot down the values for |a| in the table below.
3. Set velocity to 4 m/s. What is the new value for |a|? Jot these values down in the table below..
4. Change the velocity one more time, to 8 m/s. What is |a| in this case? Record these values as well in the table below.
Velocity / Acceleration2 m/s
4 m/s
8 m/s
5. You have doubled the velocity twice. How did |a| change each time?
______
6. You should have seen that multiplying the velocity by 2 causes |a| to be multiplied by 4. How do you think tripling the velocity affects |a|?
______
7. How do you think dividing the velocity by 5 affects |a|?
______
8. Choose your own values for the velocity and test this in the Gizmo.
______
9. Explain the relationship, in general, between velocity and the magnitude of acceleration, |a|. Use the words "directly proportional" in your answer.
______
______
Part B: Force on an Object in Uniform Circular Motion
In this activity, you will explore the nature of the net force that acts upon an object that is traveling in uniform circular motion.
A. Click Reset. Set the Gizmo back to the original settings - radius 8 m, mass 5 kg and velocity 8 m/s. Click Play. You saw in the previous activity that the puck is undergoing an acceleration. This means that some force must be acting upon it, and the direction of that force must be the same as the direction of the acceleration.
1. In the DESCRIPTION pane, select Show velocity and acceleration vectors. The two vectors are shown in the SIMULATION pane - the velocity vector in green and the acceleration vector in blue. Describe the direction of the velocity vector.
______
2. Describe the direction of the acceleration.
______
3. What does the acceleration vector always point toward?
______
4. You should notice that, when the settings of the Gizmo are held constant, the magnitude of acceleration, |a|, of an object is constant. (|a| is the "length" of the acceleration vector. If you like, you can also go to the BAR CHART pane, with Acceleration selected, to see the value of |a|.) Explain why the acceleration, however, is NOT constant.
______
______
5. Using the direction of the acceleration as a hint, what object do you think provides the force that keeps the puck traveling on its circular path?
______
6. Click Pause (). If the string were to break at this instant, what path would the puck travel?
______
7. Click the GRAPH tab. Then select Force vs. time from the dropdown menu to display a graph of the x- and y-components of the force that acts on the puck (Fx and Fy). Click Play. When the puck reaches the point in its path closest to the bottom of the screen, click Pause. What is the direction of the acceleration when the puck is at this position?
______
8. Is Fx positive, negative, or zero?
______
9. What about Fy?
______
10. What does this tell you about the direction of the net force acting on the puck in this position?
______
B. Click Reset. Set radius to 8 m, mass to 3 kg and velocity to 8 m/s. Click Play. Then determine the net force acting on the puck by looking at the magnitude of Fy acting on the object at the point closest to the bottom of the screen. (At that point, Fx = 0, so Fy is the entire force.)
1. What is the net force acting on the puck when the mass of the puck is 3 kg? Jot this value down, in the table below.
2. Set the mass of the puck to 6 kg. Then determine the net force acting on the puck in the same way. Record this data in the table below. How does the force compare with that recorded in the preceding step?
______
3. Set the mass to 9 kg and repeat the process one more time.
Mass / Net Force3 kg
6 kg
9 kg
4. What is the relationship, in general, between the mass of an object and the net force that acts on it when acceleration is held constant? Use the words "directly proportional" or "inversely proportional" in your answer.
______
______
5. Based on this relationship, what would you expect the force to be if you were to set the mass of the puck to 1.5 kg? Use the Gizmo to check your response.
______
______
SUMMARIZE:
What is the relationship between each of the following variables? Your choices are: "directly proportional", "inversely proportional", or no relation.
a. Radius and acceleration ______
b. Radius and velocity ______
c. Velocity and acceleration ______
d. Velocity and centripetal force ______
e. Mass and centripetal force ______
f. Radius and centripetal force ______
DO NOT FORGET TO ANSWER THE 5 MULTIPLE-CHOICE ASSESSMENT QUESTIONS UNDERNEATH THE GIZMO!
Exploration Guide: Uniform Circular Motion
Names: _____ANSWER KEY______
Scientists at NASA's Jet Propulsion Laboratory use their knowledge of circular motion when they launch spacecrafts. By timing the launch to take advantage of the circular motion of Earth rotating on its axis, scientists can control the speed with which the craft will travel around the Sun.
