Newton’s Laws and Free-Body Diagrams (4A)
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MCAT Chemical and Physical Foundations of Biological Systems › Newton’s Laws and Free-Body Diagrams (4A)
A $1.0,\text{kg}$ cart is attached to a hanging $0.50,\text{kg}$ mass by a light string over a frictionless pulley. The cart is on a frictionless horizontal table. Forces on the cart are tension $T$ horizontally, $mg$ downward, and $N$ upward. Forces on the hanging mass are $mg$ downward and tension $T$ upward. The system accelerates. Based on Newton’s Laws, which statement is most consistent?
Neglect string mass and pulley friction.
The cart has no horizontal net force because $N$ cancels $T$.
The tension is less than the weight of the hanging mass because that mass accelerates downward.
The tension is greater than the weight of the hanging mass because the cart accelerates.
The tension equals the weight of the hanging mass because the string is light.
Explanation
This question tests Newton's Second Law for connected objects with common acceleration. When objects are connected by a light string over a frictionless pulley, they share the same acceleration magnitude. For the hanging mass accelerating downward: mg - T = ma, giving T = m(g - a). Since acceleration is non-zero and downward for the hanging mass, tension must be less than its weight. The correct answer recognizes this constraint from Newton's Second Law. Answer A incorrectly assumes tension equals weight - this only occurs in equilibrium, not during acceleration. For accelerating connected systems, tension differs from weight by ma.
A $1.5,\text{kg}$ mass hangs at rest from a vertical spring scale. Forces on the mass are weight $mg$ downward and tension $T$ upward. The system is in static equilibrium. Based on Newton’s Laws, which statement is most consistent?
Assume the scale is massless and stationary.
$T > mg$ because tension must exceed weight to keep the mass from falling.
$T < mg$ because the spring supports part of the weight.
$T = mg$ and the net force is zero.
The net force is $mg$ downward but acceleration is zero because velocity is zero.
Explanation
This question tests Newton's First Law for static equilibrium. When an object hangs at rest, it has zero acceleration, requiring the net force to be zero according to F_net = ma. For the hanging mass, only two forces act: weight mg downward and tension T upward. These must be equal in magnitude for equilibrium, giving T = mg. The correct answer applies the equilibrium condition directly. Answer B incorrectly assumes tension must exceed weight for support - equal forces produce zero net force and zero acceleration, maintaining rest. For hanging mass problems in equilibrium, tension equals weight.
A $6.0,\text{kg}$ block is pressed against a vertical wall by a horizontal force of $120,\text{N}$ to the right. The block remains at rest; static friction between block and wall prevents sliding. Forces on the block are $mg$ downward, normal force from the wall to the left, the applied push to the right, and static friction upward. Based on Newton’s Laws, which statement is most consistent?
Assume equilibrium in both directions.
The normal force equals $mg$ because the block is at rest.
The applied push equals $mg$ because horizontal and vertical forces must match in magnitude.
Static friction acts downward because it always opposes the applied push.
Static friction must balance $mg$ in the vertical direction.
Explanation
This question tests force balance in two perpendicular directions. For the block to remain at rest against the wall, forces must balance both horizontally and vertically. Horizontally: the 120 N push right balances the normal force left. Vertically: with no other vertical forces, static friction must balance the weight mg to prevent sliding. The correct answer identifies this vertical force balance requirement. Answer A incorrectly states friction opposes the push - friction opposes relative motion, which here would be vertical sliding due to gravity. For objects pressed against vertical surfaces, friction balances weight while normal force balances the push.
A $4.0,\text{kg}$ block rests on a rough incline at $25^\circ$ above horizontal and does not slide. Forces on the block are weight $mg$ downward, normal force $N$ perpendicular to the surface, and static friction $f_s$ parallel to the surface. Based on Newton’s Laws, which statement about the direction of static friction is most consistent?
Static friction points perpendicular to the incline, opposing the normal force.
Static friction points down the incline, because friction always acts in the direction of gravity.
Static friction points up the incline, opposing the tendency of the block to slide down.
Static friction is zero because the block is not moving.
Explanation
This question tests understanding static friction's role in preventing motion on inclined planes. Newton's first law requires zero net force for the stationary block, meaning forces parallel to the incline must balance. The weight component parallel to the incline is mg sin 25° pointing down the slope, creating a tendency to slide downward. Static friction must oppose this tendency by pointing up the incline with magnitude f_s = mg sin 25°, preventing any sliding. Choice B incorrectly claims friction acts downward with gravity, while choice C incorrectly assumes zero friction for stationary objects. Choice D confuses friction's direction with the normal force direction. The key principle is that static friction always opposes the direction of impending motion - on an incline, gravity tends to cause downward sliding, so friction must point upward to maintain equilibrium.
A $10,\text{kg}$ sled is pulled across snow by a horizontal rope tension of $40,\text{N}$. The coefficient of kinetic friction is such that the friction force magnitude is $25,\text{N}$. What would be the net force acting on the sled?
Forces: tension (forward), kinetic friction (backward), weight, normal.
$15,\text{N}$ forward
$65,\text{N}$ forward
$0,\text{N}$ because vertical forces cancel
$15,\text{N}$ backward
Explanation
The skill being tested is calculating net force from tension and friction. Newton's first law needs zero net for constant velocity, but here implied acceleration from unbalanced forces per second law, with third law pairing. The sled has forward tension and backward friction, so net force is their difference. Net force is 40 N - 25 N = 15 N forward, logically choice A. Choice D is incorrect as vertical cancellation does not affect horizontal net. For such problems, subtract opposing horizontal forces. Verify by predicting acceleration if net is nonzero.
