Surface Tension of needle on water

[Aleisha]

I attempted the question but it was wrong... I don't understand where i went wrong my working seems logical, can someone please help.

When a needle is gently placed on the surface of still water (γ = 0.0730 N.m-1) it can be supported by surface tension if the mass of the needle is small enough.
Calculate the maximum mass of a needle that is 4.85 cm long that can be supported by the water. Take the acceleration due to gravity to be 9.80 m/s/s.

 

[Chestermiller]

I attempted the question but it was wrong... I don't understand where i went wrong my working seems logical, can someone please help.

When a needle is gently placed on the surface of still water (γ = 0.0730 N.m-1) it can be supported by surface tension if the mass of the needle is small enough.
Calculate the maximum mass of a needle that is 4.85 cm long that can be supported by the water. Take the acceleration due to gravity to be 9.80 m/s/s.View attachment 224645 View attachment 224646

You only included half the force.

P.S., Please use the Homework Template in the future.

 

[Aleisha]

So all I have to do is double my answer to get the full force?

 

[Chestermiller]

So all I have to do is double my answer to get the full force?

Yes. You also have to understand that, at the maximum weight, $\theta=0$.

 

[Aleisha]

I understand that now it makes sense, thank you!