A crane lifts a 100-kg concrete block to a vertical height of 25 m. Determine the work done by the crane.
You have to multiply the height or distance x gravitational pull x weight
formula:
W= h (or d for distance) x g x w
= 25 x 9.81 x 100
W= 24525J
the work being done is 24525 Joules
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Well, lifting a 100-kg concrete block to a height of 25 m sounds like quite the workout for the crane! To determine the work done, we need to use the formula:
Work = Force × Distance
In this case, the force is equal to the weight of the concrete block, which can be calculated using the formula:
Force = mass × gravity
The mass of the concrete block is 100 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So, the force would be:
Force = 100 kg × 9.8 m/s^2
Now, let's plug in the values and calculate the force exerted by the concrete block.
Afterward, we multiply the force by the distance (25 m). Once we do that, we will know the amount of work done by the crane. So, let me do the math for you...
(100 kg) × (9.8 m/s²) × (25 m) = 24,500 joules
So, the crane did approximately 24,500 joules of work to lift the concrete block. I hope it didn't break a sweat!
To determine the work done by the crane, we can use the formula:
Work = Force x Distance x Cosine(theta)
Where:
- Force is the force exerted by the crane to lift the block.
- Distance is the vertical height the block is lifted.
- Theta is the angle between the force and the direction of motion.
In this case, the force is equal to the weight of the block, which can be calculated using the formula:
Force = Mass x Acceleration due to gravity
Given that the mass of the concrete block is 100 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force:
Force = 100 kg x 9.8 m/s^2 = 980 N
Since the height lifted is 25 m and the force acts vertically, the angle theta is 0 degrees (cosine(0) = 1).
Now we can calculate the work done by plugging in the values into the formula:
Work = 980 N x 25 m x 1 = 24,500 N·m (or Joules)
Therefore, the crane does 24,500 Joules of work to lift the 100-kg concrete block to a vertical height of 25 meters.