Fluids and Newton's Laws - AP Physics 1

A hollow sphere is neutrally buoyant in water and drifts at rest. Forces are buoyant force upward and weight $mg$ downward; drag is negligible. Which statement is correct?
Answer: The buoyant force equals $mg$ . This question examines equilibrium conditions for neutrally buoyant objects in fluids. The sphere experiences buoyant force upward and weight mg downward, with negligible drag. Since the sphere drifts at rest (zero acceleration), Newton's first law requires zero net force, meaning upward and downward forces must be equal in magnitude. Therefore, the buoyant force must exactly equal mg. Choice A incorrectly assumes being in water automatically creates upward net force, but equilibrium requires force balance regardless of the fluid medium.
A block sinks at constant speed in a fluid. Forces are weight $mg$ downward, buoyant force upward, and drag upward. What is the net force?
Answer: Zero This question examines net force analysis for objects at terminal velocity in fluids. The block experiences weight mg downward, buoyant force upward, and drag upward. Since the block sinks at constant speed, its acceleration is zero, requiring zero net force by Newton's first law. Therefore, the downward weight must equal the sum of upward forces (buoyant force plus drag), creating equilibrium. Choice A incorrectly assumes downward motion requires downward net force, but constant velocity specifically requires zero net force.
A solid plastic cube is held fully submerged and then released. At release, only buoyant force upward and weight $mg$ downward act; drag is negligible. The cube rises but its speed is constant. Which is true about the vertical forces?
Answer: The buoyant force equals $mg$ , so the net force is zero. This question examines force analysis when an object moves at constant velocity in a fluid. The cube experiences buoyant force upward and weight mg downward, with negligible drag initially. Since the cube rises at constant speed, its acceleration is zero, requiring zero net force by Newton's first law. This means the upward buoyant force must exactly equal the downward weight mg. Choice B incorrectly assumes upward motion requires upward net force, but constant velocity motion requires zero net force regardless of direction.
A sphere is neutrally buoyant and is given a brief push upward in water. After the push, it moves upward at constant speed; drag is negligible and only buoyant force and weight act. Which is true after the push ends?
Answer: Net force is zero, so buoyant force equals $mg$ . This question involves equilibrium analysis for neutrally buoyant objects after external impulses. The sphere experiences buoyant force upward and weight mg downward, with negligible drag. Since the sphere moves upward at constant speed after the push, its acceleration is zero, requiring zero net force by Newton's first law. Therefore, the buoyant force must equal mg for force balance. Choice A incorrectly assumes upward motion requires upward net force, but constant velocity motion requires zero net force.
A solid block is fully submerged and held at rest by a downward applied force. Which relationship must be true?
Answer: $F_B>mg$ because an extra downward force is needed to balance. This question tests force analysis when external forces act on submerged objects. When the block is held at rest underwater by a downward applied force, three vertical forces act: weight (mg) downward, applied force (Fapp) downward, and buoyant force (FB) upward. For equilibrium with zero acceleration, the upward force must balance the total downward forces: FB = mg + Fapp. This means FB > mg, since the applied force adds to the weight. The need for a downward force indicates the block would rise without it, meaning it's less dense than the fluid. Choice C incorrectly ignores the applied force in the equilibrium equation. When analyzing multi-force problems, include all forces in your free-body diagram and equilibrium equations.
A light ball rises through a fluid and slows down while still moving upward. Forces are buoyant force upward, weight $mg$ downward, and drag downward. What is the direction of the net force?
Answer: Downward, because acceleration is downward when slowing upward. This question examines net force direction when objects decelerate while moving upward in fluids. The ball experiences buoyant force upward, weight mg downward, and drag downward. Since the ball rises but slows down, its acceleration is downward (opposite to velocity). By Newton's second law, downward acceleration requires downward net force, meaning the sum of downward forces (weight plus drag) exceeds the upward buoyant force. Choice A incorrectly assumes upward motion requires upward net force, but deceleration creates net force opposite to velocity direction.
A buoyant object rises in water and speeds up upward. Forces are buoyant force upward and weight $mg$ downward (drag negligible). Which statement is correct?
Answer: Buoyant force is greater than $mg$ . This question examines force relationships when objects accelerate upward in fluids. The object experiences buoyant force upward and weight mg downward, with negligible drag. Since the object rises and speeds up upward, its acceleration is upward. By Newton's second law, upward acceleration requires upward net force, meaning the buoyant force must exceed the weight mg. Choice A incorrectly assumes net force is zero during motion, but acceleration requires non-zero net force in the acceleration direction.
