Mass measures resistance to a change in velocity. A net force accelerates a trolley; the same force produces less acceleration on a larger mass. Remove the push and both continue at their own constant velocities. Zero net force permits rest or uniform motion.
Momentum is mv. Newton’s second law links force to its rate of change; integrating force over time gives impulse. Both the short and long triangular force pulses remove the same incoming momentum. The broader pulse needs a lower peak but produces a longer stopping distance.
Each skater exerts a force on the other. The two forces are equal and opposite at the same instant, but act on different bodies. They therefore cannot cancel in the force equation for one skater. The lighter skater changes velocity more; their momentum changes remain equal and opposite.
The spring pushes both carts internally. With no external impulse, total momentum remains its initial value, even while spring energy becomes kinetic energy. From rest, momenta are opposite. With an initial common drift, the centre of mass continues moving at that drift velocity.
Equilibrium requires the net force to vanish in every direction. Three large pulls can balance because their vector components cancel. Changing a magnitude or direction usually leaves a resultant. The required third force is the negative of the sum of the first two.
Static friction matches the applied push up to a maximum μsN. It does not always equal that maximum. Above the threshold, a block starts sliding and resistance becomes μkN. Wheels have a smaller effective rolling resistance in this simplified trolley comparison.
A lubricant can reduce direct contact between rough surfaces and change their friction. Here you choose lower coefficients and compare identical blocks. A weaker push may move the lubricated block while the dry block remains stuck. Real lubricants also produce viscous resistance; that additional behavior is outside this model.
A vehicle needs inward net force mv²/r. On a level road static friction supplies it. On a banked road the tilted normal contributes. At the design speed no friction is needed; below or above it friction acts in opposite directions. Grip is possible only when the required friction is within μN.
A scale measures the normal support force. Upward acceleration requires N greater than mg; downward acceleration requires less. During free fall both lift and person accelerate at −g, so the support force vanishes. In the accelerating lift frame a pseudo-force −ma restores the equilibrium-form equation.