Certainly! Let's solve this problem step-by-step in detail.
### Step 1: Identify the Given Data
- Mass of the steel beam ([tex]\( m \)[/tex]): [tex]\( 600.0 \, \text{kg} \)[/tex]
- Distance the beam is lifted ([tex]\( d \)[/tex]): [tex]\( 38.0 \, \text{m} \)[/tex]
- Acceleration due to gravity ([tex]\( g \)[/tex]): [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] (This is a standard value)
### Step 2: Write the Equation for Work Done
The work done ([tex]\( W \)[/tex]) in lifting an object vertically against gravity is given by the equation:
[tex]\[ W = m \times g \times d \][/tex]
where:
- [tex]\( W \)[/tex] is the work done
- [tex]\( m \)[/tex] is the mass of the object
- [tex]\( g \)[/tex] is the acceleration due to gravity
- [tex]\( d \)[/tex] is the distance the object is lifted
### Step 3: Substitute the Given Values into the Equation
We substitute the values into the equation:
[tex]\[ m = 600.0 \, \text{kg} \][/tex]
[tex]\[ g = 9.81 \, \text{m/s}^2 \][/tex]
[tex]\[ d = 38.0 \, \text{m} \][/tex]
### Step 4: Calculate the Work Done
Now, we perform the calculation:
[tex]\[ W = 600.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 38.0 \, \text{m} \][/tex]
First, multiply the mass and gravity:
[tex]\[ 600.0 \times 9.81 = 5886.0 \, \text{N} \][/tex]
(Note: [tex]\( \text{N} \)[/tex] stands for Newton, which is [tex]\( \text{kg} \cdot \text{m/s}^2 \)[/tex])
Now, multiply the result by the distance:
[tex]\[ 5886.0 \, \text{N} \times 38.0 \, \text{m} = 223668.0 \, \text{J} \][/tex]
### Step 5: State the Final Answer
The amount of work done in vertically lifting the steel beam is:
[tex]\[ 223668.0 \, \text{J} \][/tex]
where [tex]\( \text{J} \)[/tex] stands for Joules, the unit of work.
So, the work done in lifting the steel beam vertically through a distance of 38.0 meters is:
[tex]\[ 223668.0 \, \text{J} \][/tex]
