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1.4 Friction and Gravity Lab 1.4 Friction and Gravity Lab Student Name: Biniam Bltom In the first lab, we touched on Newton’s 1 st and 2 nd laws. Here’s a review of these two laws: Newton’s First Law : If the Net Force on an object is zero, it will not accelerate. If an object is at rest, it will remain at rest. If an object is in motion, it will move with constant velocity, that is, at constant speed in a straight line. Newton’s Second Law : If the Net Force on an object is not zero, it will accelerate in the direction of the net force. Acceleration = Net Force Mass Part 1: Friction You will need to open the PhET Simulation Forces and Motion, Basics . Navigate to the 4 th window labeled Acceleration and click on it twice to open it. Once you are in the simulation, apply the following settings: ● Leave the friction slider at the default position. ● Check all the boxes. This simulation will serve as an introduction to the effect that friction has on resting and moving objects. The force of friction depends upon the physical nature of the surfaces in contact with one another as well as how heavy the object is. In general, when you apply a force to move an object, you must overcome the force of static friction between object and surface. Once moving, the force of friction decreases compared to the maximum force of static friction. Start with the crate on the surface. Follow directions carefully! Using the double-arrow key on the right side of the Applied Force setting, adjust the applied force up to 100 N. Just 2 clicks! Using the single-arrow key to adjust the applied force up to 125 N. Do not go over 125 N. 1

1.4 Friction and Gravity Lab Observe the motion of the object. Fill in the table, using a negative number to indicate a force pushing to the left. Type of Force Amount of Force Force Unit Applied Force 125 N Friction Force 94 N Net Force (Sum of Forces) 219N N In motion or at rest? Motion If in motion, constant velocity or constant acceleration? Leave blank if at rest and remaining at rest. constant acceleration ● Add 1 Newton to the Applied Force, making it 126 N. The crate should start to move. Let it accelerate a bit and pause the simulation. Fill in the table below. Type of Force Amount of Force Force Unit Applied Force 126 N Friction Force 94 N Net Force (Sum of Forces) 220 N In motion or at rest? rest If in motion, constant velocity or constant acceleration? Leave blank if at rest and 2

1.4 Friction and Gravity Lab remaining at rest. ● With the simulation paused, adjust the Applied Force, using the arrow keys on the left side of the Applied Force display, until the net force (sum of forces) is zero. Note: the first answer below will not be graded. Using Newton’s Laws as a guide (see page 1) predict what will happen when the play button is clicked and the crate is free to move. With the object in motion and the net force of the object zero, the object will a Stop instantly. x b Begin to slow down and come to rest. c Continue moving at a constant velocity. d Continue to move with constant acceleration. Click play and observe the motion and indicate the result by answering the same question based on your observation. 3

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1.4 Friction and Gravity Lab What happened when the play button was clicked and the crate was free to move. With the object in motion and the net force of the object zero, the object a Stop instantly. x b Begin to slow down and come to rest. c Continue moving at a constant velocity. d Continue to move with constant acceleration. Part 2 Newton’s Universal Law of Gravity Introduction In this lab, you are going to explore the application of Newton’s Universal Law of Gravitation. This important relationship between masses was the first force law quantified in the history of modern science. The formula provides a means for determining the gravitational pull between two masses but does not explain how gravity works. F gravity = G m 1 m 2 d 2 G = 6.67 × 10 − 11 N m 2 kg 2 As an example, let’s apply this formula to the screenshot from the simulation below. In this setup, we have mass 1 = 2,000,000,000 kg (2x10 9 kg) and mass 2 = 4,000,000,000 kg (4x10 9 kg). The distance between them is labeled as 4 kilometers, but we must convert this to meters for the calculation so the distance will be 4,000 m. With these parameters set, we see that the gravitational force exerted on mass 1 by mass 2 is 33.4 N and the gravitational force exerted on mass 2 by mass 1 is also 33.4 N (equal and opposite). 4

1.4 Friction and Gravity Lab Now, let’s input these values into the formula to see if we get 33.4 N. F = ( 6.67 × 10 − 11 N ⋅ m 2 k g 2 )( 2 × 10 9 kg )( 4 × 10 9 kg ) ¿¿ You are welcome to use any scientific calculator you choose for the labs in this course. Just make sure that you know how to properly input numbers in scientific notation into your calculator. Here is what a calculation looks when you use the Desmos Online Calculator ( https://www.desmos.com/scientific ) : The calculation is simpler using a feature of the eCalc Scientific Online Calculator ( https://www.eeweb.com/tools/online-scientific-calculator/ ). Instead of writing the exact calculation of scientific notation numbers, you can instead enter the number part, then the EE key, and then the exponent. The calculator will display this using the letter “e” to stand for the “×10” part. Important: do not use the multiplication key “×” or enter the number 10. Example: To enter 6.67 × 10 − 11 Hit the following sequence of keys: 6 . 6 7 EE (-) 1 1 Display will show 6.67e-11. You do not need to put each number in parentheses in this calculation. 5

