Answer :
To determine how high the load was lifted, we need to use the relationship between work, force, and distance. The work done by the electric hoist in raising the load can be described by the equation:
[tex]\[ \text{Work Done} = \text{Force} \times \text{Height} \][/tex]
Since the force here is the gravitational force acting on the load, we use:
[tex]\[ \text{Force} = \text{Weight} = \text{mass} \times \text{gravitational acceleration} \][/tex]
The formula for work done can then be rewritten as:
[tex]\[ \text{Work Done} = \text{mass} \times \text{gravitational acceleration} \times \text{Height} \][/tex]
Given:
- Work Done = 196,000 Joules
- Mass = 250 kg
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.8 m/s[tex]\(^2\)[/tex]
We want to find the height, so we rearrange the formula to solve for height:
[tex]\[ \text{Height} = \frac{\text{Work Done}}{\text{mass} \times \text{gravitational acceleration}} \][/tex]
Plugging in the values:
[tex]\[ \text{Height} = \frac{196,000}{250 \times 9.8} \][/tex]
Calculating the denominator:
[tex]\[ 250 \times 9.8 = 2,450 \][/tex]
So,
[tex]\[ \text{Height} = \frac{196,000}{2,450} \][/tex]
Finally, when you do the division:
[tex]\[ \text{Height} = 80 \text{ meters} \][/tex]
Therefore, the load was lifted to a height of 80 meters.
[tex]\[ \text{Work Done} = \text{Force} \times \text{Height} \][/tex]
Since the force here is the gravitational force acting on the load, we use:
[tex]\[ \text{Force} = \text{Weight} = \text{mass} \times \text{gravitational acceleration} \][/tex]
The formula for work done can then be rewritten as:
[tex]\[ \text{Work Done} = \text{mass} \times \text{gravitational acceleration} \times \text{Height} \][/tex]
Given:
- Work Done = 196,000 Joules
- Mass = 250 kg
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.8 m/s[tex]\(^2\)[/tex]
We want to find the height, so we rearrange the formula to solve for height:
[tex]\[ \text{Height} = \frac{\text{Work Done}}{\text{mass} \times \text{gravitational acceleration}} \][/tex]
Plugging in the values:
[tex]\[ \text{Height} = \frac{196,000}{250 \times 9.8} \][/tex]
Calculating the denominator:
[tex]\[ 250 \times 9.8 = 2,450 \][/tex]
So,
[tex]\[ \text{Height} = \frac{196,000}{2,450} \][/tex]
Finally, when you do the division:
[tex]\[ \text{Height} = 80 \text{ meters} \][/tex]
Therefore, the load was lifted to a height of 80 meters.
