Calculate work

 To calculate the work done by a 10 lb ball bearing dropped from a height of 10,000 ft, we can use the formula for gravitational potential energy, which is converted to work as the ball bearing falls.


### Formula

The gravitational potential energy (and therefore the work done) can be calculated using the formula:


\[

\text{Work} = m \cdot g \cdot h

\]


Where:

- \( m \) = mass (in pounds)

- \( g \) = acceleration due to gravity (approximately \( 32.2 \, \text{ft/s}^2 \))

- \( h \) = height (in feet)


### Given Values

- \( m = 10 \, \text{lb} \)

- \( g = 32.2 \, \text{ft/s}^2 \) (This value is used for calculations in imperial units)

- \( h = 10,000 \, \text{ft} \)


### Calculation

1. Convert the weight to mass:

   - Weight \( = m \cdot g \) 

   - Therefore, the mass \( m \) in slugs (since \( 1 \, \text{slug} = 32.2 \, \text{lb} \)):

   \[

   m = \frac{10 \, \text{lb}}{32.2 \, \text{ft/s}^2} \approx 0.3106 \, \text{slugs}

   \]


2. Calculate the work done:

   \[

   \text{Work} = 10 \, \text{lb} \cdot 10,000 \, \text{ft} = 100,000 \, \text{ft-lb}

   \]


### Conclusion

The work done by the 10 lb ball bearing dropped from a height of 10,000 ft is approximately **100,000 ft-lb**. 


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