A bridge worker on the top deck of a double decked bridge needs to lift a 30 kg tool box, with a cable of uniform density 2 kg/meter, from the ground 15 meters below him to the lower deck of the bridge which is 10 meters above the ground. How much work is needed?
To calculate the work needed to lift the tool box, we can use the formula:
Work = Force × Distance
First, let's calculate the force required to lift the tool box. The force required can be determined by considering the weight of the tool box and the weight of the cable.
Weight of the tool box = mass × acceleration due to gravity
= 30 kg × 9.8 m/s^2
= 294 N
Weight of the cable = mass × acceleration due to gravity
= 2 kg/m × 15 m × 9.8 m/s^2
= 294 N
Total force required = Weight of the tool box + Weight of the cable
= 294 N + 294 N
= 588 N
Now, let's calculate the distance over which the force is applied. In this case, the distance is the sum of the height of the lower deck of the bridge (10 meters) and the distance between the worker and the tool box (15 meters). So, the total distance is 10 meters + 15 meters = 25 meters.
Finally, we can calculate the work needed:
Work = Force × Distance
= 588 N × 25 meters
= 14,700 joules
Therefore, the work required to lift the tool box is 14,700 joules.