A $12,\text{kg}$ crate rests on a horizontal floor. A student pulls it with a rope at $30^\circ$ above the horizontal with tension $T=60,\text{N}$. The crate moves at constant velocity. Kinetic friction acts between crate and floor. Considering forces on the crate (weight, normal force, tension, friction), which statement about the force balance is most consistent with Newton’s Laws?
(Assume air resistance is negligible.)
The friction force equals the horizontal component of the tension, $T\cos 30^\circ$.
The net force must point in the direction of motion even at constant velocity.
The friction force equals $T\sin 30^\circ$ because friction balances the vertical component of tension.
The normal force equals the weight because the crate is on a horizontal surface.
Explanation
The skill being tested is applying Newton's laws to analyze force balances in systems with inclined tension and friction. Newton's first law states that an object in uniform motion continues unless acted on by a net force, the second law equates net force to mass times acceleration, and the third describes action-reaction pairs. In this system, the crate moves at constant velocity, so the net force is zero in both horizontal and vertical directions per Newton's first law. The friction force equals the horizontal component of tension, T cos 30°, because it balances the forward pull to maintain zero net horizontal force, making choice C correct. Choice D is incorrect because at constant velocity, acceleration is zero, so net force must be zero, not in the direction of motion. For similar questions, draw a free-body diagram and resolve all forces into horizontal and vertical components. Ensure the sum of forces in each direction equals zero if there's no acceleration.
A $3.0,\text{kg}$ block on a horizontal surface is attached to a rope. Two students pull on opposite ends of the rope so that the block experiences $15,\text{N}$ tension to the right and $15,\text{N}$ tension to the left (equal magnitudes). The block is observed to remain at rest. Which statement is most consistent with Newton’s Laws?
Forces on block: leftward tension, rightward tension, weight, normal.
The weight cancels one of the tensions, producing equilibrium.
The block must accelerate because two forces are acting on it.
The net horizontal force is zero, consistent with no acceleration.
The block is in equilibrium only if the tensions are greater than the weight.
Explanation
The skill being tested is recognizing equilibrium with balanced opposing forces. Newton's first law states zero net force for no motion change, the second equates force to m a, and the third describes reactions. The block is at rest with equal opposing tensions, so net horizontal force is zero. This consistency with no acceleration supports choice B. Choice A is incorrect because balanced forces can result in zero acceleration despite multiple forces. In similar cases, calculate net force by vector sum. Verify equilibrium if observed motion is absent.
A $4.0,\text{kg}$ block slides down a rough incline at constant speed. The incline angle is fixed. Forces on the block include gravity, normal force, and kinetic friction. Based on Newton’s Laws, which statement is most consistent with the force components parallel to the incline?
Take the downhill direction along the incline as positive.
Kinetic friction points downhill because it opposes gravity.
The downhill component of gravity equals the kinetic friction magnitude.
The net force parallel to the incline is positive because the block is moving downhill.
The normal force equals the component of gravity parallel to the incline.
Explanation
The skill being tested is resolving forces on inclines for constant speed motion. Newton's first law implies zero net force for uniform motion, the second relates force to acceleration, and the third involves pairs. The block slides at constant speed, so net force parallel to the incline is zero. The downhill gravity component equals kinetic friction, balancing for no acceleration, supporting choice B. Choice A is incorrect because net parallel force is zero, not positive. In similar incline problems, resolve gravity into parallel and perpendicular components. Ensure friction opposes relative motion and balances for constant speed.
A $1.5,\text{kg}$ book is held pressed against a vertical wall by a horizontal hand force $F$ directed into the wall. The book remains at rest. Static friction between the book and wall acts vertically. Which statement about the forces on the book is most consistent with Newton’s Laws?
Forces on the book: weight (down), static friction (up or down), normal force from wall (horizontal), hand force (horizontal).
The normal force from the wall must equal the book’s weight.
Static friction acts upward and its magnitude equals the book’s weight.
The hand force must be equal to $mg$ to keep the book from falling.
Static friction acts downward because the hand pushes into the wall.
Explanation
The skill being tested is analyzing vertical static friction in equilibrium against a wall. Newton's first law demands zero net force for rest, the second relates force to acceleration, and the third involves reaction pairs. The book is at rest, so net vertical and horizontal forces are zero. Static friction acts upward equaling the weight to balance gravity, as horizontal forces cancel, supporting choice B. Choice C is incorrect because the normal force balances the hand force horizontally, not the weight vertically. In like questions, separate forces into components perpendicular to each other. Check equilibrium by ensuring opposing forces sum to zero in each direction.
A $6.0,\text{kg}$ box is at rest on a horizontal surface. A horizontal force is applied and gradually increased. The maximum static friction force available is $18,\text{N}$. When the applied force reaches $12,\text{N}$, the box still does not move. Which statement is most consistent with Newton’s Laws and static friction?
Forces: applied (right), static friction (left), weight, normal.
Static friction is $18,\text{N}$ because that is the maximum possible.
Static friction is zero because the box is not moving.
Static friction is $12,\text{N}$ opposing the applied force.
The net force is $12,\text{N}$ to the right, but acceleration is prevented by inertia.
Explanation
The skill being tested is understanding static friction in pre-motion scenarios. Newton's first law maintains rest with zero net force, the second links to acceleration, and the third pairs. The box remains at rest, so static friction balances the applied force. Friction is 12 N opposing, less than maximum, fitting choice B. Choice C is incorrect because friction is nonzero to counter the applied force. For friction problems, note static friction adjusts to match applied up to max. Verify by checking if applied < max friction implies no motion.