To find the work done against gravity when a body of mass \( m \) elevates to a height \( h \), we use the formula for gravitational potential energy, which is given by:
\[ W = mgh \]
where:
- \( W \) is the work done against gravity (in joules),
- \( m \) is the mass of the body (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) on the surface of the Earth),
- \( h \) is the height (in meters).
Given:
- \( m = 50 , \text{kg} \)
- \( h = 3.0 , \text{m} \)
- \( g = 9.81 , \text{m/s}^2 \)
Now, we can substitute these values into the formula:
\[ W = 50 , \text{kg} \times 9.81 , \text{m/s}^2 \times 3.0 , \text{m} \]
Calculating the work done:
\[ W = 50 \times 9.81 \times 3.0 = 1471.5 , \text{J} \]
Thus, the work done against gravity is 1471.5 joules.
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