Olive and her friend Wellington are playing down by CaptainDon's docks when they find an old chain. The old chain has onlythree links. By measuring with an old fish scale which is apermanent feature of the dock area, they determine that the totalmass of the chain is 2.55  kg (the scale reads innewtons, but Olive knows how to calculate the mass of the chainfrom its weight). While playing with the scale and the chain (thechain is hanging vertically from the end of the scale, and Olive isholding on to the top of the scale with both hands, either movingthe entire system upwards or downwards), Olive notices that if sheis accelerating the chain either upwards or downwards, the scale nolonger accurately reads the weight of the chain.

When the Scale Reading is Larger than the Weight of the Chain:At one point in their experiments with the chain and the scale,Wellington observes that the scale reads 42.00  N

A: When the scale reads 42.00  N, what is the tensionin the chain at the point where the lowest two links connect?

B: When the scale reads 42.00  N, what is the tensionin the chain at the point where the topmost two links connect?

C: Consider all the downward forces which are acting on themiddle link. When the scale reads 42.00  N, what is themagnitude of the sum of all those downward forces?

When the Scale Reading is Smaller than the Weight of the Chain:At another point in their experiments, Wellington observes that thescale reads only 11.50  N. (We could ask the samequestions for this case as were asked for the case when the scaleread 42.00  N. Instead, to further test yourunderstanding, we will ask a slightly different set ofquestions.)

D: When the scale reads 11.50  N what is the Up-Downcomponent of the acceleration of the old chain? Let Up bepositive.

E: When the scale reads 11.50  N what is the Up-Downcomponent of the force on the lowest link by the middle link? LetUp be positive.

F: Consider all the downward forces which are acting on themiddle link. When the scale reads 11.50  N, what is themagnitude of the sum of all those downward forces?

Using the Chain to Tow a Sled: Old Captain Don is overjoyed whenhe sees the kids playing with the chain, because he had lost thechain sometime last winter. It turns out that Captain Don uses thechain to connect his snowmobile to his homemade sled in which hetows loads of fish, or ice, or supplies, etc. back and forth fromhis nearby house and office to his dock in the wintertime. Assume,for the purposes of this problem, that the little homemade sledslips across the winter snows with little friction of any kind.Suppose the mass of the sled and its load is 33.00  kg,and suppose that Captain Don is speeding up on level ground at arate of 39.00  cm/s2 cm/s2 as he is just starting out ona towing trip. Also, assume that the chain stretches horizontallyfrom a hook on the snowmobile to a hook on the homemade sled, i.e.ignore any sagging in the chain which is connecting the snowmobileto the homemade sled.

G: What is the tension in the chain at the meeting of linkswhich is closest to the sled?

H: What is the tension in the chain at the meeting of linkswhich is closest to the snowmobile?