Irodov 1.121 | Work Done on a Curved Hill- A Surprising Result! | Friction | Physics | JEE Main Adv

Problem- 1.121: A body of mass m is slowly hauled up a hill by a force F, which at each point is directed along a tangent to the trajectory. Find the work performed by this force if the height of the hill is h, the length of its base is l, and the coefficient of friction is k. Does the work needed to haul a body up a curved hill depend on the hill’s shape? I.E. Irodov Problem 1.121 connects work, friction and gravity through a surprisingly elegant result. A body is pulled slowly uphill by a force that always acts along the tangent to its path. The slope changes continuously—so how can we calculate the total work without knowing the exact shape of the hill? In this episode of Unfolding Ideas of Physics, we break down the mechanics and explore how a small displacement helps simplify the entire journey. 🎯 WHAT YOU WILL LEARN • How to interpret “slowly hauled” in a mechanics problem • How to draw the forces at a point on a curved hill • Why the normal reaction changes with the local slope • How to calculate the work required against gravity • How to express frictional work over a small displacement • How horizontal and vertical displacement simplify the calculation • How to combine the contributions to find the total work 💡 THE CENTRAL IDEA The applied force must overcome both gravity and friction. The gravitational contribution connects to the vertical rise, while the frictional contribution can be simplified using the horizontal projection of each small displacement. This makes the problem a useful exercise in choosing the right approach before starting a lengthy calculation. ⚠️ COMMON MISTAKES TO WATCH FOR Taking the normal reaction as mg everywhere. Using the full curved path length with a constant frictional force. Ignoring the significance of the word “slowly.” Confusing the work done by friction with the work done against friction. ✍️ TRY BEFORE WATCHING Draw a small section of the hill inclined at an angle θ. Resolve the weight into tangential and normal components, then write the work done over a small distance ds. Can you connect ds cos θ and ds sin θ to horizontal and vertical displacement? 💬 SHARE YOUR APPROACH Did you expect the answer to require the hill’s exact shape? Comment with the step that helped you understand the result. This problem is valuable practice for JEE Advanced mechanics and for students strengthening work–energy concepts, friction and applications of Newton’s laws. ▶️ CONTINUE THE IRODOV SERIES Explore the channel for more solutions from I.E. Irodov’s Problems in General Physics. Watch Problem 1.120 for another example involving a curved trajectory, tangential force and energy. Subscribe to Physics in Style of Vivek – Workspace for more physics numericals and concept-based explanations. Unfolding Ideas of Physics Concept • Clarity • Confidence • Direction #irodov #workenergytheorem #friction #irodov1121 #irodovsolutions #ieirodov #workpowerenergy #workdone #curvedpath #inclinedplane #gravity #normalreaction #mechanics #physicsnumericals #jeeadvanced #jeephysics #jeemain #neetphysics #class11physics #problemsingeneralphysics #unfoldingideasofphysics #physicsinstyleofvivek