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Physics

Friction

Friction as the Component of Contact Force

11
⚡ Quick Summary
Friction is a force that opposes motion between two surfaces in contact. It's part of the overall contact force.
N/A
Friction is a component of the contact force between two surfaces. It acts parallel to the surface and opposes the relative motion or tendency of motion.

Kinetic Friction

11
⚡ Quick Summary
Kinetic friction acts when two surfaces are sliding against each other. It opposes the motion.
F_k = μ_k * N
Kinetic friction is the force that opposes the motion of two surfaces sliding against each other. It is proportional to the normal force.

Static Friction

11
⚡ Quick Summary
Static friction prevents two surfaces from sliding against each other. It can vary up to a maximum value.
F_s ≤ μ_s * N
Static friction is the force that prevents two surfaces from sliding against each other when a force is applied. It can vary up to a maximum value.

Laws of Friction

11
⚡ Quick Summary
Friction depends on the normal force and the type of surfaces in contact. It doesn't depend on the area of contact.
N/A
The laws of friction state that friction is proportional to the normal force and is independent of the area of contact (within certain limits).

Understanding Friction at Atomic Level

11
⚡ Quick Summary
Friction is caused by microscopic bumps and attractions between the surfaces.
N/A
At the atomic level, friction arises from the interaction of microscopic asperities (bumps) on the surfaces and the attractive forces between the atoms.

A Laboratory Method to Measure Friction Coefficient

11
⚡ Quick Summary
You can measure friction coefficients using an inclined plane. The angle at which the object starts to slide is related to the coefficient of static friction.
μ_s = tanθ
The coefficient of static friction can be measured by gradually increasing the angle of an inclined plane until the object starts to slide. The tangent of this angle is equal to the coefficient of static friction.

Contact Force

Class 11
⚡ Quick Summary
When two things touch, they push on each other. This push is the contact force. Think of it as the total force between the objects at the point of contact.
None
  • Electromagnetic forces act between charged particles at the surfaces of bodies in contact.
  • Each body exerts a contact force on the other.
  • The magnitudes of the contact forces are equal, but their directions are opposite (Newton’s third law).

Normal Force and Friction

Class 11
⚡ Quick Summary
Imagine the contact force like a superhero with two powers! One power (Normal Force) pushes the objects straight apart, preventing them from going through each other. The other power (Friction) resists the objects sliding past each other.
None
  • The contact force can be resolved into two components: Normal Force (N) and Friction (f).
  • Normal force (N) is the component of the contact force perpendicular to the contact surface.
  • Friction (f) is the component of the contact force parallel to the contact surface.

Kinetic Friction

Class 11
⚡ Quick Summary
Kinetic friction is the force that opposes the motion of two surfaces sliding against each other. It always acts in the opposite direction of the relative motion, trying to slow things down.
f_k = μ_k * N
  • Kinetic friction occurs when two bodies in contact move with respect to each other, rubbing the surfaces.
  • The direction of the frictional forces opposes the relative slipping motion.
  • The kinetic friction on body A slipping against body B is opposite to the velocity of A with respect to B.
  • The velocity used to determine the direction is the velocity of the body *relative* to the surface applying the force of friction.
  • The magnitude of kinetic friction is proportional to the normal force (N) acting between the two bodies.
  • The coefficient of kinetic friction (μk) depends on the nature of the two surfaces in contact. Smoother surfaces have smaller μk, and rougher surfaces have larger μk.
  • Kinetic friction is approximately independent of the speed of the sliding bodies for speeds not too large (e.g., < 10 m/s).
  • Kinetic friction is independent of the area of contact, as long as the normal force remains the same.

Types of Friction: Kinetic and Static

Class 11
⚡ Quick Summary
Friction comes in two flavors: static (when things are stuck) and kinetic (when things are sliding). Static friction is like the 'grip' that prevents things from moving, while kinetic friction is the resistance you feel when you're already sliding.
None
  • Kinetic friction: The force of friction when two solid bodies slip over each other.
  • Static friction: The force of friction when two solid bodies do not slip on each other.

Static Friction

Class 11
⚡ Quick Summary
Static friction is the force that prevents two surfaces from sliding against each other when they are at rest relative to each other. It's like an invisible glue that holds things in place until you push hard enough.
f_s ≤ f_{s,max} = μ_s N
  • Static friction acts between two bodies in contact that are not sliding with respect to each other.
  • It is a self-adjusting force, meaning its magnitude and direction change to maintain 'relative rest' between the surfaces, up to a maximum limit.
  • The maximum static friction is called limiting friction.
  • The maximum possible force of static friction does not depend on the area of the surfaces in contact.

