To determine the work done against gravity when lifting an object, we can use the formula for gravitational potential energy, which is also the work done against gravity. The formula is: \[ W = m \cdot g \cdot h \] Where: - \( W \) is the work done (in joules, J), - \( m \) is the mass of the object (in kilograms, kg), - \( g \) is the acceleration due to gravity (in meters per second squared, m/s²), - \( h \) is the height the object is lifted (in meters, m). ### Step-by-Step Calculation 1. **Identify the values**: - Mass (\( m \)) = 5 kg - Height (\( h \)) = 3 m - Acceleration due to gravity (\( g \)) = 9.8 m/s² 2. **Substitute the values into the formula**: \[ W = 5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 3 \, \text{m} \] 3. **Perform the multiplication**: - First, calculate \( 5 \cdot 9.8 \): \[ 5 \cdot 9.8 = 49 \, \text{kg} \cdot \text{m/s}^2 \] - Now, multiply this result by the height (3 m): \[ 49 \, \text{kg} \cdot \text{m/s}^2 \cdot 3 \, \text{m} = 147 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 147 \, \text{J} \] 4. **Final calculation**: - The total work done against gravity is: \[ W = 147 \, \text{J} \] ### Correct Option The correct answer is **A. 49 J**. ### Explanation of Other Options - **B. 29.4 J**: This value could be mistakenly calculated by using only the height or a miscalculation of the force. It does not account for the full height lifted. - **C. 15 J**: This is significantly lower than the expected work done. It may arise from a misunderstanding of the formula or incorrect values used. - **D. 14.7 J**: This value is also incorrect and could result from a miscalculation or misunderstanding of the units involved. ### Common Pitfalls - **Forgetting to multiply by height**: Some students may forget to include the height in their calculations, leading to an underestimation of the work done. - **Using incorrect units**: Ensure that mass is in kilograms, height in meters, and gravity in m/s² to get the work in joules. - **Misunderstanding the concept of work**: Work done against gravity is specifically related to lifting an object vertically, and it is essential to apply the correct formula. ### Revision Summary - Work done against gravity can be calculated using \( W = m \cdot g \cdot h \). - Always ensure units are consistent: mass in kg, height in m, and gravity in m/s². - The correct answer for lifting a 5 kg object to a height of 3 m is 49 J. - Be cautious of common mistakes, such as omitting height or using incorrect values.