Unit 2 practice test: Force and Translational Dynamics

The left cord pulls up and to the left, the right cord up and to the right. With equal tensions and equal angles, the sideways parts F_T cos 30° are equal and opposite, so the horizontal net force is zero, as it must be for a sign at rest.

• Correct: Equal tensions at equal angles pull equally hard to opposite sides: Right: equal tensions, equal angles, opposite sideways parts.
• The cords pull up, and horizontal pulls do not affect a hanging sign: Each cord does pull partly sideways; those parts cancel each other rather than having no effect.
• The weight of the sign cancels the horizontal pulls: The weight points straight down, so it cannot cancel a horizontal force.
• The ceiling pushes sideways on the sign to cancel them: The ceiling touches the cords, not the sign; the only forces on the sign are the two cords and Earth.

The cords still hold up the same 49 N. Each cord's upward part is F_T sin θ, and sin 15° is smaller than sin 30°, so each cord must pull harder: F_T = mg ÷ (2 sin 15°) ≈ 95 N.

• Correct: It increases, since less of each pull is upward: Right: a flatter cord needs a larger tension for the same upward pull.
• It decreases, since the cords are longer: The length of the cord does not set the tension; the angle does.
• It stays the same, since the weight is the same: The total upward pull is the same, but each cord gives less of its tension upward, so the tension rises.
• It increases, since the sign's weight increases: The weight, mg, does not change when the cords change.

Each cord is a separate agent, so each gets one whole arrow along its cord, plus the weight from Earth. Components belong in your equations beside the diagram, not on it, and the net force (zero here) is never an arrow.

• Correct: Three arrows: two cord tensions up and outward, and F_g down: Right: one whole arrow per agent.
• Seven arrows: two tensions, their four parts, and F_g down: Drawing components as extra arrows double-counts each pull; the exam does not accept components on a free-body diagram.
• Two arrows: one total tension up and F_g down: Two cords are two agents and two forces; merging them hides their directions.
• Three arrows: two tensions and a net force arrow down: The net force is the sum of the arrows, not an arrow of its own, and here it is zero.

Two objects act on the bucket: the rope pulls up (F_T) and Earth pulls down (F_g). When the velocity stays constant the forces in each direction are equal in size (2.4 shows why), so the arrows are the same length.

• Correct: F_T up and F_g down, the same length: Right: two forces, equal lengths, because the velocity does not change.
• F_T up, longer than F_g down: A longer tension arrow would mean a net force upward, which would make the bucket speed up. Rising does not need a larger upward force.
• F_T up, F_g down and a lifting force up: A "lifting force" has no separate agent: the rope is what lifts, and its pull is already F_T.
• F_T up alone, since the bucket rises: Earth pulls on the bucket whether it rises or falls, so F_g is always on its diagram near Earth.

Only objects that touch the bucket can exert contact forces on it, and the rope is the only one attached to it. The hands pull on the rope, not on the bucket.

• Correct: The rope: Right: the rope is attached to the bucket and pulls up on it.
• The person's hands: The hands touch the rope, not the bucket; their pull reaches the bucket through the rope as tension.
• Earth: Earth pulls the bucket down, not up.
• The sand inside it: The sand is part of the bucket-and-sand object; it does not push the object as a whole up.

At rest and at a constant velocity the velocity is not changing, so in both cases the rope's pull equals the bucket's weight. The diagram is the same.

• Correct: It does not change: F_T and F_g, equal in size: Right: rest is just a constant velocity of zero.
• F_T shrinks, since the bucket is no longer rising: Moving up at a steady speed needs no extra pull, so stopping does not reduce the tension.
• F_T disappears, leaving F_g by itself: The rope still holds the bucket up; if it pulled with no force the bucket would fall.
• F_g grows, since the bucket is now at rest: Weight is mg; it does not depend on whether the bucket moves.