Limiting Friction

Class 11
⚡ Quick Summary
Limiting friction is the maximum static friction that can be exerted before an object starts to move. If you exceed this force, the object will start sliding.
f_{s,max} = μ_s N
  • Limiting friction is the maximum force of static friction that a body can exert on another body in contact.
  • It is proportional to the normal contact force between the two bodies.

Coefficient of Static Friction

Class 11
⚡ Quick Summary
The coefficient of static friction (μ_s) is a measure of how 'sticky' two surfaces are to each other. A higher coefficient means more force is needed to start them sliding.
f_{s,max} = μ_s N
  • The coefficient of static friction (μ_s) is the constant of proportionality between the maximum static friction and the normal force.
  • It depends on the material and roughness of the two surfaces in contact.
  • μ_s is generally slightly greater than μ_k (coefficient of kinetic friction).

Laboratory Method to Measure Friction Coefficient - Horizontal Table Method

Class 11
⚡ Quick Summary
Use a plank, pulley, block, and weights to measure static and kinetic friction. Gradually increase the weight on the hanger until the block starts to move to find static friction. Then, reduce the weight until the block moves at a constant speed to find kinetic friction. Divide friction by the block's weight to get the coefficient of friction.
μ<sub>s</sub> = f<sub>max</sub> / N = W₂ / W₁; μ<sub>k</sub> = f<sub>k</sub> / N = W₂' / W₁
  • Apparatus: Wooden plank, pulley, block, hanger, string, standard weights.
  • Static Friction Measurement: Increase the weight (W₂) on the hanger until the block just starts to slide. The maximum static friction force (fmax) is equal to W₂. The normal force (N) is equal to the weight of the block (W₁).
  • Kinetic Friction Measurement: Reduce the weight on the hanger and gently push the block to initiate movement. Adjust the weight (W₂') on the hanger until the block moves at a constant speed. The kinetic friction force (fk) is equal to W₂'. The normal force (N) is equal to the weight of the block (W₁).

Static Friction and Angle of Repose

11
⚡ Quick Summary
When a block is placed on an inclined plane and the angle is gradually increased, the block starts slipping when the angle reaches a certain value. At this point, the static friction force has reached its maximum value. The tangent of this angle is equal to the coefficient of static friction.
μs = tanθ
  • When a block is on the verge of slipping on an inclined plane, the angle of inclination (θ) is related to the coefficient of static friction (μs).
  • The forces acting on the block are: weight (mg), normal force (N), and static friction (fs).
  • In limiting equilibrium: fs = mg sinθ and N = mg cosθ.
  • Coefficient of static friction: μs = fs/N = tanθ.

Kinetic Friction

11
⚡ Quick Summary
Once a block starts sliding down an incline, the friction acting on it becomes kinetic friction. If the block moves with uniform speed, the angle of the incline is related to the coefficient of kinetic friction.
μk = tanθ
  • If the block moves with uniform velocity once started on an incline, the forces are balanced.
  • The kinetic friction force is fk = mg sinθ and the normal force is N = mg cosθ.
  • The coefficient of kinetic friction is μk = fk/N = tanθ.

Rolling Friction

11
⚡ Quick Summary
Rolling friction is much smaller than kinetic or static friction because the surfaces at contact do not rub each other; the wheel rolls. Ball bearings are used in machines to reduce friction.
N/A
  • Rolling friction occurs when a wheel rolls on a surface instead of sliding.
  • The velocity of the point of contact between the wheel and the floor is ideally zero.
  • Rolling friction is significantly smaller than static or kinetic friction.
  • Ball bearings are used to reduce friction between rotating parts of machines.

Static Friction (Limiting Equilibrium)

Class 11
⚡ Quick Summary
When an object is just about to slip, that's when static friction is at its maximum. It's like the friction is fighting as hard as it can to hold the object in place!
f = μsN
In the case of limiting equilibrium, the static friction force reaches its maximum value (f = μsN). This represents the threshold just before the object begins to move.

Static Friction (General Case)

Class 11
⚡ Quick Summary
Static friction is a force that prevents an object from moving when you push it gently. It adjusts itself to match your push, up to a limit.
f ≤ μsN
Static friction (f) acts to prevent relative motion between surfaces in contact. Its magnitude can vary, but it is always less than or equal to the maximum static friction force (μsN).

