Student Exploration_ Pith Ball Lab

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Feb 20, 2024

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Name: Date: 2-5-24 Student Exploration: Pith Ball Lab Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: Coulomb’s law, electrostatic force, gravitational force, induced charge, pith ball, Pythagorean Theorem, tension, vector Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. A girl rubs a balloon on her head and then holds it a short distance away. Why does her hair stick to the balloon? The balloon receives a negative charge from the movement of electrons from the hair, while the hair retains a positive charge. The negative balloon attracts the positive hair. 2. Why do you think the individual strands of hair are spread apart? I think her hair strands that are positive are attracted to one another. Gizmo Warm-up The girl’s hair was attracted to the balloon by the electrostatic force , a force between all charged objects. Most objects acquire a charge ( q ) by gaining or losing electrons. Objects that gain electrons become negatively charged, while objects that lose electrons become positively charged. The Pith Ball Lab Gizmo shows two pith balls hanging by strings. Pith balls are made from lightweight material that can easily acquire a charge. To begin, check that the charge on each pith ball ( q 1 and q 2 ) is 0.0 × 10 -6 coulombs (C). Use the sliders to test each combination of charges listed below. State whether the electrostatic force is attractive (balls move together), repulsive (balls move apart), or zero (balls don’t move). Charge on left ball ( q 1 ) Charge on right ball ( q 2 ) Electrostatic force Positive Zero Zero Zero Negative Zero Positive Positive Repulsive Negative Negative Repulsive Positive Negative Attractive Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

Activity A: Coulomb’s law Get the Gizmo ready: ● Set q 1 and q 2 to 0.0 × 10 -6 C. ● Set the mass of the pith balls to 5 grams. ● Check that g is 9.8 m/s 2 and L is 0.50 m. Question: What factors affect the force between charged objects? 1. Summarize: Summarize what you have learned so far by filling in the blanks: If the two charges are the same, the force is repulsive. If the two charges are opposite, the force is attractive. If one of the charges is zero, the force is zero. *Note: For simplicity, the Pith Ball Lab Gizmo does not show induced charge . An induced charge occurs when a charged object is brought near a neutral object, causing the electrons in the neutral object to move away from or towards the charged object. This results in an attractive force between the charged object and the neutral object. 2. Predict: How do you think the strength of electrostatic force is related to the charges on the balls and the distance between them? The electrostatic force, in my opinion, increases with increasing charges and decreases with increasing distance. 3. Observe: Set q 1 to -5.0 × 10 -6 C. Gradually decrease q 2 below 0.0 × 10 -6 C. A. What do you observe? The pith balls are driven farther apart by repulsion as q2 lowers. B. What does this tell you about the force between the pith balls? The repelling force between the pith balls grows as q2 decreases. 4. Observe: Now slowly increase q 2 above 0.0 × 10 -6 C. What do you observe, and what does this tell you about the electrostatic force? The balls draw closer and closer together as q2 rises. The pith balls are drawn closely together, suggesting that when q2 rises, the electrostatic force becomes attractive. 5. Gather data: Turn on Show angle . For each combination of charges in the table below, record the product of the two charges and the resulting angle. (Note: If you like, you can type the charge values directly into the text boxes to the right of each slider and hit “Enter.”) Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

q 1 q 2 q 1 × q 2 Angle 6.0 × 10 -6 C 4.0 × 10 -6 C 2.4 x 10 -11 49.060° 8.0 × 10 -6 C 3.0 × 10 -6 C 2.4 x 10 -11 49.060° 16.0 × 10 -6 C 1.0 × 10 -6 C 1.6 x 10 -11 40.620° -4.0 × 10 -6 C -4.0 × 10 -6 C 1.6 x 10 -11 40.620° 6. Analyze: How does the electrostatic force relate to the product of the charges? Explain. The product of the charges results in an increase in the electrostatic force. Regardless of the specific charges utilized, the electrostatic force remains constant if the product of the charges remains constant. 7. Calculate: Coulomb’s law states that the electrostatic force ( Fq ) between charged objects is equal to a constant k multiplied by the product of the charges divided by the square of the distance between them: Turn on Show geometric dimensions and Show force vectors and magnitudes . Set q 1 and q 2 to -5.0 × 10 -6 C and the mass to 50 grams. A. What is the distance between the pith balls ( R )? 1.422 m B. What is the value of the electrostatic force ( Fq )? 0.111 N C. Based on the known values, use Coulomb’s law to solve for the proportionality constant, k . Show your work. (Note: The units of k are N·m 2 /C 2 .) k = 0.111((1.422 2 )/(-5.0 x 10 -6 ) 2 ) = 0.111((2.022)/(2.5 x 10 -11 )) = 8.98 x 10 9 k= 8.98 x 10 9 Nm 2 /C 2 8. Apply: Turn off Show force vectors and magnitudes . Choose your own values for q 1 and q 2 that are between -5.0 × 10 -6 C and 20 × 10 -6 C. Based on these values and R , calculate the force between the pith balls and write it below. Use the Gizmo to check your answer. q 1 1uC q 2 1uC R 1.2 m Fq = 0.006 N Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

