To calculate the work done by the cheerleader in lifting his partner, we can use the formula for gravitational potential energy, which is related to work. The work done \( W \) in lifting an object is given by:
\[ W = m \cdot g \cdot h \]
where:
- \( W \) is the work done,
- \( m \) is the mass of the partner (in kg),
- \( g \) is the acceleration due to gravity (in m/s²),
- \( h \) is the height lifted (in m).
Given:
- \( m = 77.6 \) kg,
- \( g = 9.8 \) m/s²,
- \( h = 0.574 \) m.
First, we'll calculate the work done for one lift:
\[ W_{single} = 77.6 , \text{kg} \cdot 9.8 , \text{m/s}^2 \cdot 0.574 , \text{m} \]
Now, let's calculate that step-by-step:
- Calculate \( m \cdot g \):
\[ m \cdot g = 77.6 , \text{kg} \cdot 9.8 , \text{m/s}^2 = 760.48 , \text{N} \]
- Now multiply by the height \( h \):
\[ W_{single} = 760.48 , \text{N} \cdot 0.574 , \text{m} \approx 436.29 , \text{J} \]
Now, since he does this 29 times, the total work done \( W_{total} \) will be:
\[ W_{total} = W_{single} \cdot \text{number of lifts} = 436.29 , \text{J} \cdot 29 \]
Calculating this:
\[ W_{total} \approx 436.29 , \text{J} \cdot 29 \approx 12656.41 , \text{J} \]
Therefore, the total work done by the cheerleader in lifting his partner 29 times is approximately:
\[ \boxed{12656.41 , \text{J}} \]