1.5.1 Effects of forces

Deformation commonly results from forces acting at different points or in different directions, such as pulling both ends of a spring or squeezing opposite sides of a sponge.

Use sensible linear scales, label axes with units, plot points accurately and draw a best-fit line or smooth curve. A straight line through the origin shows extension proportional to load over that region.

Read extension, not loaded length, unless the graph explicitly asks for length. If original length is known, convert with loaded length = original length + extension.

Secure the clamp stand, keep the load close to the bench, and do not add loads beyond the safe range of the solid.

Choose one direction as positive, give every collinear force a sign, add the signed values, then report the magnitude and direction indicated by the sign.

For 9 N right, 3 N left and 2 N left, the resultant is $9-3-2=4$ N to the right.

Forces can act while the resultant is zero: equal opposing forces are balanced. For example, driving force can equal total resistance while a car moves at constant speed.

During a sudden stop, an unrestrained passenger tends to continue moving forwards; a seat belt provides the resultant force needed to change that motion.

Velocity includes both speed and direction, so an object moving at constant speed around a curve still has changing velocity.

Identify the resultant direction before predicting the change; individual forces do not determine the motion independently.

Friction acts parallel to the contact surfaces and opposes the relative motion or tendency to move between them.

Surface condition matters: water, oil or ice can reduce useful friction, while rougher contact may increase it.

Drag acts against the object's motion relative to the liquid. A ship driven forwards therefore experiences a backward water-resistance force.

To accelerate forwards, the driving force must exceed the liquid drag; at constant velocity the horizontal forces are balanced.

Air resistance acts against motion relative to the air. For a vehicle moving forwards through still air, it acts backwards.

If driving force stays constant while speed rises, increasing air resistance reduces the resultant force and therefore reduces the acceleration.

Find extension by subtracting original length from loaded length, convert it to the unit required for $k$, then calculate $F/x$. Rearrangements are $F=kx$ and $x=F/k$.

For a force-against-extension graph in the proportional region, $k$ is the gradient $\Delta F/\Delta x$.

On a load–extension graph, identify the end of the initial straight-line proportional region—the point where the graph first begins to curve away from that line.

Below this limit, doubling the load doubles the extension and $F/x$ is constant. Beyond it, equal increases in load no longer produce equal increases in extension.

When asked for a range that obeys proportionality, give values from zero up to and including the identified limit, using the graph's units.

First combine all forces to find the resultant. Then use $a=F/m$, $F=ma$, or $m=F/a$, keeping direction or a consistent sign convention.

A 800 kg car accelerates at 1.0 m/s$^2$, so its resultant force is 800 N in the acceleration direction. If the engine force is 5000 N forwards, resistive forces total 4200 N backwards.

The force continuously changes the direction of velocity. An object can therefore accelerate while its speed remains constant.

At any point, draw the motion tangent to the circle and the resultant force radially inwards; these directions are perpendicular.