Reference no: EM133768819
Activity #1: Balancing yourself
The first activity will help us better understand our own sense of balance and center of mass.
1. First, stand up straight in the center of the room with nothing around you, or have a lab assistance do this. Next bend at the waist and touch your toes, or ankles if you are not quite as flexible as you used to be. Do not bend your knees during this experiment. Write down any observations here, and include a photo/sketch of you or the assistant touching the ground/feet. Annotate the photo/sketch with an estimate of the location of your center of mass.
2. You will have to be very careful in this experiment. Stand with your back and the heels of your feet against a wall (or a lab assistant can do this). SLOWLY, try to reach down and touch the floor/feet/ankles, without bending your knees. The moment you start to fall forward, be sure to catch yourself, so you do not get hurt! Write down any observations, noting the similarities and differences to #1. Include a photo or sketch of the moment right before falling. Annotate this photo/sketch with an estimate of the location of your center of mass. Describe how this center of mass differs from #1.
Activity #2: Torque
We have explored the concept of center of mass a bit, but now it's time to apply it coupled with the concept of torque. As illustrated in lectures and textbooks, any unbalanced torque will create rotation. However, that implies that BALANCED torques will keep a rigid body stationary, or as we say in physics, the object is in static equilibrium. There is no translation, nor rotation.
3. Describe a situation in your daily life, where something BIG is static equilibrium. Describe what would happen if the BIG object were not in static equilibrium.
4. Now take a ruler or meter stick and "balance" it on your finger. You should do this in such a way that the ruler or meter stick does not rotate on any axis. Take a photo or sketch the "balanced" stick in the space below. Describe how you placed your finger to get it to balance best. Also describe any failed attempts at balancing it, which caused the stick to fall off your finger repeatedly.
5. Measure the mass of your stick with a kitchen scale, or a grocery store scale, and write it here. Note, you should convert to kilograms for your final answer.
6. Assuming that the mass of your stick is PERFECTLY distributed, how much mass is on either side of your finger? Include a justification for your estimate.
7. From the photo or sketch in #4, draw a force diagram notating all forces involved in balancing the stick. Include distances to the force vectors from the finger, in your diagram.
8. Write out Newton's Second Law of Rotational Motion for the diagram in #7. There is no need to solve for anything, simply write it out in symbolic form.
9. Now you will have to use some sound judgment, as each experiment will be slightly different for each student. You should place some mass that is roughly 10%-20% of the mass of the stick, on the zero end of your ruler/meter stick. There is no need to be terribly precise in how much mass you add, just try to estimate the added mass given your answer in #5. You should attach the mass such that the masses do not fall off, by using some tape. These masses could be a few paperclips for a small ruler, or a few pens or pencils for a larger meter stick. Now balance the stick on your finger as you did in #4, only now you will likely have one difference, the position of the finger! Take a photo or make a sketch of the balanced stick and notate the position of your finger in the space below.
10. From your photo or sketch, draw a force diagram including distances to the forces from your finger.
11. Estimate how far your finger is from the center of mass of the ruler, the ½ way point. Also note how far your finger is away from the zero point, where the masses are. Write your estimates for the positions below.
12. Using Newton's Second Law of Rotational Motion, write out the equation for the diagram in #10. Note that you can place actual numbers in for the positions of your extra masses and center of mass of the ruler. Lastly, you know the value of the weight of the ruler. Using these values, solve for the mass you added on the end of the stick.
13. Using your kitchen scale, a grocery scale, or google, estimate the mass of the objects you used and compare this to the calculated mass in #12. Find the percent difference using the appendices, and explain the difference in terms of the physics learned in this lab.
14. Looking back at your answer to #3, comment on the following items:
A. Does your example in #3 truly exemplify static equilibrium?
B. Do Newton's Laws of Rotational Motion directly apply to your example?
C. What do you think would happen if the object were not in static equilibrium?
D. Try to find a video online, of such a situation, where the object you have mentioned is not in static equilibrium, and copy the link to the video in the space below your answer.
Now that you have had some practice with rotational motion, torque, moment of inertia, center of mass, and the like you may want to include some of these concepts in your own lab video project.
15. Does your video project include any rotation of any kind? Maybe the wheels of your car are rotating as you drive. Or the wheels of your bike rotating as you do a trick. If your video does not include any rotation, try to brainstorm for ideas on how to include rotation in your video and write them below. Contact your instructor if you are struggling with this.