Physics 1020 Laboratory #6 Equilibrium of a Rigid Body. Equilibrium of a Rigid Body

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1 Equilibrium of a Rigid Body

2 Contents I. Introduction II. III. IV. Finding the center of gravity of the meter stick Calibrating the force probe Investigation of the angled meter stick V. Investigation of the level meter stick VI. Conclusion and summary

3 Part I: Introduction Learning about equilibrium

4 Introduction Static equilibrium is defined as a state where an object is not accelerating in any way. The two conditions for the equilibrium of a rigid body (such as a meter stick) are 1. the vector sum of forces on the body must be zero and 2. the vector sum of torques on the body must be zero F r = 0 r τ = 0 For a simple r linear body fixed at some pivot, torque depends on two things; the force vector F and lever arm. The torque is l τ = Fl Torques that act to rotate the body in the counter-clockwise direction are positive and those that rotate the body clockwise are negative. The pivot point may be taken to be any point on the rigid body.

5 Introduction In this laboratory you will investigate the concepts of torque and equilibrium. Your objectives are: 1. become familiar with the concept of lever arms and torque 2. become familiar with the two conditions for static equilibrium You will also determine the weight and center of gravity of a meter stick. You will investigate the equilibrium conditions for a case where some of the forces may be at an angle to the rigid body. You will investigate a level meter stick.

6 Apparatus You should have this apparatus at your station.

7 Part II: Finding the Center of Gravity of the Meter Stick The center of gravity is the single point through which all the weight of the rigid body appears to act.

8 Finding the Center of Gravity The weight of a rigid body is a downward force acting at the center of gravity (CG) of the body. First attach two metal clamps to the meter stick; one at the 10 cm mark and the other near the middle. To find the CG of the meter stick, place the meter stick on the pivot using the pivot clamp located near the center. Adjust the position of the pivot clamp that is near the middle of the meter stick until the meter stick is balanced and level. If the stick oscillates slowly and by equal amounts on each side of the pivot then it is balanced. Take the meter stick off the stand and measure the position of the pivot clamp on the meter stick. Do not move either clamp for the rest of the lab.

9 Center of Gravity and Weight Do not move either clamp for the remainder of the lab. Record the position of the center of gravity and its uncertainty in Table 1. Measure the mass of the meter stick, with clamps still attached, on a triple beam balance. Record this value and its uncertainty in Table 1. Calculate the weight of the meter stick along with its experimental uncertainty. Record these values in Table 1. Note: You may assume δg = 0.

10 Part III: Calibrating the Force Probe The force probe will not display the correct force in newtons unless we calibrate it by applying two forces of known values.

11 Set up the Force Probe Clamp the short aluminum rod to the long rod screwed into the bench. Mount the force probe onto the short rod as shown and tighten the thumbscrew.the hook should be pointing straight down. Ensure the force probe is set to 5 N or 10 N and not to 50 N. Plug the Force Probe into CH 1 on the LabPro. Launch Logger Pro by clicking on the icon below. CLICK HERE CLICK HERE The Logger Pro window should contain a graph of Force vs Time. If it does not, consult an instructor.

12 Using Weight to Calibrate The force probe needs to be calibrated before you can use it for measurements. A 200 g mass is to be used for calibration. QUESTION 1: What is the weight in newtons of the 200 g mass? Click

13 Calibrating the Force Probe Click Calibrate Now. Do two readings: 1. With nothing hanging on the force probe, enter 0 in the Value box, then click Keep. 2. Hang the 200 g mass and enter its weight (in newtons) in the Value box, then click Keep. Channel Inputs should be different. Click Done. Remove the mass and click the Zero button near the Collect button. Check your calibration: press Collect with 200 g on the probe. If the weight is not close to N, recalibrate! You are ready to collect data

14 Part IV: Investigation of the Angled Meter Stick Considering equilibrium conditions on a meter stick that is at some angle to the horizontal.

