To determine how much work is done against gravity when lifting a 5 kg object to a height of 10 meters, we can use the formula for work done against gravity, which is given by: \[ \text{Work} = \text{Force} \times \text{Distance} \] ### Step 1: Calculate the Force The force required to lift the object is equal to the weight of the object, which can be calculated using the formula: \[ \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \] Given: - Mass (m) = 5 kg - Acceleration due to gravity (g) = 9.8 m/s² Now, substituting the values into the formula: \[ \text{Weight} = 5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 49 \, \text{N} \] ### Step 2: Calculate the Work Done Now that we have the force (weight) acting on the object, we can calculate the work done in lifting it to a height of 10 meters. The distance (h) is 10 m. Using the work formula: \[ \text{Work} = \text{Force} \times \text{Distance} \] Substituting the values we have: \[ \text{Work} = 49 \, \text{N} \times 10 \, \text{m} = 490 \, \text{J} \] ### Conclusion The work done against gravity when lifting the 5 kg object to a height of 10 meters is **490 J**. Therefore, the correct option is: **D. 490 J** ### Explanation of Other Options - **A. 49 J**: This option represents the weight of the object (5 kg × 9.8 m/s²) but does not account for the distance over which the object is lifted. Work requires both force and distance. - **B. 98 J**: This value could be mistakenly calculated by multiplying the weight (49 N) by 2 meters instead of the correct height of 10 meters. It does not reflect the actual work done over the full distance. - **C. 245 J**: This option might arise from a miscalculation, perhaps by incorrectly using half the height (5 m) or misunderstanding the relationship between force and distance. It does not represent the correct work done against gravity. ### Common Pitfalls - **Forgetting to multiply by the full height**: Always ensure you use the correct height when calculating work. - **Confusing weight with work**: Remember that weight is a force, while work is the product of force and distance. - **Neglecting units**: Always check that your units are consistent (e.g., mass in kg, distance in meters, force in Newtons). ### Revision Summary - Work done against gravity is calculated using \( \text{Work} = \text{Force} \times \text{Distance} \). - The force is equal to the weight of the object, calculated as \( \text{Weight} = \text{mass} \times g \). - For a 5 kg object lifted 10 m, the work done is 490 J. - Always ensure to use the correct height and understand the difference between force and work.