Question

The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m. a. How much work is done by gravity? b. How much work is done by tension

Answer 1

To solve this exercise it is necessary to apply the equations concerning Work, both by general definition and by conservation of energy.

In other words, the work done by an object due to gravity is the equivalent to that defined by the potential energy equations, that is

$W= mg\Delta h$

Where,

m=mass

g=gravitational acceleration

$\Delta h =$ Change in height

On the other hand we have that the work done by tension is defined by the conservation of kinetic and potential energy, that is to say

$W= \Delta KE + \Delta PE$

Where,

$\Delta KE =$ Change in Kinetic Energy

$\Delta PE =$Change in Potential Energy

PART A) As defined by the work done by gravity would be given by,

$W = mg\Delta h$

$W = (750)(9.8)(3.5)$

$W = 25.725kJ$

Therefore the work done by gravity is 25.725kJ

PART B) The work done by the tension applies the energy conservation equation, that is to say

$W= \Delta KE + \Delta PE$

$W = (\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2)+(mgh_f-mgh_i)$

$W = \frac{1}{2}m(v_f^2-v_i^2)+mg(h_f-h_i)$

Replacing with our values,

$W = \frac{1}{2}(750)(0.75^2-0.25^2)+(750)(9.8)(3.5)$

$W = 25.912kJ$

Therefore the work done by tension is 25.9kJ