A small cube is fully submerged and moving upward at constant speed in a fluid. What is the net force on the cube?
Answer: Zero, because constant speed implies zero acceleration. This question tests Newton's laws for constant velocity motion in fluids. When an object moves at constant speed, its velocity is unchanging, meaning acceleration is zero. By Newton's second law, zero acceleration requires zero net force, regardless of the direction of motion. The upward buoyant force must exactly balance the downward weight for any fully submerged object moving at constant velocity. Choice A incorrectly assumes upward motion requires upward net force, confusing velocity with acceleration. To solve constant velocity problems, remember that Newton's first law states objects maintain constant velocity when net force is zero, regardless of whether that velocity is upward, downward, or zero.
A cube is fully submerged in water and held at rest by a string tied to the bottom. Forces are buoyant force upward, weight $mg$ downward, and tension downward. Which equation must be true?
Answer: $F_B = mg + T$ This question involves equilibrium analysis for submerged objects held by downward tension. The cube experiences buoyant force upward, weight mg downward, and tension downward while at rest. Since the cube is in equilibrium, Newton's first law requires zero net force, so upward forces must equal the sum of downward forces. Therefore, FB = mg + T, with buoyant force balancing both weight and tension. Choice A incorrectly adds tension to buoyant force instead of recognizing tension acts downward with weight.
A cork is pushed under water and released. Right after release it accelerates upward. Forces are buoyant force upward, weight $mg$ downward, and negligible drag. Which is true?
Answer: The buoyant force is greater than $mg$ . This question involves force analysis for objects accelerating upward in fluids. The cork experiences buoyant force upward and weight mg downward, with negligible drag. Since the cork accelerates upward after release, Newton's second law requires upward net force, meaning the upward buoyant force must exceed the downward weight mg. Therefore, the buoyant force is greater than mg. Choice C incorrectly assumes future floating behavior determines current force relationships, but instantaneous acceleration depends only on the current force imbalance.
A submerged object accelerates upward from rest with negligible drag. Forces are buoyant force upward and weight $mg$ downward. Which statement is correct about the forces?
Answer: Buoyant force is greater than $mg$ . This question tests force comparison when objects accelerate upward from rest in fluids. The object experiences buoyant force upward and weight mg downward, with negligible drag. Since the object accelerates upward from rest, Newton's second law requires upward net force, meaning the buoyant force must exceed the weight mg. Therefore, buoyant force is greater than mg. Choice A incorrectly assumes equal forces because of starting from rest, but upward acceleration requires force imbalance favoring the buoyant force.
A rock is held fully submerged and motionless in water by an upward tension in a string. Which statement is correct?
Answer: The forces balance so $T+F_B=mg$ . This question tests force equilibrium for a three-force system in a fluid. When the rock is held motionless underwater, its acceleration is zero, so the net force must be zero by Newton's first law. Three forces act vertically: weight (mg) downward, buoyant force (FB) upward, and tension (T) upward. For equilibrium, the upward forces must balance the downward force: T + FB = mg. Since the rock would sink without the string (mg > FB for rocks in water), the tension provides the additional upward force needed for equilibrium. Choice A incorrectly claims FB = mg, which would mean the rock could float without the string. When multiple forces act on a submerged object, sum all forces and set equal to zero for equilibrium.
A sealed container floats at rest in water with half its volume submerged. Forces are $mg$ downward and buoyant force $F_B$ upward. Which statement is correct?
Answer: $F_B=mg$ because the container is in equilibrium This question tests equilibrium for partially submerged floating objects. The container is at rest, requiring zero net force and therefore FB = mg. Two forces act: weight mg downward and buoyant force FB upward. For a floating object at rest, these forces must balance regardless of how much is submerged. Choice A incorrectly relates the exposed portion to force inequality, not recognizing that equilibrium depends on force balance, not submersion fraction. The strategy is to recognize that "at rest" always means balanced forces, with buoyant force adjusting to match weight for floating objects.
A helium balloon rises in air and speeds up upward. Forces are buoyant force upward and weight $mg$ downward; air resistance is negligible. Which is correct?