1.4 Friction and Gravity Lab Continued on next page. 6

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1.4 Friction and Gravity Lab The Effect of Mass and Distance on Gravitational Force To complete this lab, you will need to open the simulation: Gravity Force Lab . You have been assigned an initial set of mass values to use in the simulation based upon the first letter of your last name. Consult the table below: chose J- L First letter of Last Name Mass 1 (billions kg) Mass 2 (billions kg) A-C 1 10 D-F 2 9 G-I 3 8 J-L 4 7 M-O 5 6 P-R 1 5 S-U 2 4 V-Z 3 2 Setup the simulation with your assigned mass values and set the distance between the masses to 2.5 km. At this point, we will watch the video on the assignment instruction page on scientific notation and metric prefixes. As an exercise, write mass of object 1 as it is written in the simulation. Then rewrite it using decimal notation. Write it a third time using a metric prefix. Finally, write it using the standard unit of kg and scientific notation. Mass 1 (as described in the sim.) 4 billion Kg Mass 1 (decimal number) 4,000,000,000 kg Mass 1 (with metric prefix) 4,000 metric tons Mass 1 (using scientific notation, kg) 4.0 x 10^9 kg Fill in the table below using scientific notation for the masses (in kg). State the distance in the units provided by the simulation and then convert to standard units of meters. For the force, give the simulation value and unit. Mass 1 4 kg Mass 2 7 kg Distance 2.5 km 7

1.4 Friction and Gravity Lab Convert distance to meters 2500 m Sim Force on mass 1 by mass 2 299.0 N Sim Force on mass 2 by mass 1 299.0 N If the force is pointing to the left, use a negative sign in front of the force value. Now, use the formula for the force of gravity to confirm the value of the gravitational force obtained in the simulation: F gravity = G m 1 m 2 d 2 G = 6.67 × 10 − 11 N m 2 kg 2 Note: the formula only gives the magnitude of the force, not the direction. To confirm your understanding regarding the functionality of the Universal Law of Gravitation formula, you will perform your confirmation calculation using an online scientific calculator app, take a screenshot, and paste below. Paste screen shot of your calculator entries and the answer. CALCULATOR: 8

1.4 Friction and Gravity Lab Do not screen shot the simulation , just the online calculator . The result may not match the simulation number exactly. Note: this is like problem #10 of Week 1 Practice Problems. Look at the pair of forces produced. Put an X in the left next to the correct answer. X a The larger mass exerts a larger force than the smaller mass. b The masses produce the same amount of force on each other. c The smaller mass exerts a larger force of the larger mass. This is due to Put an X in the left next to the correct answer. a Newton’s First Law of Motion b Newton’s Second Law of Motion X c Newton’s Third Law of Motion d Conservation of momentum e Conservation of energy It may help you answer these questions if you watch the video on the assignment instruction page on Newton’s Third Law. 9

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1.4 Friction and Gravity Lab Part 3: Free Fall Open the PhET Projectile Motion Simulation . Click on the “Lab” tab two times. Click on the base of the cannon and drag the pedestal up to maximum height (15 meters). Set the Initial Speed slider at the bottom left to 0 m/s. Adjust the gravity setting on the right to read 9.80 m/s 2 . Simulation should look like this: Trial 1: Click on the red button showing the cannon firing. The effect will be to drop the cannonball so it falls straight down. The simulation is showing what would happen if there were no air resistance to the motion. Click on the measuring tool next to the simulated tape measure and drag it into the simulation. Position the crosshairs over the point where the object hit the ground. The tool will show the time it took to reach the ground. Make sure you click on the yellow eraser button between each trial. trial 1: 10

1.4 Friction and Gravity Lab 11

1.4 Friction and Gravity Lab Record the height, time, and default mass in trial 1 of the table below. Put units with the numbers. Leave the mass as the default value provided by the simulation at the top right. We will calculate the acceleration rather than use the value provided by the simulation. Trial Height (d) Time (t) Mass Acceleration (g) 1 0 m 1.75 s 17.60 kg 9.8 m/s/s 2 0m 1.75 s 31.00 kg 9.8 m/s/s To calculate the acceleration, we use the formula g = 2 d t 2 . Round the answer to 3 places after the decimal. Note: this equation is derived from the equation d = 1 2 at 2 , using g for the acceleration variable. Trial 2 : Increase the mass to the maximum value of 31 kg. Be sure to erase the previous trial values by clicking on the yellow eraser button. Repeat the experiment to see how long it takes a larger mass to fall. You should observe what Galileo demonstrated centuries ago that objects of different weights (or masses) fall at the same acceleration, provided air resistance is not significant. trial 2: This somewhat counterintuitive result can be explained by Newton’s 2 nd Law of motion. By increasing the mass, you increase the object’s inertia, making it harder to accelerate. You also increase the weight of the object, which applies a greater force that exactly compensates for the increased mass or inertia. 12

