A child pulls a friend in a little red wagon with constant speed. If the child pulls with a force of 22.0 N for 15.0 m, and the handle of the wagon is inclined at an angle of 33.0 degrees above the horizontal, how much work does the child do on the wagon?
Answer
🚀 Physics Problem Solved: Work Done by a Force at an Angle
🔍 Given Data:
- Force (F) = 22.0 N
- Distance (d) = 15.0 m
- Angle (θ) = 33.0° above the horizontal
🧠 Concept Applied:
The formula to calculate work done when a force is applied at an angle is:
Work (W) = F × d × cos(θ)
Here, only the component of force in the direction of motion contributes to the work done.
✏️ Step-by-Step Calculation:
- First, calculate cos(33.0°) ≈ 0.8387
- Now, multiply the values:
W = 22.0 N × 15.0 m × cos(33.0°)
W ≈ 22.0 × 15.0 × 0.8387
W ≈ 276.771 J
✅ Final Answer:
The child does approximately 276.77 joules of work on the wagon.
💡 Physics Insight: When calculating work, always consider the component of the force in the direction of displacement. Angled forces require trigonometry to find that component.