This lab can be done with simple objects from home. The center of mass is an important topic that becomes more intuitive after you have balanced a few objects!
Center of mass of a symmetrical object.
For symmetrical objects, the geometric center is also the center of mass. The center of a square can be found by connecting the corners:
Set the block on it's edge, and think about how hard it is to push over depending on where the force is applied with respect to the center of mass.
Write down how you would design the sail of a sailboat if you wanted the wind to push the sailboat forward, rather than push it over?
Next:
Hang a plumb-bob from the nail in the center of your square. (String with washers tied to the end of it). Balance your block on it's corner, watch the plumb-line, and think about which way the block wants to tip over.
1. Write down an equation that explains the relationship between the stability of an object, and it's center of mass.
Finding the center of mass of an irregularly shaped object.
Figure out, and then write a procedure for finding the center of mass of an irregularly shaped piece of wood using a plumb-bob, some string, and nails. (Hint: tie the string onto one of the nails, and let the piece of wood just dangle down. What is the moment around the nail? Where is the center of mass with respect to the point of support (nail)?)
Use your procedure to find the center of mass of the irregularly shaped pieces of wood you have. Check that you were able to find the correct center of mass by marking the center with a sticky-note, and balancing the piece of wood on your finger.
Next, measure your piece of wood, and calculate the center of mass using methods from chapter 5. Do your calculations match what you found with the plumb-bob?
Spin it!
Find the two small wooden blocks with one nail in them, and the flat piece of wood with a hole in it. Notice that one of the wooden blocks has the nail in the center of mass, while the other does not. Place their nail in the hole, and try spinning them like tops.
Now take the large flat square piece of wood, the nail in the center down, and spin it like a top on the table.
Watch this MIT Physics Demo -- Center of Mass Trajectory:
https://www.youtube.com/watch?v=DY3LYQv22qY
Grab a serving spoon, and a racket, and try it out!
1. Balance the spoon and racket on your finger to find the center of mass.
2. Tape a bright colored sticky note onto the spoon / racket to mark the center of mass.
3. Take turns tossing the racket and spoon between two people, while the third person watches the trajectory of the center of mass.
Write down your observations about the relationship between the center of mass, and the rotational tendencies of solid objects. Use what you know about balancing forces, and write a few equations down to explain what you have observed.
Balance It!
Balance the long pole with a weight on the end of it in your hand.
Next, balance the short pencil with play-dough on the end of it in your hand.
Which is easier to balance? Why?
Consider a rocket-ship "balancing" on top of a force. How do rocket-scientists keep the rocket from tipping over during take-off?
Tight-rope walking!
Why do tight-rope walkers use long poles to balance?
Take out the two pieces of hangers. Attach the clips at the ends, and try to balance it on your finger. Is it easier to balance the straight hanger? or the triangle hanger? Explain why using the center of mass.
Try attaching the clips at different lengths, and in different orientations. Sketch out 6 different positions, and label the approximate center of mass on your diagrams. Comment on the difficulty of balancing each configuration. Why are some easier to balance than others? How does this relate to the tight-rope walkers?
https://www.youtube.com/watch?v=qRsJXXb9WNE
No comments:
Post a Comment