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 (\( g \)) = 9.81 m/s² ### Step-by-Step Calculation 1. **Substitute the values into the formula**: \[ W = 5 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 10 \, \text{m} \] 2. **Calculate the product of mass and gravity**: \[ 5 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 49.05 \, \text{N} \quad (\text{where N is Newtons, the unit of force}) \] 3. **Now multiply by the height**: \[ W = 49.05 \, \text{N} \cdot 10 \, \text{m} = 490.5 \, \text{J} \] ### Conclusion The work done against gravity when lifting the object is: \[ \boxed{490.5 \, \text{J}} \] Thus, the correct option is **C. 490.5 J**. ### Explanation of Other Options - **Option A: 49.05 J** - This value represents the force due to gravity (5 kg * 9.81 m/s²) but does not account for the height. It is not the work done. - **Option B: 98.1 J** - This value is incorrect as it seems to be a miscalculation, possibly from using a height of 1 meter instead of 10 meters. - **Option D: 980 J** - This value is incorrect as it appears to be a miscalculation, possibly from using an incorrect value for gravity or height. ### Common Pitfalls - **Forgetting to multiply by height**: Some students may only calculate the force due to gravity and forget to multiply by the height. - **Using incorrect units**: Ensure that mass is in kilograms, height in meters, and gravity in m/s² to get the work in joules. - **Rounding errors**: Be careful with rounding during calculations; keep as many decimal places as possible until the final answer. ### 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 490.5 J. - Always ensure to use the correct units and values in calculations. - Double-check calculations to avoid common mistakes.