A 120-MT concrete beam is lifted from the floor by two tandem heavy lift cranes up to a target height of 7.5 meters.
Calculate the potential energy of the beam when it is halfway the target height
To calculate the potential energy of the beam when it is halfway the target height, we need to determine the gravitational potential energy formula and substitute the values into it.
The gravitational potential energy formula is given by:
Potential Energy = mass x gravity x height
Given:
Mass of the beam (m) = 120 MT = 120,000 kg (since 1 MT = 1000 kg)
Target height (h) = 7.5 meters
To find the potential energy when the beam is halfway the target height, we need to divide the target height by 2:
Halfway height = 7.5 meters / 2 = 3.75 meters
Now, we can substitute the values into the formula:
Potential Energy = mass x gravity x height
Potential Energy = 120,000 kg x 9.8 m/s^2 x 3.75 meters
Calculating the potential energy:
Potential Energy = 4,410,000 Joules
Therefore, the potential energy of the beam when it is halfway the target height is 4,410,000 Joules.
To calculate the potential energy of the beam when it is halfway to the target height, we need to determine the mass of the beam and the height at the halfway point.
Given:
Mass of the beam (m) = 120 MT = 120,000 kg
Target height (h) = 7.5 meters
Step 1: Determine the height at the halfway point
Since the halfway point is at half the target height, the height at the halfway point (h_half) = h/2 = 7.5/2 = 3.75 meters.
Step 2: Calculate the potential energy at the halfway point
The potential energy (PE) of an object can be calculated using the formula:
PE = m * g * h
where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
Using the given values:
m = 120,000 kg
g ≈ 9.8 m/s^2 (acceleration due to gravity)
h = 3.75 meters
PE = 120,000 * 9.8 * 3.75
Calculating the potential energy using these values:
PE ≈ 4,410,000 Joules