Applying Newton’s laws to friction, pulleys and circular paths
In Class 11, Newton’s laws are applied with free-body diagrams that show every force on a single body. The second law in its general form is F = dp/dt, and impulse, F × Δt, equals the change in momentum. For connected bodies, such as two masses joined by a string over a pulley, you write F = ma for each body and solve together. For example, masses of 3 kg and 2 kg on an ideal pulley accelerate at (3 − 2)g/5 = 0.2g.
Friction comes in two forms: static friction can rise up to a limit μsN, and kinetic friction during sliding is μkN, usually smaller. On an inclined plane, a block begins to slide when tan θ equals the coefficient of static friction. An object moving in a circle needs a centripetal force mv²/r directed towards the centre. On a banked road, the safe speed without friction is given by v² = rg tan θ.
Why it matters
These methods are used to design lifts, cranes and conveyor belts, to bank railway tracks and highway curves, and to decide tyre grip limits for cars. Sports such as cycling and athletics on curved tracks rely on centripetal force. Free-body diagrams are the key problem-solving tool for the rest of mechanics, including work, energy and rotation.
Key terms
- Free-body diagram
- A sketch of a single object showing every external force acting on it.
- Impulse
- The product of a force and the time for which it acts, equal to the change in momentum.
- Coefficient of friction
- The ratio of the friction force to the normal reaction between two surfaces.
- Centripetal force
- The net inward force required to keep an object moving in a circular path.