A crane lifts 1 tonne of concrete through a height of 25 m. How much work does it do? (1 kg has a weight of 9.81 N.)
1 tonne is 1000 kg. Multiply the weight (in Newtons) by 25 m.
2500
To find the work done by the crane, we need to understand the formula for work. Work is defined as the product of force and displacement. Mathematically, it can be represented as:
Work = Force x Displacement x cos(angle)
In this case, the force is the weight of the object being lifted, which is equal to its mass multiplied by the acceleration due to gravity. The displacement is the vertical distance the object is lifted.
Given:
Mass of concrete = 1 tonne = 1000 kg
Acceleration due to gravity = 9.81 m/s²
Height = 25 m
First, let's calculate the force:
Weight = Mass x Acceleration due to gravity
Weight = 1000 kg x 9.81 m/s²
Weight = 9810 N
Now, we can find the work done:
Work = Force x Displacement x cos(angle)
Since the displacement is vertical, the angle between the force and displacement vectors is 0 degrees. The cosine of 0 degrees is 1.
Work = 9810 N x 25 m x cos(0)
Work = 245,250 N·m
Therefore, the crane does a total work of 245,250 N·m (or joules) to lift 1 tonne of concrete through a height of 25 m.