Week 3 lab report physics

General Physics I Laboratory (PHY221L) Scalars, Vectors and Algebra Name: Aliyah Zito Date: 9 / 12 / 23 ______________________________________________________________________________ Introduction State what you show or demonstrate in this laboratory experiment. Include the background/theory and any useful equations used in the lab. (5 points) There are two different types of physical quantities. Scalar quantities have a single number and unit such as time and temperature. Vector quantities are described by magnitude and direction such as displacement and velocity. This lab was conducted by using a force table to determine the vector and by trial and error to get the masses to equilibrium. Record the masses, forces, and the angle in a table. Materials: Force Table, masses, mass hangers, Protractor, and a ruler. Method 1. Write the precisions of your measurement tools (i.e. ruler and protractor). (2 points) Ruler: 1mm Protractor: 1 degree Force table: 1 degree Part I: Force Table Force table is a circular platform with a ring in the center. Attached to the ring are strings which extend radially outward to the edge of platform, pass over pulleys, and attach to hanging weights. The ring is held fixed by a pin. When the pin is pulled, if the ring remains stationary, then the ring is in equilibrium (i.e. the forces provided by the strings all add up to zero). If the net force on the ring is zero, then the ring will stay at rest if it is initially at rest (Newton’s First Law). If the force on the ring is non-zero, then the ring of mass m will accelerate with an acceleration ´ a . 1. Measure the mass of the hanger and the 100 g masses. Record their values in table 1. 2. Let vector ⃗ F A be the force of the mass hanger (with no weights) at 5◦ and let vector ⃗ F B be the force of the mass hanger with the 100 g mass at 110◦. The total mass should include the

mass of the hanger ( m A = m hanger and m B = m hanger + m 100 g, 1 ). All angles are measured from the +x-axis (counterclockwise). 3. Compute the force due to the gravity for each mass in the previous step (i.e. F A = m A g , and F B = m B g , where g = 9.80 m / s 2 ). Record your results for the force in table 1. 4. Determine by trial and error the angle at which the 200 g mass (hanger + 100 g mass) must be placed for the ring to be in equilibrium. Calculate the magnitude of the Equilibrant Force ⃗ F E , and the angle with respect to +x axis (counterclockwise). Record your results in table 1. 5. Calculate the resultant force ⃗ F R and it’s angle from your findings in step 4. Record your results in table 1. Part II: Graphical Method 1. In this part, we will determine the resultant and equilibrant graphically using graph paper. Convert the force vectors ⃗ F A and ⃗ F B (from part I) using a drawing scale ( 0.196 N = 1 cm ) and record it in table 2. 2. Create x and y axis on the graph paper. Use a ruler and protractor to draw the force vectors ⃗ F A and ⃗ F B . You need to use the tail to tip graphical method to draw the vectors graph. First draw vector ⃗ F A , then draw vector ⃗ F B such that the tail of vector ⃗ F B coincides with the head of vector ⃗ F A . 3. Draw a vector from the tail of vector ⃗ F A to the tip of vector ⃗ F B . This vector is the resultant ⃗ F R . Measure the length of this vector and the angle with respect to the +x-axis (counterclockwise). Record your results in table 2. Remember to convert the length of this vector to Newtons using the drawing scale ( 0.196 N = 1 cm ). 4. Draw a vector from the head of vector ⃗ F B to the tail of vector ⃗ F A . This vector is the equilibrant ⃗ F E . Measure the length of this vector and the angle with respect to the +x-axis (counterclockwise). Record your results in table 2. Remember to convert the length of this vector to Newtons using the drawing scale ( 0.196 N = 1 cm ). Results (53 points) Place your data in this section 2

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Data Analysis (25 points) 1. What was the equilibrant and resultant force (magnitude and direction) using the force table (Table 2)? (3 points) Equilibrium magnitude is 1.96 direction is 258 degrees Resultant magnitude is 1.96 and the direction 78 degrees 2. What was the equilibrant and resultant force (magnitude and direction) using the graphical method? (3 points) 1.96 and 260 1.96 and 80 3. Compare between the force table and graphical method results by calculating percent difference for equilibrant and resultant force. (3 points) percent difference = | E 1 − E 2 | E 1 + E 2 2 × 100% 0% 5

Determine the resultant vector. Magnitude of the resultant vector ⃗ F R is given by | ⃗ F R | . | ⃗ F R | = √ F Rx 2 + F Ry 2 0.3 2 +1.95 2 = 3.8925= 1.97 The direction of the resultant vector is given as θ R = tan − 1 ( F Ry F Rx ) Tan -1 (1.95/0.3)=81.3degrees Determine the equilibrant vector. 81.3+180=261.3 degrees The magnitude of the equilibrant vector is 1.97 with an angle at 261.3 degrees 5. Compare between the analytical method and force table results by calculating percent error for equilibrant and resultant force. The analytical method result is the true value. (4 points) percent error = | E − T | T × 100% (1.97-1.97)/1.97=0x100=0% error 7

Conclusion (10 points) State the main conclusion(s) in the first paragraph along with a discussion of your results. Throughout this experiment is has been concluded that there is not much difference between the force table and the graphical method. The percent error being 0% shows that there was absolutely no error and they were both spot on. 8