Question

(see fluids in the news article titled "walking on water ," section 1.9 .) (a) the water strider bug shown in fig. p1.131 is supported on the surface of a pond by surface tension acting along the interface between the water and the bug's legs. determine the minimum length of this interface needed to support the bug. assume the bug weighs 1 × 10-4 n and the surface tension force acts vertically upwards. (b) repeat part (a) if surface tension were to support a person weighing 640 n.

Answer 1

To support the water strider bug on the surface of the pond, the minimum length of the interface between the water and the bug's legs needs to be determined using the surface tension. The calculation involves dividing the weight of the bug by the surface tension. The same principle applies to calculate the minimum length needed to support a person on the water's surface.

Step-by-step explanation:

In order for the water strider bug to be supported on the surface of the pond by surface tension, the minimum length of the interface between the water and the bug's legs needs to be determined. Assuming the bug weighs 1 × 10-4 N and the surface tension force acts vertically upwards, we can use the equation T = F/L, where T is the surface tension, F is the weight of the bug, and L is the length of the interface. Rearranging the equation to solve for L, we get L = F/T. Substituting the given values, the minimum length of the interface needed to support the bug is 1 × 10-4 N / T.

To calculate the minimum length of the interface needed to support a person weighing 640 N, we can use the same equation. Substituting the new weight into the equation, the minimum length of the interface needed to support the person is 640 N / T.

Answer 2

Part a)

Surface tension of water

`S = 72 * 10^(-3) N/m`

Weight of the bug is

`W = 1 * 10^(-4) N`

now we can say

`F = S*L`

`1*10^(-4) = 72 * 10^(-3) * L`

L = 1.39 mm

Part b)

Now if the same surface is to balance a man of weight 640 N

Now by same formula

`F = S*L`

`640 = 72*10^(-3) * L`

`L = 8.89 * 10^3 m`