To find the work done by the tension in the cable while lifting the girder, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

Steps:

1. Given Data:

   • Mass of the girder, $m = 850 \, \text{kg}$
   • Initial velocity, $v_i = 0.25 \, \text{m/s}$
   • Final velocity, $v_f = 0.75 \, \text{m/s}$
   • Distance moved, $d = 2.3 \, \text{m}$

2. Change in Kinetic Energy: The work done by the tension is equal to the change in the kinetic energy of the girder. $W = \Delta KE = \frac{1}{2} m (v_f^2 - v_i^2)$

   Substituting the values: $W = \frac{1}{2} \times 850 \times (0.75^2 - 0.25^2)$

3. Now let's calculate the result.

Let me calculate this for you.The work done by the tension in the crane's cable is 212.5 joules.

Would you like more details on the process, or do you have any questions?

Here are some related questions for further practice:

1. How would the work change if the girder's mass were doubled?
2. What is the force exerted by the tension during the lifting process?
3. If the crane lifted the girder at a constant speed, what would the work done by the tension be?
4. How would the work done change if the distance traveled was halved?
5. How much kinetic energy does the girder have at the final speed of 0.75 m/s?

Tip: The work-energy theorem is a powerful tool to connect force, displacement, and kinetic energy.