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1.4 Friction and Gravity Lab Change the mass of your object in the simulation to any value between 2 and 29 kg (do not use the default value of 17.60 kg nor the instructor’s demonstration value). Calculate the weight of this new mass, using the formula weight = ( mass ) ( accelerationof gravity ) For this calculation, you can use an alternative acceleration unit based on Newton’s 2 nd Law: g = 9.80 N kg , since a 1 kg object will weigh 9.8 N. Weight 104.04 N Round to 2 places after the decimal. Be sure to include the unit (standard force unit). 13 New mass setting 10.62 kg

1.4 Friction and Gravity Lab Next, make the following changes to the simulation: ● Erase your earlier trial trajectory. ● Do not mimic any of the instructor’s example settings in your data. ● Adjust the gravity away from the standard earth value of 9.8 m/s^2. ● Keep the mass the same as used in the previous calculation. ● Adjust the height of the pedestal to any value between 3 and 14 m. ● Record these values in the table below. ● Drop the object and record the time it takes to fall. ● Use the formula g = 2 d t 2 to calculate the acceleration of gravity. ● Round this result to 3 digits after the decimal. ● This simulates Week 1 Practice Problem #6. ● Calculate the weight of the object using the formula weight = ( mass ) ( accelerationof gravity ) , using the simulation acceleration of gravity and your experimental simulated mass. ● This simulates Week 1 Practice Problem #8. Quantity Magnitude Unit Simulated Gravity, g 11.93 m/ s/s Mass of object, m 10.62 kg Height of drop, d 11 m Time to reach the ground, t 1.36 s Calculated acceleration of gravity 11.89 m/ s^2. Weight of object in this gravity 126.32 N The following part will only be done if there is enough time. Listen for instructions. See next page. 14

1.4 Friction and Gravity Lab Falling Objects with Air Resistance For the next part, check the box by the Air Resistance indicator. ● Erase your previous trajectory. ● Change the acceleration back to earth gravity: 9.80 m/s 2 . ● Raise the pedestal back to full height of 15 m. ● Change the object to Custom. ● Adjust the mass and diameter as indicated in the table. ● Record the time to fall. Object Mass Diameter Time to fall 15 m (s) Custom 100 kg 1.0 m 1.76 s Custom 10.0 kg 1.0 m 1.85 s Custom 10.0 kg 3.0 m 2.65 s Make any general observations based on these experiments. What type of object is likely to take the longest to fall? ● The duration for an object to fall increases as its mass increases. It takes heavier objects longer to descend than lighter ones. ● Additionally, the duration to fall increases as the object's diameter increases. Larger-diameter objects experience greater air resistance, which delays their descent. ● The object with a mass of 100 kilograms and a diameter of 1 meter fell the slowest among those tested (1.76 seconds). The table records values for the last setting (10 kg object 3 m diameter). Point Height Time Δd Δt Instantaneous speed ∆d ∆t 1 1.70 m 2.4 s 15

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1.4 Friction and Gravity Lab 2 1.01 2.5 s 0.69 m 0.1 s 6.9 m/s 3 0.32 m 2.6 s 0.69 m 0.1 s 6.9 m/s Is the object accelerating between these two measurements? yes If not, why not? Make reference to Newton’s Laws as needed. Yes, acceleration exists between these two measurements. Newton's Laws of Motion state that an object will accelerate when a neutral force acts upon it. Yes, In this situation, the only force acting on the object is gravity, which pulls it toward the earth. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, according to Newton's Second Law of Motion. The formula for this law is as follows: \[ F = ma \] where - (F ) is the net force exerted on the object, - (m ) is the object's mass, and - (a ) is the object's acceleration. In the falling object scenario, the net force operating on the object is gravity (weight). The object's mass and acceleration due to gravity remain constant as it falls (approximately 9.80 m/s2 and 9.80 m/s2, respectively). Consequently, the object experiences a constant acceleration throughout its fall, regardless of the measurement intervals. As the object descends, its instantaneous speed (velocity) increases at a constant rate because its acceleration remains constant. This is evident from the data, as the instantaneous velocity (d/t) of the object between Point 1 and Point 2 and Point 2 and Point 3 is approximately constant. Gravity's constant acceleration causes the falling object to continuously acquire speed as it approaches the ground. 16

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