Static Friction and Equilibrium

Class 11
⚡ Quick Summary
When an object is at rest, the friction force (static friction) adjusts itself to prevent motion, up to a maximum limit. If you gently push a heavy box, static friction pushes back equally. If you push harder and harder, the friction also increases to match, but it can only increase up to a certain point.
f<sub>max</sub> = μ<sub>s</sub>N
  • When a system is in equilibrium, the net force acting on it is zero.
  • Static friction (f) opposes the applied force to maintain equilibrium.
  • The maximum value of static friction is proportional to the normal force (N) between the surfaces in contact: fmax = μsN, where μs is the coefficient of static friction.

Motion with Kinetic Friction

Class 11
⚡ Quick Summary
When an object is sliding, the friction (kinetic friction) opposes its motion. The force of friction is related to the normal force and a coefficient.
f = μN
  • When an object is moving, kinetic friction (fk) acts on it, opposing the motion.

Normal Force on an Inclined Plane

Class 11
⚡ Quick Summary
When an object is on a slope, the surface pushes back perpendicular to the slope. This push is called the normal force, and it's related to the object's weight and the angle of the slope.
N = mg * cos(θ)
  • A block of mass m is placed on an inclined plane with an angle of 30 degrees.
  • There is no acceleration perpendicular to the incline.
  • The normal force (N) is calculated as N = mg cos(30°).
  • cos(30°) = √3 / 2, so N = mg * (√3 / 2)

Kinetic Friction

Class 11
⚡ Quick Summary
When something is sliding, friction tries to stop it. This 'sliding friction' (kinetic friction) depends on how hard the surfaces are pressed together (normal force) and how rough they are (coefficient of kinetic friction).
f_k = μ_k * N
  • When a block is slipping on an incline, kinetic friction (f_k) acts.
  • The kinetic friction is proportional to the normal force: f_k = μ_k * N, where μ_k is the coefficient of kinetic friction.

Static Friction

Class 11
⚡ Quick Summary
Static friction is the force that prevents an object from starting to move. It increases up to a maximum value before the object starts sliding.
f_s = μ_s * N
  • When a block is in limiting equilibrium (just about to move), the static friction (f_s) reaches its maximum value.
  • f_s = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.

Forces on a Block on an Inclined Plane (Limiting Equilibrium)

Class 11
⚡ Quick Summary
When a block is about to slip (limiting equilibrium) on an inclined plane, friction reaches its maximum value (μN). We analyze forces parallel and perpendicular to the plane to find relationships between mass, friction coefficient, and tension.
N = Mg cos θ, T + f = Mg sin θ, f = μN
  • Consider a block of mass M on an inclined plane with angle θ.
  • Forces acting on the block: Weight (Mg), Normal Reaction (N), Tension (T), and Friction (f).
  • In limiting equilibrium, f = μN where μ is the coefficient of static friction.
  • Resolve forces parallel and perpendicular to the inclined plane.
  • For equilibrium, the net force in each direction must be zero.
  • By balancing forces in each direction, we can derive equations relating tension, mass, friction coefficient, and angle of inclination.

Minimum and Maximum Mass for Equilibrium (Connected Blocks)

Class 11
⚡ Quick Summary
When two blocks are connected by a string over a pulley on an inclined plane, there's a range of masses for one block where the system remains at rest. The minimum mass prevents the first block from slipping down, and the maximum mass prevents it from slipping up. Friction plays a crucial role.
m(1 + μ) = M(1 − μ) (for minimum mass, friction assisting M), m(1 - μ) = M(1 + μ) (for maximum mass, friction opposing M)
  • Consider two blocks connected by a string over a pulley, with one block on an inclined plane.
  • Let M be the mass of the block on the incline, and m be the mass of the hanging block.
  • The static friction force on the block on the incline can act upwards or downwards, depending on whether m is too small or too large.
  • For minimum m, friction acts upwards, opposing the tendency of M to slide down.
  • For maximum m, friction acts downwards, opposing the tendency of M to be pulled up.
  • By analyzing the forces on each block and applying the conditions for equilibrium, we can determine the minimum and maximum values of m.

