Olive and her friend Wellington are playing down by Captain Don\'s docks when th

Question

Olive and her friend Wellington are playing down by Captain Don's docks when they find an old chain. The old chain has only three links. By measuring with an old fish scale which is a permanent feature of the dock area, they determine that the total mass of the chain is 2.07  kg (the scale reads in newtons, but Olive knows how to calculate the mass of the chain from its weight). While playing with the scale and the chain (the chain is hanging vertically from the end of the scale, and Olive is holding on to the top of the scale with both hands, either moving the entire system upwards or downwards), Olive notices that if she is accelerating the chain either upwards or downwards, the scale no longer 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 36.50  N .

Part A

When the scale reads 36.50  N , what is the tension in the chain at the point where the lowest two links connect?

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____N

Part B

When the scale reads 36.50  N , what is the tension in the chain at the point where the topmost two links connect?

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____N

Part C

Consider all the downward forces which are acting on the middle link. When the scale reads 36.50  N , what is the magnitude of the sum of all those downward forces?

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____N

When the Scale Reading is Smaller than the Weight of the Chain

At another point in their experiments, Wellington observes that the scale reads only 11.70  N .

We could ask the same questions for this case as were asked for the case when the scale read 36.50  N . Instead, to further test your understanding, we will ask a slightly different set of questions.

Part D

When the scale reads 11.70  N , what is the Up-Down component of the acceleration of the old chain? Let Up be positive.

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____m/s2  

Part E

When the scale reads 11.70  N , what is the Up-Down component of the force on the lowest link by the middle link? Let Up be positive.

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____N

Part F

Consider all the downward forces which are acting on the middle link. When the scale reads 11.70  N , what is the magnitude of the sum of all those downward forces?

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____N

Using the Chain to Tow a Sled

Old Captain Don is overjoyed when he sees the kids playing with the chain, because he had lost the chain sometime last winter. It turns out that Captain Don uses the chain to connect his snowmobile to his homemade sled in which he tows loads of fish, or ice, or supplies, etc. back and forth from his nearby house and office to his dock in the wintertime. Assume, for the purposes of this problem, that the little homemade sled slips across the winter snows with little friction of any kind. Suppose the mass of the sled and its load is 27.00  kg , and suppose that Captain Don is speeding up on level ground at a rate of 69.00  cm/s2 as he is just starting out on a towing trip. Also, assume that the chain stretches horizontally from a hook on the snowmobile to a hook on the homemade sled, i.e. ignore any sagging in the chain which is connecting the snowmobile to the homemade sled.

Part G

What is the tension in the chain at the meeting of links which is closest to the sled?

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____N

Part H

What is the tension in the chain at the meeting of links which is closest to the snowmobile?

Note: this question has a tolerance of only 1.0%, not the usual 2.0%.

Answer=_____N

Explanation / Answer

the mass of the chain is 2.07 kg

since the chain has three links and if the mass of each link is ml then the mass of the one link will be

ml = 2.07 kg / 3

= 0.69 kg

(a)

at the point where the lowest two links connect there will be only one link left to hang so that

ml g = (0.69 kg)(9.8 m/s2)

= 6.762 N

the tension in the chain at the point where the lowest two links connect will be

T = 36.5 N - 6.762 N

= 29.738 N

(b)

at the top most two links connect there will be only two links left to hang so that

2 ml g = (2) (0.69 kg)(9.8 m/s2)

= 13.524 N

the tension in the chain at the point where the top most two links connect will be

T = 36.5 N - 13.524 N

= 22.976 N

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