Forces

Separate the object from its surroundings before adding forces. A trolley's horizontal pull and resistance act on the trolley, while the force the trolley exerts on the pulling hand belongs on a different object's diagram. Adding every interaction in the scene together would obscure the particular acceleration you are calculating.

A resultant opposite to the velocity initially reduces speed, whereas a resultant perpendicular to the velocity can change direction. With zero resultant force, there is no acceleration and the existing velocity continues. A force can also deform a real object, but a calculation using F = ma describes the acceleration of its centre of mass under the stated model.

A spring graph can use centimetres even when the requested spring constant is in N/m. Either convert the extensions before finding the gradient or convert the resulting N/cm value afterwards. Choose well-separated points on the straight line, rather than taking a tiny triangle that magnifies reading uncertainty.

A graph that does not pass through the origin needs investigation. The horizontal quantity may be total length, there may be an initial tension, or there may be a measurement offset. Do not automatically call every straight line through the displayed points Hooke's law without checking what the measured variables and zero positions represent.

Compare velocity arrows at two nearby points on the circle. They can have equal lengths but different directions, so they are not the same vector. The inward resultant continually bends the path. It may be supplied by tension in a string, friction on a road or gravitational attraction, depending on the situation.

Centripetal names the inward role of the resultant rather than an extra interaction to add to a force diagram. If a string supplying the force breaks, the object initially follows the tangent at the release point, not a straight line directly away from the centre. Cambridge's qualitative circular-motion treatment belongs to Supplement content.

When a hand pushes a trolley, the hand exerts a force on the trolley and the trolley exerts an opposite force on the hand. The trolley's acceleration depends on the force on the trolley together with its other forces, such as resistance. It does not depend on adding the reaction on the hand to that individual diagram.

For the combined hand-and-trolley system, the contact pair is internal and cancels in the system's total force balance. External forces then determine the combined momentum change. Also distinguish this pair from weight and support acting on one resting object: those may balance, but they are separate interactions and are not each other's third-law partners.

Hooke's law predicts a straight force–extension graph through the origin over the proportional region. Elastic behaviour instead requires a loading-and-unloading comparison. If you remove the force and the original length is recovered, the deformation was reversible even if doubling the force did not exactly double the extension.

To check recovery experimentally, record the unloaded length, add loads in controlled steps and then remove them. A remaining extension after the force has been removed is evidence of permanent deformation. Report what the data demonstrate rather than identifying every first visible curve as both limits at once; the detailed material terminology required varies between courses.

If the engine stops supplying the required driving force while resistance continues, the forces no longer balance and the car slows. The need for a powered engine is therefore compatible with Newton's first law. Energy is still transferred to the surroundings through resistance during the steady-speed journey.

Compare this with an ideal frictionless surface: an object could keep moving at constant velocity without a continuing push. Also check the route. A car rounding a bend at constant speed requires a sideways resultant because its direction changes; constant speed on its own is insufficient to conclude that every component of resultant force is zero.