8867 / 2027
Forces and Moments overview

Topic 1 of 4

Identify the body and its forces

Choose the body you are analysing. Then identify each interaction that exerts a force on that body, including its source, direction and line of action.

A free-body diagram separates the chosen body from its surroundings and shows the external forces on it. A force the body exerts on something else belongs on that other body's diagram.

Force is a vector measured in newtons, N. Its components are an alternative representation of the same force. The vector methods explain how to resolve a force and combine signed components.

A block held on a smooth slope

A string holds a block stationary on a slope inclined at 30° to the horizontal. The block's weight is 10 N. The slope is smooth, so friction is neglected; the string lies parallel to the slope.

  • Earth on block: weight W = 10 N vertically down, acting at the centre of gravity.
  • String on block: tension T = 5.0 N up the slope, along the string.
  • Slope on block: normal force N = 8.66 N, perpendicular to the contact surface and away from it.

Choose the body, then show the forces on it

1. The physical arrangement

A stationary body on a smooth thirty-degree inclineA rectangular body rests on a surface rising thirty degrees to the right. A light string attached to the body's upslope side runs parallel to the incline and is fixed above it. The chosen body has weight ten newtons. Smooth means friction is absent in this model. The scene shows the physical contacts and string; forces are shown separately in the next panel.30°Chosen bodyLight stringSmooth surfaceStationary; weight = 10.0 N

2. Forces on that body

The three external forces balanceAll force arrows start at the same point, using fourteen drawing units per newton. Weight is ten newtons vertically down. Tension is five newtons along the slope, thirty degrees above the horizontal. The normal contact force is five times the square root of three newtons, approximately 8.66, perpendicular to the incline and pointing up and left. The arrow components sum to zero. The dotted surface-direction guide is not an extra force. No friction force is included.W = 10.0 NT = 5.00 NN = 8.66 NSurface directionArrow length uses one force scale.

Earth exerts the weight, the string exerts tension and the surface exerts the normal force. The normal force is perpendicular to the slope; it is not equal to the weight.

The physical scene and free-body diagram refer to the same stationary block. The normal is perpendicular to the slope, while the tension is along it. Only forces on the block belong in its force diagram.

Resolving weight gives 10 sin 30° = 5.0 N down the slope and 10 cos 30° = 8.66 N into it. Tension balances the first component; the normal force balances the second. The normal force is not equal to the full weight here.

Use either the weight arrow or its components in a force calculation. Counting the 10 N weight and both its components as three separate forces would count the same interaction twice. Here N is a quantity symbol for the normal force; N after a number is the unit newton.

Optional check A string holds a block stationary on a smooth slope. Which force belongs on the string's free-body diagram, but not on the block's?
A string holds a block stationary on a smooth slope. Which force belongs on the string's free-body diagram, but not on the block's?

Field forces act without contact

Mass in a gravitational field
A mass experiences gravitational force along the field. Near Earth's surface this force is its weight, directed down towards Earth.
Charge in an electric field
A positive charge experiences force along the electric field. A negative charge experiences force in the opposite direction. State the charge sign before choosing the force arrow.
A current-carrying conductor in a magnetic field
The conductor can experience a force perpendicular to both the conventional current and the magnetic field. For current to the right and field into the page, the force is upward. Reversing either direction reverses this force. If current and field are parallel, this magnetic force is zero.

Different fields act on different physical properties

These arrows show directions schematically. Their lengths do not compare field strengths or force magnitudes. Green indicates field direction; purple indicates force.

Gravitational force on a massThe gravitational field points down, and the weight of the mass points down along it. Field and force arrows are separated so their directions can be compared.Mass in a gravitational fieldgMassWWeight is along the field.
Electric force on a positive chargeThe electric field points right. A positive charge experiences force to the right, along the field. A negative charge in the same field would experience force to the left.Positive charge in an electric fieldE+FPositive charge: force along E.
Magnetic force on a current-carrying conductorCrosses mean the magnetic field points into the page. Conventional current flows right along a straight conductor. The magnetic force on the conductor points up, perpendicular to both current and field. This is a direction model, not a force-magnitude scale.Current in a magnetic fieldI rightF upB into page; I is conventional current.
The arrows distinguish field direction from force on the selected body. The magnetic example uses conventional current to the right and field into the page, giving an upward force on the conductor.

In an end-view symbol, a cross represents a direction into the page and a dot represents a direction out of the page. Read which quantity the symbol labels: it may represent a field or a current, rather than a force.

Contact forces depend on the interaction

Normal force
The support force is perpendicular to the local surface. It is vertical only if that surface is horizontal. Its magnitude follows the force balance and need not equal the weight.
Tension
A taut string pulls along its length, away from the body to which it is attached. A string does not provide a pushing force.
Friction
Friction acts along the contact surface, opposing relative sliding or its tendency there. It can oppose a sliding block's motion, but it can also act forward on a driven wheel whose contact point tends to slip backward on the road.
Viscous resistance or drag
A fluid exerts resistance against an object's motion relative to that fluid. Air resistance is one example. Drag generally changes with speed and depends on the body and fluid; one universal proportionality to speed or speed squared should not be assumed.

Static friction adjusts to what is needed for the stated stationary balance, up to the point where sliding begins. If a horizontal 2 N pull acts on a block that remains stationary, with friction as the only other horizontal force, static friction is 2 N in the opposite direction. It is not automatically one fixed maximum value.

Friction does not always oppose the body's overall direction of travel. Examine the relative sliding, or tendency to slide, at the contact. For drag, examine motion relative to the surrounding fluid.