Kinetic Friction and Acceleration (Connected Blocks)

Class 11
⚡ Quick Summary
If the connected blocks are moving, kinetic friction acts. We use Newton's Second Law (F=ma) on each block, taking into account kinetic friction, to find the acceleration of the system.
f_k = μ_k * N, Acceleration a = [M(sinθ - μ_k cosθ) - m]g / (M+m) (derived from Newton's Second Law)
  • When the blocks are in motion, kinetic friction (f_k = μ_k * N) acts on the block on the inclined plane.
  • Apply Newton's Second Law (F = ma) to each block separately.
  • For the block on the incline: Mg sin θ − T − f_k = Ma
  • For the hanging block: T − mg = ma (Considering the appropriate sign convention)
  • Solve the system of equations to find the acceleration (a) of the blocks.

Contact Force (F)

11
⚡ Quick Summary
The total force between two surfaces in contact. It's like the 'overall' push or pull one object feels from the other.
F = √(F_N² + f²)
The contact force (F) is the resultant of the normal force (F_N) and the friction force (f). It represents the total interaction force between two surfaces.

Friction and Contact Force

Class 11
⚡ Quick Summary
When a body is kept on a rough surface, the surface exerts a contact force. This contact force can be resolved into two components: Normal reaction (perpendicular to the surface) and frictional force (parallel to the surface). The frictional force opposes the motion or impending motion.
F = √(N² + f²), where F is the contact force, N is the normal force, and f is the frictional force
  • The contact force is the resultant of the normal force and the frictional force.
  • The direction of the contact force changes as the frictional force changes.
  • Even when a body is at rest on a rough surface and an external force is applied (but the body doesn't move), a frictional force exists to prevent motion.

Normal Force (F_N)

11
⚡ Quick Summary
The 'supporting' force that prevents objects from passing through each other. It's always perpendicular to the surface.
F_N is usually equal to mg cosθ on an inclined plane (where θ is the angle of inclination)
The normal force (F_N) is the component of the contact force that acts perpendicular to the surfaces in contact. It arises due to the resistance of the materials to compression.

Walking on Ice

Class 11
⚡ Quick Summary
Taking small steps on ice helps prevent slipping because it reduces the force you exert, decreasing the chance of exceeding the maximum static friction.
f ≤ μN, where f is the frictional force, μ is the coefficient of friction, and N is the normal force
  • Smaller steps lead to a smaller horizontal force component.
  • A smaller horizontal force requires a smaller frictional force to prevent slipping.
  • By taking small steps, you are less likely to exceed the limiting static friction.

Friction (f)

11
⚡ Quick Summary
The force that opposes motion when surfaces rub against each other. It's like a 'resistance' to sliding.
f ≤ μF_N (where μ is the coefficient of friction)
Friction (f) is the force that opposes the relative motion (or tendency of motion) between two surfaces in contact. It acts parallel to the surfaces.

Force by a Surface on a Body at Rest

Class 11
⚡ Quick Summary
When a body is at rest on a rough horizontal surface and an external force is applied but the body doesn't move, the surface exerts a force (F) that balances the applied force and the weight of the object. The magnitude of F can be between Mg and Mg√(1+μ²).
Mg ≤ F ≤ Mg√(1+μ²), where M is mass, g is acceleration due to gravity, and μ is the coefficient of friction.
  • F includes both the normal reaction (Mg) and the frictional force.
  • If a horizontal force is applied, the frictional force will oppose it.
  • The resultant force F is the vector sum of the normal force and the frictional force.

Static Friction

11
⚡ Quick Summary
Friction that prevents an object from *starting* to move. It adjusts itself to match the applied force, up to a limit.
f_s ≤ μ_sF_N (where μ_s is the coefficient of static friction)
Static friction (f_s) is the frictional force that acts between two surfaces in contact when there is no relative motion between them. It is a self-adjusting force, up to a maximum value.

Stopping Distance and Tyres

Class 11
⚡ Quick Summary
To stop a car in the shortest distance, apply the brakes hard enough to prevent slipping. Similar tyres on cars with unequal masses imply the heavier car has a slightly larger stopping distance.
Stopping distance ∝ mass
  • Maximum deceleration is achieved when friction is maximized without slipping.
  • Slipping reduces the friction force, increasing the stopping distance.
  • The heavier car has more inertia and hence stopping distance would be slightly more.