If the spacecraft travels around the Sun at a slightly higher speed than Earth does, the radius of its orbit will slowly increase, and it will move outward through the Solar System. This way, the craft could intersect with the orbits of Mars, Jupiter, Saturn, Uranus, Neptune, or Pluto.
If the spacecraft travels around the Sun at a slightly lower speed than the Earth does, the radius of its orbit will slowly decrease, and it will move inward toward the Sun. This could bring the probe near the inner planets, Venus and Mercury.
Acceleration of an Object in Uniform Circular Motion
In this activity, you will explore the acceleration of an object that travels a circular path at constant speed. Motion of this kind is called uniform circular motion.
A. The Gizmotm shows both a top view and a side view of a puck constrained by a string, traveling a circular path on an air table. Be sure the Gizmo has these settings: radius 8 m, mass 5 kg, and velocity 8 m/s. Then click Play and observe the motion of the puck.
1. The puck in the Gizmo is traveling at a constant speed, but it is NOT traveling at a constant velocity. Explain why.
______because its direction is constantly changing______
(Hint: Velocity is a vector quantity that includes both a magnitude and a direction.)
2. Because the velocity of the puck is changing (because its direction is changing), the puck must be experiencing an acceleration. Click BAR CHART and choose Acceleration from the dropdown menu. Check Show numerical values. The leftmost bar shows the magnitude of the acceleration, or |a|. (The other two bars show the x- and y-components of the acceleration, ax and ay.) What is the value of |a|?
Jot this value down, along with radius = 8 m, in the table below.
3. Keeping velocity set to 8 m/s, set radius to 4 m. (To quickly set a slider to a value, typing the number in the field to the right of the slider and press Enter.) What is the new magnitude of the acceleration, |a|?Jot down this new value along, with radius = 4 m, with your previous data, in the table below
4. Now set the radius to 2 m. What is the resulting value for |a|?
5. Record these values along with the others, in the table below.
Radius / Acceleration8m / 8 m/s2
4m / 16 m/s2
2m / 32 m/s2
6. Examine the corresponding pairs of values for the radius and the magnitude of the acceleration, |a|. How does |a| change when the radius is divided by 2?
_When you divide the radius by 2, you multiply the acceleration by 2. ______
7. How do you think |a| changes when the radius is multiplied by 2?
_When you multiply the radius by 2, you divide the acceleration by 2.______
8. Multiplied by 3?
_When you multiply the radius by 2, you divide the acceleration by 3.______
9. Choose your own values for the radius to test your answers in the Gizmo. What were your results?
_Answers will vary. r = 3m a = 21.33 m/s2 , 2r = 6m a = 10.67 m/s2 , 3r = 9m a = 7.11 m/s2__
10. You should have found that, in general, when the radius is multiplied by a number, |a|is divided by that same number. Also, when the radius is divided by a number, |a| is multiplied by the same number. One way to say this is, the magnitude of acceleration is inversely proportional to the radius.
B. Click Reset (). Set radius to 8 m, mass to 5 kg and velocity to 2 m/s. Click Play ().
1. Display the BAR CHART pane and be sure that Acceleration is selected. Check Show numerical values to display the magnitude of the acceleration. What is |a|?
______a = 0.50 m/s2______
2. Jot down the values for |a| in the table below.
3. Set velocity to 4 m/s. What is the new value for |a|? Jot these values down in the table below..
4. Change the velocity one more time, to 8 m/s. What is |a| in this case? Record these values as well in the table below.
Velocity / Acceleration2 m/s / 0.5 m/s2
4 m/s / 2.0 m/s2
8 m/s / 8.0 m/s2
5. You have doubled the velocity twice. How did |a| change each time?
___You multiplied the original acceleration by 4 each time. ______
6. You should have seen that multiplying the velocity by 2 causes |a| to be multiplied by 4. How do you think tripling the velocity affects |a|?
___You multiplied the original acceleration by 9. ______
7. How do you think dividing the velocity by 5 affects |a|?
___You divided the original acceleration by 25. ______