Why Won’t It Budge?

Starting to push a heavy cupboard is harder than keeping it moving.

Block pushed by a hand with arrows showing applied force
First shove must beat static friction; after that sliding is easier.

Scenario

You push a heavy cupboard resting on the floor.

What happens

  • Static friction opposes your force up to its maximum value.
  • You must exceed this maximum to set the cupboard in motion.
  • Once moving, smaller kinetic friction keeps resisting, so less push is needed.

Takeaway: Static friction is usually larger than kinetic friction—hence the tough first shove.

Multiple Choice Question

Question

The sofa resists motion chiefly because of _____ between its legs and the floor.

1
static friction
2
kinetic friction
3
air drag
4
normal force

Hint:

It acts before motion begins.

What Causes Friction?

Microscopic view: rough peaks, interlocking, and adhesion.

  1. 1

    Microscopic roughness

    Even polished surfaces have tiny bumps called asperities.

  2. 2

    Interlocking bumps

    Asperities fit together and resist relative motion until enough force breaks the locks.

  3. 3

    Adhesive forces

    Atoms at the contact points share electrons, creating adhesion that adds to friction.

Heavier loads press asperities closer, strengthening both interlocking and adhesion.

Static vs Kinetic Friction

Use relative motion to tell them apart.

Static friction

  1. No relative motion between surfaces.
  2. Adapts up to a limit: \(F_s \le \mu_s N\).
  3. Opposes impending motion.

Kinetic friction

  1. Surfaces slide in relative motion.
  2. Nearly constant: \(F_k = \mu_k N\).
  3. Opposes actual motion.

Common ground

  • Both act parallel to the contact surface.
  • Magnitude depends on normal force \(N\) and surface pair.
  • Disappear if contact is removed.

Usually \( \mu_s > \mu_k \). Decide relative motion first, then choose the correct formula.

Maximum Static Friction

\( f_s^{\text{max}} = \mu_s N \)

Maximum static friction equals the coefficient of static friction multiplied by the normal reaction \(N\), which acts perpendicular to the surface.

Here, \( \mu_s \) is unit-less and typically lies between 0 and 1.

Source: NCERT Eq. 4.13

Kinetic Friction Law

\(f_k = \mu_k N\)

Kinetic friction opposes sliding motion. Its magnitude equals the product of the coefficient of kinetic friction and the normal reaction.

\(\mu_k\) stays nearly constant for a given surface pair at moderate speeds—use the relation to find friction on any steadily moving object.

Source: NCERT Eq. 4.14

Block on an Incline

Resolve forces and spot the friction direction.

N mg \(mg\sin\theta\) \(mg\cos\theta\) \(f_s\)
Gravity splits into \(mg\sin\theta\) along and \(mg\cos\theta\) perpendicular; static friction opposes the slide.

Will it slide down?

The downhill pull \(mg\sin\theta\) must beat the maximum static friction to start motion.

  • Parallel pull: \(mg\sin\theta\) down the plane.
  • Normal force: \(N = mg\cos\theta\) perpendicular.
  • Static friction \(f_s\) points up the plane, opposing possible slide.

Tip: Motion begins when \(mg\sin\theta = \mu_s N\). Increase θ to reach the “angle of repose.”

Worked Example

2 kg block on \(30^{\circ}\) incline, \(\mu_k = 0.2\). Find its acceleration.

  1. 1

    Draw forces

    Show \(mg\sin\theta\) down-slope, \(N\) normal, \(f_k\) up-slope.

  2. 2

    Normal force

    \(N = mg\cos\theta = 2 \times 9.8 \times \cos30^{\circ} \approx 17 \text{ N}\).

  3. 3

    Calculate \(f_k\)

    \(f_k = \mu_k N = 0.2 \times 17 \approx 3.4 \text{ N}\).

  4. 4

    Net force

    \(F_{\text{net}} = mg\sin\theta - f_k \approx 9.8 - 3.4 = 6.4 \text{ N}\).

  5. 5

    Acceleration

    \(a = \frac{F_{\text{net}}}{m} = \frac{6.4}{2} = 3.2 \text{ m/s}^2\).

Use \(\mu_k\) because the block is moving; \(\mu_s\) applies only before motion starts.

Multiple Choice Question

Question

A 10 kg crate rests on a level floor where the coefficient of static friction is 0.5.  What horizontal force just starts it moving? Choose the closest value of  \(f_s^{\text{(max)}}\).

1
25 N
2
49 N
3
50 N
4
98 N

Hint:

Normal force \(N = mg\) on level ground.

Common Pitfall: Direction of Friction

Friction opposes relative motion of the two surfaces.

It is not always opposite to the object’s velocity.

Pull a rug under a vase: friction drags the vase forward with the rug.

Key Takeaways — Friction

Know these four points to recall the concept.

1

Static > Kinetic

Starting friction is higher than sliding for most dry surfaces.

2

Linear law

\(f_s^{\text{max}}=\mu_s N\), \(f_k=\mu_k N\).

3

Opposes motion

Acts opposite to relative motion or its tendency.

4

Material dependent

Coefficients \(\mu\) vary with the surface pair.

Multiple Choice Question

Question

On a level road, the car experiences forward friction during acceleration because:

1
Tyres push the road backward
2
Vehicle weight increases
3
Air pushes the car forward
4
The normal force tilts forward

Hint:

Think action–reaction between tyre and road.