STATICS Introduction: A system is said to be in a state of static equilibrium when it is undergoing no translational or rotational motion. Structures such as buildings and bridges are carefully engineered so that they remain in static equilibrium, even under extreme conditions such as earthquakes. In order for a system to be in static equilibrium, two conditions must hold: (1) There is a balance of forces, Fret = 0 (2) There is a balance of torques, Inet = 0 We have worked with the concept of force throughout the semester, but the concept of torque may be unfamiliar to you. Just as forces can be thought of as the cause of translational motion, torques can be thought of as the cause of rotational motion. The magnitude of a torque can be calculated as follows: 1 = IF Where F is the applied force and r is the distance from the pivot point to the point where the force is applied. Much like forces, the direction of a torque matters. If a torque tends to cause counterclockwise rotation, we give it a positive sign and if a torque tends to cause clockwise rotation, we give it a negative sign. Note that this is just a convention. positive torque negative torque pivot point pivot point Materials: meter stick, three meter stick clamps, force probe, force probe stand, weight holder and assorted slatted masses Note before starting: One of the primary goals of this lab is accurate measurement with attention to detail. I know that you can finish this lab quickly - but don't. Squeeze as much precision as you can out of this set of equipment. As you go through the lab, don't move on to the next step until you are absolutely certain you did the previous step correctly. If you are stuck or unsure about any part of the lab, please don't hesitate to ask me for help.Procedure: 1. Check the calibration of the force probe. Hang the force probe on the stand so the hook is facing downwards. Click on Zero, Zero Force. Click on Collect. Wait about 1-2 seconds and then put 400g on the hook (use the 50G weight holder plus a slotted mass of 50G and three slotted 100G masses) The graph should show zero force for the first 1-2 seconds and a horizontal line at slightly less than 4N at the end. If it did not, then call the instructor to check your setup. 2. Slide the meter stick through the clamp to the middle of the meter stick (50.0 cm) so that the screw is facing down. Cut a short piece of string, and tie one end to the meter stick clamp and tie the other end to the force probe hook. Make sure the centimeter marks are facing you and the numbers are facing up. Adjust the relative position of the meter stick in the clamp until the stick is balanced, then tighten the screw to hold the meter stick in place. This balancing point is called the center of mass of the meter stick and it should within a few mm of the 50.0 cm mark. Read the exact balance point off the meter stick scale to the nearest mm. Record this value below. Xem= 48.9 3. Hold the meter stick up so that the string goes slack. Zero the force probe, then gently let the meter stick back down so that it is in its original hanging position. Record the reading from the force probe below. This force is the tension in the string. T= 1372N 4. Use the space below to draw a free body diagram of your meter stick in its current configuration. To have a complete free body diagram, you must show all forces acting on an object with arrows denoting the direction. Make sure to correctly show where on the meter stick each force is applied. There are two forces to consider: the weight of the meter stick with the clamp on it (Wetick) and the tension in the string (T). 5. You system is in static equilibrium, which means that all forces are balanced. Based on this fact, what is the weight of the meter stick (with the clamp on it)? Watick N 6. Slide another clamp (call this one #1) onto the left end your meter stick to that the screw is facing up. Put this clamp at the 15 cm mark and then tighten the screw to hold it in place. Hang a weight holderfrom this clamp and slide one 100 g slotted mass onto the weight holder. This will cause your meter stick to tip counterclockwise. 7. Slide yet another clamp (call this one #2) onto the right end of your meter stick so that the screw is facing up. Hang a weight holder from this clamp and slide two 100 g slotted masses on to the weight holder. Now slide the clamp along the meter stick to adjust its position until the meter stick is perfectly balanced. Record the position of the clamp below. cm Figure this one out X2 8. Very carefully lift up the meter stick so that the string goes slack. Zero the force probe, then gently let the meter stick back down so that it is in its original hanging position. Record the reading from the force probe below. This force is the tension in the string. T= _3:268 N 9. Use the space below to draw a free body diagram of your meter stick in its current configuration. To have a complete free body diagram, you must show all forces acting on an object with arrows denoting the direction. Make sure to correctly show where on the meter stick each force is applied. There are now four forces to consider: the weight of the meter stick with the clamp on it (Wstick), the tension in the string (T), the weight hanging from the left end of the meter stick (W,), and the weight hanging from the right end of the meter stick (W2). 10. Take the weight holder off the left end of your meter stick and slide the clamp off. Place the clamp, the weight holder, and the slotted mass(es) on the triple beam balance to measure the total mass that was on the left end of your meter stick. Record the mass below. mi = 0.15 kg Recall that weight = mg. Multiply by g = 9.8 m/'s to find the corresponding weight. WI= 1 1. Take the weight holder off the right end of your meter stick and slide the clamp off. Place the clamp, the weight holder, and the slotted mass(es) on the triple beam balance to measure the total mass that was on the right end of your meter stick. Record the mass below.m = 0.25 kg Recall that weight = mg. Multiply by g = 9.8 m's to find the corresponding weight. W2 = N In the next few steps, we will perform some calculations to verify that there was a balance of forces and torques in the system you set up. 12. Look at your free body diagram on the previous page. Which forces act downwards? Find the total downward force. Record this value below. Fdown N 13. Look at your free body diagram on the previous page. Which forces act upwards? Find the total upward force. Record this value below. Fup = N 14. If there is a balance of forces, we expect the total upward force to exactly equal the total downward force. Find the % difference between the value of Fdown and Fup that you measured. Show your calculation below.15. Again, refer to your free body diagram. Forces that act at the pivot point do not cause a torque. Which forces in your diagram act at the pivot point? 16. The force in your diagram that causes a counterclockwise torque is Wj. Remember that t = rF, where F is the applied force and r is the distance between the point where the force is applied and the pivot point. Calculate this torque and record your result below. N m 17. The force in your diagram that causes a clockwise torque is Wa. Calculate this torque and record your result below. N m18. If there is a balance of forces, we expect the total counterclockwise torque to exactly equal the total clockwise torque. Find the % difference between the value of Tew and Tecw that you measured. Show your calculation below