a crane lifts a metal beam with a mass of 1350 kg. Calculate the amount of work done against gravity if the beam is lifted 37.5 meters in the air.
W = F*h.
F = m*g = 1350kg * 9.8N/kg = 13,230 N.
W = 13230 * 37m = 489,510 J.
To calculate the amount of work done against gravity when lifting the metal beam, we need to use the formula:
Work = Force × Distance
In this case, the force we are working against is the weight of the object, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s²).
Given that the mass of the beam is 1350 kg and the distance it is lifted is 37.5 meters, we can calculate the amount of work done as follows:
Work = (1350 kg) × (9.8 m/s²) × (37.5 m)
Calculating this equation:
Work = 498,375 Joules
Therefore, the amount of work done against gravity when lifting the metal beam is 498,375 Joules.
To calculate the amount of work done against gravity, you need to use the formula:
Work = Force × Distance × cos(θ)
In this case, the force is the weight of the beam, which can be calculated using the formula:
Force = mass × gravitational acceleration
The mass of the beam is given as 1350 kg. The standard value for gravitational acceleration is approximately 9.8 m/s².
So, let's calculate the force first:
Force = 1350 kg × 9.8 m/s²
Next, multiply the force by the distance the beam is lifted:
Work = Force × Distance
Work = (1350 kg × 9.8 m/s²) × 37.5 m
Finally, calculate the work done against gravity:
Work = 5,284,500 Joules
Therefore, the amount of work done against gravity when the crane lifts the beam 37.5 meters into the air is approximately 5,284,500 Joules.