Applications: Objects in Equilibrium — JEE Advanced Physics

Key Concepts

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Examples

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Introduction to Applications: Objects in Equilibrium

Welcome to Applications: Objects in Equilibrium. Content to be added.

Problem-Solving Strategies and Practice

Systematic Problem-Solving Approach

Follow these steps for dynamics problems:

Identify the system: What object(s) are you analyzing?
Draw FBDs: For each object, show all external forces
Choose coordinates: Align axes with acceleration when possible
Apply Newton's Second Law: $\sum \vec{F} = m\vec{a}$ in component form
Solve equations: Use algebra or simultaneous equations
Check: Do signs make sense? Are units correct?

Practice 1: Hanging Lamp

A 2 kg lamp hangs motionless from a wire. Find tension.

Lamp hanging

FBD of lamp

Solution: Equilibrium ( $a_y = 0$ )

Forces: Weight $W = mg = 20$ N (down), Tension $T$ (up)

$\sum F_y = 0 \implies T - W = 0 \implies T = 20 \, \text{N}$

Practice 2: Block Pushed on Surface

A 10 kg block on smooth horizontal floor pushed with 20 N horizontally. Find normal force and acceleration.

Block pushed on surface

FBD of pushed block

Solution:

Vertical: Equilibrium → $N = W = 100$ N

Horizontal: $F = ma \implies 20 = 10a \implies a = 2 \, \text{m/s}^2$

Normal force = 100 N, acceleration = 2 m/s² (horizontal push doesn't affect vertical forces!).

In the pushed block example, does the 20 N horizontal push affect the normal force?

Practice 3: Block Against Wall

A 2 kg block held against smooth vertical wall by 30 N horizontal force and vertical string. Find normal force and tension for equilibrium.

Block against wall

FBD of block

Solution: Equilibrium ( $a_x = 0$ , $a_y = 0$ )

Horizontal: $F - N = 0 \implies N = 30$ N

Vertical: $T - W = 0 \implies T = mg = 20$ N

Practice 4: Weighing Machine in Elevator

An 80 kg person on a scale in an elevator. Find scale reading when elevator:

Person in elevator

FBD of person

(a) Moving at constant 2 m/s upward:

$a = 0$ → $N = W = 800$ N → Reading = 80 kg

(b) Accelerating upward at 2 m/s²:

$N - W = ma$ → $N = 800 + 160 = 960$ N → Reading = 96 kg

(c) Accelerating downward at 2 m/s²:

$N - W = m(-2)$ → $N = 800 - 160 = 640$ N → Reading = 64 kg

Does a person feel heavier (higher scale reading) when an elevator accelerates upward?

Practice 5: Force on Pulley Support

An Atwood machine with $m_1 = 4$ kg, $m_2 = 6$ kg has tension $T = 48$ N. What force does the clamp exert on the pulley axle?

Solution: Pulley is massless and stationary (equilibrium)

Forces on pulley:

Tension $T = 48$ N downward (from $m_1$ side)
Tension $T = 48$ N downward (from $m_2$ side)
Support force $F_{clamp}$ upward

$F_{clamp} - T - T = 0 \implies F_{clamp} = 2T = 96 \, \text{N}$

The clamp exerts 96 N upward on the pulley.

Key Problem-Solving Tips

Always start with a clear FBD
Be consistent with sign conventions
For connected systems, identify constraints (same acceleration, etc.)
Check if object is in equilibrium or accelerating
Remember: $N \neq mg$ in general!
Friction is self-adjusting (static) or constant (kinetic)
Pseudo forces appear only in non-inertial frames