Kinetic Friction

11
⚡ Quick Summary
Friction that opposes the motion of an object that's *already* moving. It's usually weaker than static friction.
f_k = μ_kF_N (where μ_k is the coefficient of kinetic friction)
Kinetic friction (f_k) is the frictional force that acts between two surfaces in contact when they are in relative motion. It is generally constant for a given pair of surfaces and a given normal force.

Sliding on an Inclined Plane

Class 11
⚡ Quick Summary
The angle at which a block just begins to slide on an inclined plane depends on the coefficient of static friction between the block and the surface, and not on mass of the block.
μs = tan θ, where μs is the coefficient of static friction and θ is the angle of inclination.
  • The angle of repose (the angle at which sliding begins) is related to the coefficient of static friction (μs = tan θ).
  • Different blocks starting to slide at different angles of inclination implies they have different coefficients of friction.

Limiting Friction

11
⚡ Quick Summary
The maximum static friction. The moment the applied force is *greater* than limiting friction, the object starts to move.
f_{s,max} = μ_sF_N
Limiting friction is the maximum value of static friction. It is the frictional force that acts when the object is just about to move.

Sliding a Box

Class 11
⚡ Quick Summary
It's impossible to slide a box if the coefficient of friction between your shoes and the floor is less than the coefficient of friction between the box and the floor, and your mass is greater than the box's mass.
F_max = μMg, where F_max is the maximum force you can exert, μ is the coefficient of friction between your shoes and the floor, and M is your mass.
  • The force you can exert is limited by the friction between your shoes and the floor.
  • If this force is less than the force needed to overcome the friction between the box and the floor, you cannot move the box.

Coefficient of Static Friction (μ_s)

11
⚡ Quick Summary
A number that tells you how 'sticky' two surfaces are when they're not moving. Higher number means more friction.
μ_s = f_{s,max} / F_N
The coefficient of static friction (μ_s) is a dimensionless quantity that represents the ratio of the maximum static friction force to the normal force between two surfaces.

Coefficient of Kinetic Friction (μ_k)

11
⚡ Quick Summary
A number that tells you how 'sticky' two surfaces are when they're sliding. Usually less than the static friction coefficient.
μ_k = f_k / F_N
The coefficient of kinetic friction (μ_k) is a dimensionless quantity that represents the ratio of the kinetic friction force to the normal force between two surfaces.

Angle of Friction (λ)

11
⚡ Quick Summary
The angle between the total contact force and the normal force. It's a way to visualize the combined effect of friction and normal force.
tan λ = f / F_N. Also, λ ≤ tan⁻¹ μ
The angle of friction (λ) is the angle between the resultant contact force (F) and the normal force (F_N).

Static Friction

11
⚡ Quick Summary
Static friction is the force that prevents an object from starting to move when a force is applied. It adjusts itself to be equal and opposite to the applied force, up to a maximum limit.
f_s ≤ μ_s * N, where f_s is the static friction, μ_s is the coefficient of static friction, and N is the normal force.
  • Static friction opposes the initiation of motion.
  • It is a self-adjusting force.
  • The maximum value of static friction is proportional to the normal force between the surfaces in contact.

Limiting Friction

11
⚡ Quick Summary
Limiting friction is the maximum static friction that can exist between two surfaces. If the applied force exceeds this limit, the object will start to move.
f_{s,max} = μ_s * N, where f_{s,max} is the maximum static friction (limiting friction), μ_s is the coefficient of static friction, and N is the normal force.
  • Limiting friction is the maximum value of static friction.
  • It is the threshold beyond which motion begins.
  • At the point of limiting friction, the object is about to move, but is still at rest.

Normal Force

11
⚡ Quick Summary
Normal force is the force exerted by a surface on an object in contact with it, acting perpendicular to the surface.
N = mg (on a horizontal surface with no other vertical forces), where N is the normal force, m is the mass, and g is the acceleration due to gravity.
  • The normal force is a contact force.
  • It acts perpendicular to the surface of contact.
  • Its magnitude is often equal to the weight of the object on a horizontal surface, but can vary in other situations (e.g., inclined planes, applied vertical forces).

Coefficient of Friction

11
⚡ Quick Summary
The coefficient of friction (μ) is a number that represents how rough two surfaces are against each other. A higher coefficient means more friction.
μ = f/N, where μ is the coefficient of friction, f is the frictional force, and N is the normal force.
  • The coefficient of friction is a dimensionless quantity.
  • It depends on the nature of the two surfaces in contact.
  • There are two types: coefficient of static friction (μ_s) and coefficient of kinetic friction (μ_k).