To determine the work done against gravity when lifting a 2 kg object to a height of 5 meters, we can use the formula for work done against gravity, which is given by: \[ \text{Work} = m \cdot g \cdot h \] Where: - \( m \) is the mass of the object (in kilograms), - \( g \) is the acceleration due to gravity (in meters per second squared), - \( h \) is the height the object is lifted (in meters). ### Step-by-Step Calculation 1. **Identify the values**: - Mass (\( m \)) = 2 kg - Acceleration due to gravity (\( g \)) = 9.8 m/s² - Height (\( h \)) = 5 m 2. **Substitute the values into the formula**: \[ \text{Work} = 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 5 \, \text{m} \] 3. **Perform the multiplication**: - First, calculate \( 2 \cdot 9.8 \): \[ 2 \cdot 9.8 = 19.6 \] - Next, multiply this result by the height (5 m): \[ 19.6 \cdot 5 = 98 \, \text{J} \] 4. **Final result**: \[ \text{Work} = 98 \, \text{J} \] ### Correct Answer The correct answer is **C. 98 J**. ### Explanation of Other Options - **Option A: 9.8 J**: This value represents the work done to lift the object by only 1 meter (since \( 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 1 \, \text{m} = 19.6 \, \text{J} \)). It is incorrect because it does not account for the full height of 5 meters. - **Option B: 19.6 J**: This value is the work done to lift the object by 1 meter (as calculated above). It is also incorrect for the same reason as option A. - **Option D: 49 J**: This value does not correspond to any correct calculation based on the given mass, height, and gravitational acceleration. It is incorrect as it does not reflect the proper multiplication of the values. ### Common Pitfalls - **Forgetting to multiply by height**: Some students may forget to include the height in their calculations, leading to underestimating the work done. - **Using incorrect units**: Ensure that mass is in kilograms, height in meters, and gravity in meters per second squared to maintain consistency in units. - **Misunderstanding the concept of work**: Work done against gravity is always positive when lifting an object, as it requires energy to overcome gravitational force. ### Revision Summary - Work done against gravity can be calculated using the formula \( \text{Work} = m \cdot g \cdot h \). - Always ensure to use the correct values for mass, gravity, and height. - Double-check calculations to avoid common mistakes. - Remember that work done is measured in joules (J).