15 Angled Meter Stick Remove the metal stand. Set up the meter stick as shown. Make sure that the force probe and string are vertical.

16 Free Body Diagram QUESTION 2: How do you know the meter stick is in static equilibrium? QUESTION 3: Draw a sketch of the meter stick and indicate the three forces acting on it. Also show the pivot point, and each of the lever arms. Label them with appropriate symbols (for example, e.g. ). l T QUESTION 4: Write down an equation (no numbers, just symbols from Question 3) for each of the torques associated with the forces in your diagram. (Be sure to include the correct sign based on the convention for torque.)

17 Lever Arm You will now measure the lever arms for the weight and the tension l T Use a set square to find the point on the lab bench directly below the point at which the tension acts. Mark this location as precisely as possible using a pencil mark on masking tape (do NOT mark on the bench). Then measure l W Similarly, measure. l T QUESTION 5: Measure the lever arms l and l T W with their experimental uncertainties [See Making Measurements in Physics.]. l W l W l T

18 Measuring the Tension In Logger Pro, press Collect. It will collect multiple force probe measurements for a few seconds and then stop. Click the statistics button,. This will give the average tension T avg, standard deviation, and the number count or number of measurements, N. Place this information in Table 2. QUESTION 6: Calculate the experimental uncertainty in T avg from Table 2. Have an instructor check your value for the tension and its experimental uncertainty.

19 Angled Meter Stick - Analysis QUESTION 7: Why is there zero torque due to the force F N exerted by the table? QUESTION 8: Calculate the torque due to the tension force T. Don t forget to include the experimental uncertainty in the torque. QUESTION 9: Using the appropriate formula, calculate the torque due to the weight of the meter stick. Don t forget to include the experimental uncertainty in the torque. QUESTION 10: Determine the sum of the torques and find the experimental uncertainty in that value? Is this sum equal to zero within experimental uncertainty?

20 Part V: Investigation of the Level Meter Stick Considering equilibrium conditions on a horizontal meter stick.

21 The Setup Leave the force probe clamped vertically to the aluminum rod. Both clamps should still be attached to the meter stick. Put the one that is at a position of 10.0 cm on the pivot stand. This will be the location of the pivot. Using a piece of string, hang the meter stick from the force probe, at a position of 95.0 cm. Be careful not to pull on the force probe as you may affect your calibration. Adjust the height of the force probe on the vertical rod to level the meter stick. Your setup should like the picture on the next slide

22 The Setup Your experimental setup should look like this. Be sure that your meter stick is horizontal!

23 Free Body Diagram QUESTION 11: Draw a sketch and indicate the three forces acting on the meter stick. Label the pivot and lever arms. QUESTION 12: Using the metal stand as the pivot point, write down the torque expression (again no numbers, just symbols) resulting from applying the second static equilibrium conditions to the meter stick. (Be sure to include the correct sign based on the convention for torque.) In Logger Pro, press Collect. Click the statistics button,. This will give the average tension T avg, standard deviation, and the number count or number of measurements, N. Place this information in Table 3. QUESTION 13: Why is there zero torque due to the metal stand? QUESTION 14: Calculate the experimental uncertainty in T avg from Table 3.

24 Torque about Metal Stand QUESTION 15: Using your equation from Question 12 and the measured tension from the force probe, determine the weight of the meter stick with its experimental uncertainty. Does this agree with your measurement from Part II?

25 Part VI: Summary and Conclusion Was the meter stick in static equilibrium? Were the static equilibrium conditions satisfied?

26 Static Equilibrium You will now reflect on what this lab demonstrated about static equilibrium. QUESTION 16: Identify two sources of uncertainty in this experiment. Are these random or systematic? QUESTION 17: Using what you have learned in this lab about static equilibrium, calculate the force exerted by the table F N (from the angled meter stick section of the lab).

27 Static Equilibrium Close all applications and log out. Put away all lab equipment and return your chairs/lab stools. Submit your laboratory workbook.

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