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) ### Given Values - Mass (\( m \)) = 5 kg - Height (\( h \)) = 10 m - Acceleration due to gravity (\( g \)) = 9.8 m/s² ### Step-by-Step Calculation 1. **Substitute the values into the formula**: \[ W = 5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 10 \, \text{m} \] 2. **Calculate the product of mass and gravity**: \[ 5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 49 \, \text{kg} \cdot \text{m/s}^2 = 49 \, \text{N} \quad (\text{since } 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2) \] 3. **Now multiply by the height**: \[ W = 49 \, \text{N} \cdot 10 \, \text{m} = 490 \, \text{J} \] ### Conclusion The work done against gravity on the object is **490 J**. Therefore, the correct option is **C**. ### Explanation of Other Options - **Option A: 49 J** - This value represents the force due to gravity acting on the object (5 kg × 9.8 m/s²), but it does not account for the height the object is lifted. Thus, it is incorrect. - **Option B: 98 J** - This value could be mistakenly calculated by multiplying the weight of the object (49 N) by a height of 2 m instead of 10 m. It does not reflect the correct height and is therefore incorrect. - **Option D: 980 J** - This value could arise from a miscalculation, such as multiplying the weight (49 N) by a height of 20 m instead of 10 m. It is also incorrect. ### Common Pitfalls - **Forgetting to multiply by height**: Some students may only calculate the weight of the object and forget to multiply by the height. - **Using incorrect units**: Ensure that mass is in kilograms, height in meters, and that the result is in joules. - **Misunderstanding the concept of work**: Remember that work done against gravity is not just the force but the force applied over a distance (height). ### 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 multiply the weight by the correct height. - Be cautious of unit conversions and ensure all values are in the correct units before calculating.