Answer: Buoyant force is greater than $mg$ . This question tests force relationships when objects accelerate upward in air (a fluid). The balloon experiences buoyant force upward and weight mg downward, with negligible air resistance. Since the balloon rises and speeds up upward, its acceleration is upward. By Newton's second law, upward acceleration requires upward net force, meaning the buoyant force must exceed the weight mg. Choice A incorrectly assumes air creates zero net force, but buoyancy in air follows the same principles as in liquids.
A sphere is neutrally buoyant in water and remains suspended at rest when released. Which statement is correct?
Answer: The net force is zero, so $F_B=mg$ . This question tests Newton's laws for neutrally buoyant objects. When an object remains suspended at rest in a fluid, it has zero acceleration, requiring zero net force by Newton's first law. For a fully submerged object with only buoyant force (upward) and weight (downward) acting, these forces must be equal: FB = mg. Neutral buoyancy occurs when an object's average density equals the fluid's density, causing the buoyant force to exactly balance the weight. Choice A incorrectly claims the buoyant force is zero for submerged objects, which would mean no upward pressure difference exists. To identify neutral buoyancy, look for objects that neither rise nor sink when released in a fluid.
A metal sphere is released from rest in oil and begins sinking with increasing speed. Which statement about forces is correct?
Answer: The net force is downward, so $mg>F_B$ at that moment. This question tests Newton's laws for objects accelerating in fluids. When the metal sphere sinks with increasing speed, it has downward acceleration, requiring a net downward force by Newton's second law. Since only buoyant force (upward) and weight (downward) act on the sphere, the weight must exceed the buoyant force: mg > FB. The buoyant force depends on the volume of fluid displaced and the fluid's density, not the object's mass or density. Choice A incorrectly reverses the force relationship, claiming FB > mg would cause downward motion. To analyze motion in fluids, first determine the direction of acceleration, then use Newton's second law to find which force must be larger.
A light object is held fully submerged by a downward tension in a string and is at rest. Forces are buoyant force upward, weight $mg$ downward, and tension downward. Which is correct?
Answer: The buoyant force equals $mg + T$ . This question involves equilibrium analysis for light objects held submerged by external forces. The object experiences buoyant force upward, weight mg downward, and tension downward while at rest. Since the object is in equilibrium, Newton's first law requires zero net force, so the upward buoyant force must equal the sum of downward forces. Therefore, the buoyant force equals mg + T, with buoyant force balancing both weight and downward tension. Choice A incorrectly assumes buoyant force equals weight only, ignoring the additional downward tension.
A block is held stationary underwater by a downward push from a student's hand. Forces are buoyant force upward, weight $mg$ downward, and hand force downward. Which must be true?
Answer: Buoyant force is greater than $mg$ . This question involves equilibrium analysis for objects held stationary by external forces in fluids. The block experiences buoyant force upward, weight mg downward, and hand force downward while stationary. Since the block is at rest, Newton's first law requires zero net force, so the upward buoyant force must equal the sum of downward forces (weight plus hand force). Therefore, buoyant force must be greater than mg alone. Choice A incorrectly assumes equilibrium means buoyant force equals weight, ignoring the additional downward hand force.
A foam block is released underwater and accelerates upward. At release, drag is negligible, so only buoyant force upward and weight $mg$ downward act. Which must be true?
Answer: $F_B > mg$ . This question involves force analysis when objects accelerate upward from release in fluids. The block experiences buoyant force upward and weight mg downward, with negligible drag at release. Since the block accelerates upward after release, Newton's second law requires upward net force, meaning the buoyant force must exceed the weight mg. Therefore, FB > mg. Choice A incorrectly assumes equilibrium exists at release despite upward acceleration, but acceleration requires force imbalance.
A sphere is fully submerged and rises upward at constant speed. Forces are buoyant force $F_B$ upward, weight $mg$ downward, and drag $F_D$ downward. Which relation is correct?
Answer: $F_B=mg+F_D$ This question tests equilibrium for objects moving at constant velocity against drag in fluids. The sphere rises at constant speed, meaning zero acceleration and zero net force. Three forces act: buoyant force FB upward, weight mg downward, and drag FD downward (opposing the upward motion). For equilibrium, the upward force must equal the sum of downward forces: FB = mg + FD. Choice C incorrectly groups drag with buoyant force, not recognizing that drag opposes motion direction. Remember that constant velocity requires zero net force, with drag always opposing the direction of motion through a fluid.

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