Physics Practice Test: Newton's Laws and Forces

a = F_net/m = 12 N ÷ 3.0 kg = 4.0 m/s². Multiplying instead of dividing gives 36, and dividing mass by force gives 0.25.

Weight is W = mg = 65 kg × 9.8 m/s² = 637 N. The value 65 confuses mass (kg) with weight (N), and 74.8 comes from adding g to the mass instead of multiplying.

Mass is the amount of matter and does not depend on location, so it stays 80 kg. Her weight on the Moon is about one-sixth as large, which is why "about 13 kg" is tempting.

By Newton's third law, the two objects exert equal and opposite forces on each other, whatever their masses. The nail moves more because its mass is smaller, not because it feels a larger force.

The net force is 30 − 18 = 12 N to the right, so a = 12 ÷ 4.0 = 3.0 m/s² to the right. Using only the 30 N force gives 7.5 m/s², and 12 is the net force, not the acceleration.

Constant velocity means zero net force, so friction equals the push, 39.2 N. The normal force is mg = 98 N, and μ = 39.2 ÷ 98 = 0.40. Dividing by the mass instead of the normal force gives 3.9.

The box stays at rest, so the net force is zero and static friction exactly balances the 60 N push. The value 98 N (0.50 × 196 N) is only the maximum static friction, reached just before the box starts to slide.

The scale pushes up with N, and N − mg = ma, so N = m(g + a) = 50 × (9.8 + 2.0) = 590 N. Subtracting a instead gives 390 N, which would be the reading for downward acceleration.

The passengers' bodies keep their forward motion (inertia) while the bus slows beneath them. No forward force acts on them; friction from the floor actually acts backward on their feet.

Constant velocity means zero acceleration, so by Newton's second law the net force is zero and the upward drag balances the weight. If weight were still larger, the skydiver would keep speeding up.

Only the component of gravity along the ramp accelerates the block: a = g sin 30° = 9.8 × 0.5 = 4.9 m/s². Using cos 30° gives 8.5 m/s², which is the perpendicular component.

Both blocks share a = 24 ÷ (6.0 + 2.0) = 3.0 m/s². The rope alone pulls the 2.0 kg block, so T = 2.0 × 3.0 = 6.0 N. The value 18 N is the net force on the 6.0 kg block, not the rope tension.

A third-law pair involves the same two objects acting on each other: Earth pulls the book, so the book pulls Earth. The table's upward push also acts on the book and balances its weight, but it is a different interaction.

The string supplies the centripetal force: F = mv²/r = 1.2 × 4.0² / 0.80 = 24 N. Forgetting to divide by r gives 19.2 N, and forgetting to square v gives 6.0 N.

Gravitational force follows an inverse-square law, F = Gm₁m₂/r², so doubling r divides the force by 2² = 4. "One-half" would be true only if the force depended on 1/r.