To determine the work done against gravity when lifting a 5 kg object to a height of 10 meters, we can use the formula for gravitational potential energy, which is also the work done against gravity: ### Formula for Work Done Against Gravity The work done (W) against gravity can be calculated using the formula: \[ W = m \cdot g \cdot h \] Where: - \( W \) = work done (in joules, J) - \( m \) = mass of the object (in kilograms, kg) - \( g \) = acceleration due to gravity (in meters per second squared, m/s²) - \( h \) = height the object is lifted (in meters, m) ### Step-by-Step Calculation 1. **Identify the values**: - Mass (\( m \)) = 5 kg - Height (\( h \)) = 10 m - Acceleration due to gravity (\( g \)) = 9.8 m/s² 2. **Substitute the values into the formula**: \[ W = 5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 10 \, \text{m} \] 3. **Perform the multiplication**: - First, calculate \( 5 \cdot 9.8 \): \[ 5 \cdot 9.8 = 49 \, \text{kg m/s}^2 \] - Now, multiply this result by the height (10 m): \[ 49 \, \text{kg m/s}^2 \cdot 10 \, \text{m} = 490 \, \text{J} \] 4. **Final Result**: The work done against gravity on the object is \( 490 \, \text{J} \). ### Conclusion The correct answer is **A. 490 J**. ### Explanation of Other Options - **B. 98 J**: This value could be mistakenly calculated by only considering the force of gravity acting on the object without accounting for the height. It might represent the force (weight) of the object (5 kg × 9.8 m/s² = 49 N) but does not include the height. - **C. 50 J**: This is an incorrect approximation and does not reflect the actual calculations. It may arise from rounding or misunderstanding the relationship between mass, gravity, and height. - **D. 10 J**: This option is far too low and does not relate to the parameters given. It could be a misunderstanding of the units or a miscalculation. ### Common Pitfalls - **Forgetting to multiply by height**: Some students may forget that work done against gravity requires both the force (weight) and the distance (height). - **Using incorrect units**: Ensure that mass is in kilograms, height in meters, and that the result is in joules. - **Misunderstanding gravitational force**: Remember that the force acting on the object is its weight, which is calculated as \( m \cdot g \). ### Revision Summary - Work done against gravity is calculated using \( W = m \cdot g \cdot h \). - For a 5 kg object lifted 10 m, the work done is 490 J. - Always ensure to include both mass and height in calculations. - Be cautious of unit conversions and ensure all values are in the correct units before performing calculations.