5.1 Forces, Motion, Friction & Equilibrium

Forces, motion, friction and equilibrium

Draw forces before predicting motion

Mechanical questions often show an object with arrows, supports, wheels, or slopes. Replace the picture with a free-body diagram: isolate the object and draw every external force acting on it.

Common forces are:

• weight: gravity acting vertically downward, W = mg;
• normal force: a surface pushing perpendicular to itself;
• friction: parallel to a contact surface and opposing relative motion or the tendency to slide;
• tension: pulling along a rope, cable, or chain;
• applied force: a push or pull from an external agent;
• spring force: opposing displacement from equilibrium;
• drag: resisting motion through a fluid.

Do not add forces that act on another object. If a crate pushes down on a floor, that force acts on the floor; the floor’s normal force acts up on the crate.

Newton’s laws

Newton’s first law says an object remains at rest or moves at constant velocity when the net external force is zero. Balanced forces do not necessarily mean the object is stationary. A cart moving steadily on a level surface can have zero net force.

Newton’s second law is:

F net = ma.

A larger net force gives greater acceleration for the same mass. A larger mass gives less acceleration for the same net force. Acceleration describes change in velocity, including speeding up, slowing down, or changing direction.

Newton’s third law pairs forces between two objects. If a person pushes a wall, the wall pushes the person with equal magnitude in the opposite direction. The forces do not cancel because they act on different objects.

Mass, weight and inertia

Mass measures matter and inertia, typically in kilograms. Weight is a force measured in newtons:

W = mg.

With g approximated as 9.8 m/s², a 20 kg object weighs about 196 N. Aptitude problems may use g = 10 m/s² for easier arithmetic; use the value stated.

Inertia is resistance to a change in velocity. A more massive object requires a greater net force to achieve the same acceleration.

Friction

Static friction prevents slipping and varies up to a maximum:

f static ≤ μs N.

It is not always equal to μsN. If a 10 N horizontal push is balanced by static friction, friction is 10 N even if the maximum is 30 N.

Once sliding begins, a common simplified model uses kinetic friction:

f kinetic = μk N.

Usually μs is greater than μk, explaining why starting motion can require more force than maintaining it. Friction acts opposite the relative motion or tendency at the contact, not automatically opposite the direction an object faces.

On a level surface with no other vertical forces, N = mg. If a person pushes downward at an angle, the normal force and friction limit increase. Pulling upward at an angle reduces the normal force.

Equilibrium

Translational equilibrium requires the vector sum of forces to be zero. Rotational equilibrium also requires the net moment or torque to be zero. An object can have balanced horizontal forces but still rotate if the forces act at different locations.

For a hanging load at rest on one ideal vertical rope, tension equals weight. With two angled ropes, their vertical components share the weight and horizontal components cancel. Each rope’s tension can exceed half the weight because only part of each angled tension acts vertically.

Inclined planes

Resolve weight relative to a slope of angle θ:

• parallel component down the slope: mg sin θ;
• perpendicular component into the slope: mg cos θ.

On a frictionless slope, the parallel component accelerates the object. The normal force equals mg cos θ. As the slope becomes steeper, the parallel component increases and the normal component decreases.

At the threshold of sliding under a simple static-friction model:

mg sin θ = μs mg cos θ, so tan θ = μs.

Use this relationship only when the stated model fits.

Centre of mass and stability

An object remains stable while the vertical line through its centre of mass falls inside its base of support. A wider base and lower centre of mass generally improve stability. Tilting shifts the projected line toward the edge. At the tipping point it passes through the pivot edge; beyond that edge gravity creates a moment that increases the tip.

Adding weight low can improve stability, while adding weight high can reduce it. An object may slide before tipping or tip before sliding depending on friction, geometry, and force application height.

Diagram checklist

Ask: What is the object? Which forces act on it? Are arrows forces, velocities, or dimensions? What is constrained? Is the system at rest, moving steadily, accelerating, sliding, or about to move? Then predict direction before calculating. Idealised aptitude diagrams often neglect air resistance, rope mass, or bearing friction; never import those losses unless the problem includes them.