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 3.12 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 47.00 N . Part A When the scale reads 47.00 N , what is the tension in the chain at the point where the lowest two links connect

Answer 1

T₁ = 15.66 N

Step-by-step explanation:

From the given information:

Using the free body system in the chain.

T - mg = ma

47 - 3.12 × 9.8 = 3.12a

47 - 30.576 = 3.12a

16.424 = 3.12a

a = 16.424/3.12

a = 5.26 m/s²

Now, by the free body diagram of the lowest link; the tension (T₁ ) in the chain is:

T₁ - (3.12/3) × 9.8 = (3.12/3) × 5.26

T₁ - 1.04 × 9.8 = 1.04 × 5.26

T₁ - 10.192 = 5.4704

T₁ = 5.4704 + 10.192

T₁ = 15.6624

T₁ = 15.66 N