Motion/C.M of composite objects

Concepts to investigate:

Composite bodies,center of mass,center of mass below point of support,stability.

Materials: 

Belt,piece of wood,saw,hammer,hinge,boards,clamp,potato,tooth-pick,two heavy forks.

Principles and procedures: 

Part 1: Center of mass above the base of support.

If two or more objects are fastened to each other,a composite body is formed with a center of mass of its own. Cut a notch into the block of wood. Place the block of wood onto the table and locate the position of the center of mass by moving the block to the last point at which it will remain balanced. Mark this point on the block. By adding another object on the block,it is possible to shift the center of mass. Place a belt in the slot and after positioning it so it once again balances,place another mark on the wood to see where the new center of mass is.

How does the belt affect the center of mass of the composite object?

Part 2: Center of mass below the base of support.

Cut a small piece from the end of a potato and stick a toothpick in its centre. Try to balance the potato on the top of a post or inverted glass. It is difficult because the center of mass is above the center of support and the base of support (diameter of tooth-pick)is very small. Now stick two forks in the potato such that the majority of the fork is below the bottom of the tth picks and again try to balance the potato,adjusting the forks if necessary. The potato balances because the center of mass has been shifted and now below the point of support. When the center of mass is below the point of support,the object is stable. After any disturbances,the object rotates so that the center of mass returns to its position under the point of support. Grasp one of the forks and give it a slight push. The center of mas will move but gravity will then pull it down to its original position under the point of support.

Part 3:

A board attached to another board by a hinge will rotate downwards when there is no weight added,if however an object is added to the freely moving board such that the center of mass for the new composite body is inside and below the pivot point,the reverse will happen. Using a rope or strap,position a hammer so that it is supported by the by the board. The board remains stationary because the center of mass is directly below the point of support. Consequently there is no net torque on the composite body. Now move the hammer so that the center of mass is inside and below the point of support. The board now rotates upwards because there is a net upward torque on the composite body. Reposition the hammer so that the center of mass is outside and below the hinge,the board rotates downwards because there is a net down ward torque on the composite body.

Questions:

(1) Describe the experimental procedure you would use to find the center of mass of a 3-dimensional object such asa cone or the potato-toothpick combination

(2) A tram suspended from a cable is stable but a person walking above on the same cable is not. Explain. {| class="collapsible collapsed" style="width:60%;" !style="line-height:100%;text-align:left;padding:0px 5px;background-color:beige;border:2px solid #F0E68C;"|

For answers Click at the drop down
In the potato toothpick combination,the center of mass of above the point of support. To keep the center of mass directly over the point of support,which is the end of the tooth-pick,you must constantly move the the support to compensate for the movement of the center of mass outside this small base. However, in the potato -toothpick-fork combination,the addition of the forks, moves the center of mass to a position below the point of support. If the center of mass is below the point of support,the object is stable.

(1) Tae a thread or string to one side of the object and let it hang. Draw an imaginary extension of the thread theough the object. Tape the thread to another location and repeat. the interscetion of the two imaginary extensions indicates the center of mass.

(2) The tram is stable because its center of mass is directly below its point of support.. On the other hand,a person standing on the cable is unstable because his or her center of mass is high above a narrow base of support.


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