physics Hw

Lab Instructions V0.0 January 29, 2018

The Resolution and Addition of Vectors: The Vector Force Table

1 Objective To experimentally verify vector addition.

2 Overview The main idea is to set up two to four vectors quantities and compute their vector sum (resultant) using vector components. Then, using the computed resultant as a guide, exper- imentally determine the actual resultant and compare it to the computed resultant.

3 Apparatus/ Tools used in Lab

Part 1. Force Table (FT) data Part 2. Force table simulation

4 Experimental set up and Procedure Figure 1 shows the experimental set up.

For use by the physics department, Ohlone College, Fremont, CA.

Figure 1: Experimental Setup

Lab Instructions V0.0 January 29, 2018

F~net

Fnet,x = ∑

Fi,x, Fnet,y = ∑

Fi,y

For use by the physics department, Ohlone College, Fremont, CA.

• Check the video to see the experimental setup: https://youtu.be/V86OLIC2Hvk • Treat the total mass (hanger plus slotted mass) in grams to represent the magnitude of

the vector in arbitrary units. For example, a total mass of 200 g represents a vector of

magnitude 200 units.

• Construct a balancing vector that is anti-parallel (1800 opposite) to the computed resultant (called Equilibrant)

• Compute the x, y components of each vector. Pay attention to the signs. Then, compute the vector sum (resultant) in component form.

• Then, convert to magnitude-angle form. • Record the components and, the magnitude and angle of the calculated resultant in the

data table.

• Experimental vector values are given to you in the data table.

Part 1

Example: How to find resultant force: https://www.phyley.com/find-resultant-force

Lab Instructions V0.0 January 29, 2018

5 Experimental data, calculations and analysis

5.1 Experimental data

Table 1 lists various vector addition cases to experiment with. Note: the angles specified are measures counter clockwise form the x−axis.

Table 1: Data Table Case Vectors Theory ~Fnet Experim. ~Fnet % Error

Fnet,x Fnet,y Fnet θ Fnet θ Fnet θ

F1 = 200g,θ1 = 20 ◦

1 F2 = 150g,θ2 = 80

◦

F1 = 200g,θ1 = 30 ◦

2 F2 = 350g,θ2 = 120

◦

F1 = 300g,θ1 = 50 ◦

F2 = 410g,θ2 = 160 ◦

3 F3 = 230g,θ3 = 240

◦

F4 = 350g,θ4 = 270 ◦

5.2 Calculations

1. For each case, draw a Figure that shows all vectors, with magnitude and angles labeled.

2. Show all your calculations: components of individual vectors, the components and magnitude-angle of the resultant, etc.

3. When calculating the angle, be careful in interpreting the answer from your calculator, and then correctly identify the quadrant in which the resultant lies.

4. Box key quantities.

For use by the physics department, Ohlone College, Fremont, CA.

5.3 Error analysis

1. Calculate the percentage error between theoretical and experimental values:

δFnet = Fnet,exp − Fnet,theory

Fnet,theory × 100

δθ = θexp − θtheory

θtheory × 100

2. Record the computed errors in the table.

305 2240

405 2670

352 300