Friction
Friction
Friction is a force that opposes relative motion between systems in contact.
- Kinetic Friction: If two systems are in contact and moving relative to one another then the friction between them is called kinetic friction.
The magnitude of kinetic friction is given by:
\[f_{\mathrm{k}}=\mu_{\mathrm{k}} N\]where \(\mu_k\) is the coefficient of kinetic friction.
- Static Friction: If the systems are not moving relative to one another, the friction between them is called static friction. The magnitude of static friction is given by:
where \(\mu_s\) is the coefficient of static friction.
PYQs
Friction
1) One end of a heavy uniform rod \(AB\) can slide along a rough horizontal rod \(AC\), to which it is attracted by a ring. \(B\) and \(C\) are joined by a string. When the rod is on the point of sliding, then \(AC^2-AB^2=BC^2\). If \(\theta\) is the angle between \(AB\) and the horizontal line, then prove that the coefficient of friction is \(\dfrac{cot\theta}{2+cot^2\theta}\).
[2019, 10M]
2) Two equal ladders of weight 4 \(\mathrm{kg}\) each are placed so as to lean at \(A\) against each other with their ends resting on a rough floor, given the coefficient of friction is \(\mu\). The ladders at \(A\) make an angle \(60^{\circ}\) with each other. Find what weight on the top would cause them to slip.
[2015, 13M]
3) A uniform ladder rests at an angle of \(45^{\circ}\) with the horizontal with its upper extremity against a rough vertical wall and its lower extremity on the ground. If \(\mu\) and \(\mu'\) are the coefficients of limiting friction between the ladder and the ground and wall respectively, then find the minimum horizontal force required to move the lower end of the ladder towards the wall.
[2013, 15M]
4) The base of an inclined plane is 4 metres in length and the height is 3 metres. A force of 8 kg acting parallel to the plane will just prevent a weight of 20 kg from sliding down. Find the coefficient of friction between the plane and the weight.
[2013, 10M]
5) A straight uniform beam of length \('2h'\) rests in limiting equilibrium, in contact with a rough vertical wall of height \('h'\), with one end on a rough horizontal plane and with the other end projecting beyond the wall. If both the wall and the plane be equally rough, prove that \(\lambda\), the angle of fraction, is given by \(2 \lambda=\sin \alpha 2 \alpha\), \(\alpha\) being the inclination of the beam to the horizon.
[2008, 12M]
6) A ladder on a horizontal floor leans against a vertical wall. The coefficients of friction of the floor and the wall with the ladder are \(\mu\) and \(\mu_{1}\) respectively. If a man, whose weight is \(n\) times that of the ladder, want to climb up the ladder, find the minimum safe angle of the ladder with the floor.
[2003, 15M]