Another quantity recorded in the aforementioned research paper is the toughness of the spider silk,
found to be 27 J/cm^3 . Toughness is the amount of energy that an object can absorb, per unit volume of the object, before breaking.

Spiderman and Mary Jane freefall a height 66.9m before having their fall halted by a strand of web 1.00cm in diameter fired upwards a height 66.9m (so the strand of web is long). If all of their kinetic energy is absorbed by the spider silk, what is their maximum combined mass?

I think I understand the question. Our prof. has taught us about Tensile strength so I'm sure we're supposed to apply it here.

Tensile strength = F/A

What I did was change 27J/cm^3 to N/m^2 to get 2.7x10^7N/m^2.

Since they give you the length and width of the web, I converted 1.00cm to 0.01m and multiplied that by 66.9m, to get 0.669m^2.

They ask for the mass, and we've learned that in this case F = mg. Therefore I get an equation that looks something like this:

2.7x10^7N/m^2 = m(9.81)/0.669

Now I should be able to solve this easily but this gives me a huge mass which is physically impossible. I was wondering if anyone would be able to show me my error. Thanks alot.

PeterO
Homework Helper
Another quantity recorded in the aforementioned research paper is the toughness of the spider silk,
found to be 27 J/cm^3 . Toughness is the amount of energy that an object can absorb, per unit volume of the object, before breaking.

Spiderman and Mary Jane freefall a height 66.9m before having their fall halted by a strand of web 1.00cm in diameter fired upwards a height 66.9m (so the strand of web is long). If all of their kinetic energy is absorbed by the spider silk, what is their maximum combined mass?

I think I understand the question. Our prof. has taught us about Tensile strength so I'm sure we're supposed to apply it here.

Tensile strength = F/A

What I did was change 27J/cm^3 to N/m^2 to get 2.7x10^7N/m^2.

Since they give you the length and width of the web, I converted 1.00cm to 0.01m and multiplied that by 66.9m, to get 0.669m^2.

They ask for the mass, and we've learned that in this case F = mg. Therefore I get an equation that looks something like this:

2.7x10^7N/m^2 = m(9.81)/0.669

Now I should be able to solve this easily but this gives me a huge mass which is physically impossible. I was wondering if anyone would be able to show me my error. Thanks alot.

It is not enough to merely match gravity [mg]. That just means the object stops accelerating. Since they have already fallen 66+ metres, they will be travelling at about 35 m/s. It is not enough to stop accelerating, they need to be brought to a halt!!

If the upward force from the strand was 2mg [an excess upwards force of mg] they will take a further 66+ metres to stop. [a net downward force of mg took 66+ metres for them to gain their speed, a net upward force of mg will take just as long to stop them again.

How quickly did you want to stop them?