Calculating force

Question

At a building site, an iron girder of mass 400 kg is suspended from a crane by a steel cable. Assume that the cable has a circular cross-section of diameter 24 mm.

a.What is the tensile force in newtons on the cable given that force = mass × g (where the acceleration due to gravity, g = 9.8 m s−2). Ignore the mass of the cable.(2 marks)
b.Calculate the cross-sectional area of the cable in square metres.(3 marks)
c.Show that the stress on the cable is 8.67 × 106 N m−2. Again ignore the mass of the cable.(3 marks)
d.If the Young’s modulus of the steel cable is 200 × 109 N m−2, calculate the strain in the cable.(3 marks)
e.When it is loaded with the iron girder, the steel cable stretches by 0.78 mm. Calculate what the original length of the steel cable was (i.e. its length prior to loading).(4 marks)
TOTAL: 15 marks
show working

Answer 1

Benjamin,

 

Here we go!

First off, the tensile force use to gravity is mass in kg times g or 400g.

Then, the cross sectional area is pi times radius squared or .012^2*3.14

We can see from units of stress that we have to divide the tensile force found in part a in newtons by the cross sectional area in meters squared found in part b.

Now de young's modulus is the ratio of stress to strain, so divide the stress found in part c by 200*109.

To find the original length after stretching .78mm you need to use the formula relating tensile force to length:

F=EAΔL/L0 where E is the modulus, A is the cross sectional are from part b,and F is the force from part a. Plug in .07 for delta L and solve for L0.

 

Hope that helps!

Deanna