A crane lifts a 100-kg concrete block to a vertical height of 25 m. Determine the work done by the crane.
work = force * distance = mgh
To determine the work done by the crane, we can use the formula:
Work (W) = Force (F) × Distance (d)
The force required to lift the concrete block is equal to its weight, which can be calculated as:
Force (F) = mass (m) × gravity (g)
Given:
Mass (m) = 100 kg
Gravity (g) = 9.8 m/s^2 (acceleration due to gravity)
Substituting these values, we have:
Force (F) = 100 kg × 9.8 m/s^2
= 980 N
The distance (d) lifted by the crane is 25 m.
Plugging these values into the work formula, we have:
Work (W) = 980 N × 25 m
= 24,500 Joules (J)
Therefore, the work done by the crane is 24,500 Joules.
To determine the work done by the crane, we can use the formula:
Work (W) = Force (F) x Distance (d) x cosine(theta)
In this case, the force applied by the crane would be the weight of the concrete block, which can be calculated using the formula:
Force = mass x gravity
First, let's calculate the force:
Force = 100 kg x 9.8 m/s^2 (acceleration due to gravity)
= 980 N
Next, we need to calculate the distance lifted, which is given as 25 m.
Now, let's calculate the work done:
Work = Force x Distance x cosine(theta)
Since the block is lifted vertically, the angle between the force and displacement is 0 degrees, and the cosine of 0 is 1.
Work = 980 N x 25 m x 1
= 24,500 J (Joules)
Therefore, the work done by the crane is 24,500 Joules.
It's important to note that the work done by the crane is equal to the potential energy gained by the block as it is lifted to a vertical height of 25 m.