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Activity B: Pith ball geometry Get the Gizmo ready: ● Set q 1 and q 2 to 0.0 × 10 -6 C. ● Set the mass of the pith balls to 50 grams. ● Turn off Show geometric dimensions and Show angle . ● Turn on Show force vectors and magnitudes . Introduction: At any time, there are up to three forces acting on the pith balls. The gravitational force ( Fg ) pulls the pith balls downward. The tension of the string ( T ) opposes gravity and pulls the pith balls up. You have already learned about the electrostatic force ( Fq ). Each force is represented by an arrow, or vector . The longer the arrow is, the greater the force. Question: How does tension relate to the electrostatic force and the force of gravity? 1. Observe: Look at the arrows on each pith ball. A. What two forces are affecting the pith balls right now? Tension and gravitational force B. What is the value of each force? 0.49 N C. What would happen if these forces were not equal in magnitude? A difference in force magnitude would cause the balls to accelerate upward or downward. 2. Gather data: The fact that the balls are stationary indicates that the forces are balanced, or equal in magnitude. Set q 1 and q 2 to 10.0 × 10 -6 C. A. What are the values of T , Fg , and Fq ? T = 0.576 N Fg = 0.49 N Fq = 0.302 N B. How does the direction of the tension vector relate to the directions of the Fg and Fq vectors? The vector of tension is perpendicular to the sum of the other two vectors. 3. Calculate: Because Fg and Fq are perpendicular, you can use the Pythagorean Theorem to calculate the combined force of gravity and the electrostatics. A. What is the combined force of gravity and electrostatics ( F Total )? 0.576 N B. How does this force compare to the string tension? The string tension is equivalent in strength to this force. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

4. Challenge: If you know Fg and Fq , you can calculate the angle of the string ( θ ). When you have finished your calculation, turn on Show angle to check your answer. Hint: You can calculate the angles of a right triangle using the following trigonometry functions: θ = 31.7° 5. Practice: Turn off Show angle and Show force vectors and magnitudes . Turn on Show geometric dimensions . Set q 1 and q 2 to 15.0 × 10 -6 C. The force of gravity on each pith ball is equal to the mass of the ball (in kilograms) multiplied by gravitational acceleration ( g ). In the space below, calculate Fg , Fq , T , and θ . Show your work. (Hint: To convert a mass in grams to kilograms, divide by 1,000.) When you have finished your calculation, turn on Show angle and Show force vectors and magnitudes to check your answer. Fg = mg = 0.050 x 9.8 = 0.49 Fq = 8.98 x 10 9 ((15.0 x 10 -6 ) 2 /1.94 2 ) = 0.537 T = √(0.49 2 + 0.537 2 ) = 0.727 θ = arctan(0.537/0.49) = 45.78 Fg = 0.49 Fq = 0.537 T = 0.727 θ = 45.8 Activity C: Exploring variables Get the Gizmo ready: ● Set q 1 and q 2 to 8.0 × 10 -6 C. ● Set the mass of the pith balls to 50 grams. ● Check that g is 9.8 m/s 2 and L is 0.50 m. Question: What factors affect the angle of the pith balls? 1. Observe: If necessary, turn on Show angle . What is the current value of θ ? 24.34 ° 2. Predict: Predict the effect of each change on the angle of the pith balls ( θ ). Fill in each blank with either “ θ increases” or “ θ decreases.” Explain each of your predictions. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

A. g increases: θ decreases g decreases: θ increases Explain: Due to their attraction, gravity is trying to bring the ball down straight and create an angle of zero. B. Mass increases θ decreases Mass decreases: θ increases Explain: Since there is an increase in mass, that causes more downward force and increased attraction, which in turn yields more Fg and reduces the angle. C. Length ( L ) increases: θ decreases L decreases: θ increases Explain: The length shortens and increases the attractionn of the balls, and lowers the Fq. 3. Test: Use the Gizmo to test each of your predictions. Write your results below. A. g increases: θ decreases g decreases: θ increases B. Mass increases: θ decreases Mass decreases: θ increases C. L increases: θ decreases L decreases θ increases 4. Interpret: How is increasing the mass of the pith balls similar to increasing the value of g ? The pith balls' gravitational force is determined by multiplying their mass by g. Thus, raising g has the same result as increasing mass. 5. Think and discuss: Why does increasing the length of the string cause the angle of the pith balls to decrease? (Hint: Why wouldn’t you expect the angle to stay the same?) The arctan of Fq divided by Fg represents the deflection angle of the pith balls. The pith balls' (Fg) weight doesn't vary during this experiment. As a result, when the string length grows, the force Fq must likewise be constant in order to maintain the same angle. But if you lengthen the string while keeping the angle, the balls will be farther apart, which lowers Fq. As a result, the angle decreases as the length of the string increases. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

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