PhET Vectors Simulations Lab Introduction: A vector quantity is one that has both a magnitude and a direction. For instance, a velocity vector will have a magnitude (24 m/'s) and a direction (northeast or 45 degrees). These simulations will demonstrate how vectors can be summed to produce a resulting vector, and how the acceleration vector affects the velocity vector. Part I: 2D Motion Simulation: Open the simulation Motion in 2D 1. Click Stop. Drag the object around with your mouse and notice the actions of the two vectors. Spend some time investigating the vectors. Which vector is velocity and which is acceleration (blue or green)? 2. Click on Linear Acc 1. Observe the motion. a. What orientation must the vectors be for the object to speed up? Draw and label this. b. What orientation must the vectors be for the object to slow down? Draw and label this. 3. Click Simple Harmonic (this is simple motion of a mass on a spring). Observe the motion. 4. Click Circular. Observe the motion. What orientation must the vectors (relative to each other) have to turn the object? Draw and label this. 5. Click Stop. Attempt to move the object like a planet in orbit (an ellipse, like an oval). What must the object do in order to turn? Part II: Vector Addition Simulation: Open the simulation Vector Addition 1. Place two vectors in the work area. Change their direction and magnitude by dragging the heads of the arrows representing each vector. Place one vector in Quadrant I and one vector in Quadrant II. . Draw these vectors. 3. Move the tail of one vector to the head of the other vector. 4. Draw the vectors again. 5. Click Show Sumn to view the resultant (sum) of the two vectors. Move the Resultant vector so that it is drawn from the open tail of one vector to the open head of the other vector. 6. Click on one vector and report the values: IR R. R, 7. Click on the other vector and report the values: IR R. Ry 8. Click the resultant vector and report the values: IR R. R,9. Click each style (1, 2, and 3), and drawn the component vectors. 10. Algebraically show the vector addition for the vectors above. R - Magnitude of the vector (M) 0 = angle of the vector R. = X component R. = Y component Part III: Calculating Resultant Vectors: review of vector addition 1. Find the mathematical sum of each set of vectors below (show your work). Recall: use trigonometry to find the x and y components of each vector. 2. Fill in the rest of the boxes below into your lab notebook. 3. Recreate (as closely as possible) the vectors in the simulation to check your work. Draw the vectors and the resultant. 4. The resultant vector's magnitude |R| is found using the Pythagorean Theorem using X, and Y as the legs of a right triangle, where the hypotenuse is the magnitude. Calculate the magnitude of the resultant (show your work). 5. The angle 0 of the resultant vector is found with the inverse tangent (tan") of the X, and Y. components. Calculate the direction of the resultant (show your work). 6. Do your calculations make sense when compared to your drawings? Explain.#1 #3 Vector 1 Vector 1 M angle, 0 X1 M angle, 0 X Y1 6.0 35 3.5 2.5 Vector 2 Vector 2 M angle, 0 M angle, 0 2.5 20. 4.0 6.0 Resultant Resultant OF X Y. M Or X Yr #2 #4 Vector 1 Vector 1 M angle, 0 X1 YI M angle, 0 X1 Y1 1.8 15. 70 4.7 Vector 2 Vector 2 M angle, 0 Y1 M angle, 0 X2 Y2 7.0 -25 -15 2.0 Resultant Resultant M X Yr Or X 12.1 10.8 Conclusion Questions: 1. The blue vector represented and the green represented 2. When the acceleration vector was in the same direction as the velocity vector, the object slowed down / sped up. 3. When the acceleration vector was in the opposite direction as the velocity vector, the object slowed / sped up. 4. Turning requires the acceleration vector to be (geometry term) to the velocity vector. 5. When a car comes to a stop, the car's brakes create an that is in the same direction / opposite direction as the velocity vector. 6. Write a conclusion