Free-body diagrams Transitional Reasoning Download PDF

Questions

1. 1.

   A metal cylinder suspended from a light vertical coil spring oscillates along a straight vertical line in a physics laboratory. At the lowest point of its oscillation, the cylinder comes to rest instantaneously before accelerating back upward. When constructing an inertial free-body diagram for the isolated cylinder at this exact instant, which statement correctly identifies every external force acting on it and their relative magnitudes?

   • A) Exactly two external forces act on the cylinder: a downward gravitational force and an upward spring force, with the spring force having a greater magnitude than the gravitational force.
   • B) Exactly two external forces act on the cylinder: a downward gravitational force and an upward spring force, with both forces having equal magnitude because the cylinder is momentarily at rest.
   • C) Three external forces act on the cylinder: a downward gravitational force, an upward spring force, and an upward dynamic rebound force generated by the turnaround.
   • D) Exactly two external forces act on the cylinder: a downward gravitational force and an upward spring force, with the gravitational force having a greater magnitude because downward displacement is maximized.
2. 2.

   A flat magnet remains completely stationary against a vertical steel refrigerator door without slipping. When constructing a standard free-body diagram for the isolated magnet, which statement correctly identifies every external force acting directly on it and describes their directional relationships in equilibrium?

   • A) Three forces: downward gravity, an upward magnetic force from the door balancing gravity, and an outward horizontal normal force exerted by the door.
   • B) Four forces: downward gravity, an upward normal force from the door balancing gravity, an inward horizontal magnetic force, and an outward horizontal friction force.
   • C) Three forces: downward gravity, an upward static friction force from the door balancing gravity, and an inward horizontal magnetic force, with zero normal force.
   • D) Four forces: downward gravity, an upward static friction force from the door balancing gravity, an inward horizontal magnetic force, and an outward horizontal normal force balancing the magnetic attraction.
3. 3.

   A solid, uniform sphere rests in static equilibrium inside a frictionless cradle supported between a flat vertical wall on its left and a flat ramp on its right inclined at 45° to the horizontal. A student constructs a standard free-body diagram to analyze the forces acting directly on the sphere. Which statement correctly identifies every external force that must be drawn on this free-body diagram and explains their physical relationships in equilibrium?

   • A) Exactly two external forces act on the sphere: the downward gravitational force and a single resultant upward normal force, because rigid contact surfaces can only exert forces directly opposing gravity in static equilibrium.
   • B) Exactly four external forces act on the sphere: the downward gravitational force, a normal force perpendicular to the ramp, a horizontal normal force from the wall, and a static friction force directed parallel to the ramp to prevent the sphere from sliding down.
   • C) Exactly five external forces act on the sphere: the downward gravitational force, the normal forces from the ramp and wall, and the downward contact forces that the sphere exerts onto the wall and ramp to maintain physical contact.
   • D) Exactly three external forces act on the sphere: the gravitational force directed vertically downward, a normal force from the vertical wall directed horizontally to the right, and a normal force from the ramp directed perpendicular to its surface (upward and to the left), whose components balance both the sphere's weight and the wall's normal force.
4. 4.

   An athlete performs a standing vertical jump on a flat, rigid floor. During the push-off phase, while the athlete's feet remain in firm contact with the floor, their center of mass accelerates vertically upward from rest. When constructing a standard free-body diagram for the athlete during this upward acceleration phase, which statement correctly identifies all external forces acting directly on the athlete and their relative magnitudes?

   • A) It contains exactly two forces: a downward gravitational force and an upward normal force exerted by the floor, with the normal force having a greater magnitude than the gravitational force.
   • B) It contains three forces: a downward gravitational force, an upward normal force equal in magnitude to the gravitational force, and an upward muscular thrust force produced by the legs.
   • C) It contains exactly two forces: a downward gravitational force and an upward normal force, with both forces having equal magnitudes because of Newton's third law.
   • D) It contains three forces: a downward gravitational force, an upward normal force exerted by the floor, and an upward net acceleration force directing the motion.
5. 5.

   A passenger stands motionless relative to a flat, horizontal step of an escalator that travels diagonally upward at a constant velocity along a straight 30° incline. A student constructs a standard free-body diagram to represent all external forces acting directly on the passenger. Which statement correctly identifies the forces that must be drawn on this free-body diagram and provides the correct physical justification?

   • A) A downward gravitational force, a normal force directed perpendicular to the 30° incline, and a parallel frictional force directed upward along the incline, because the contact forces must align with the slope of motion.
   • B) A downward gravitational force, an upward normal force perpendicular to the step, and a forward horizontal static friction force, because a continuous forward force is required to sustain steady horizontal translation.
   • C) A downward gravitational force and a single contact force acting upward at 30° along the direction of motion, because the net external force on an object must always point in the direction of its velocity.
   • D) Exactly two forces: a downward gravitational force and an upward normal force perpendicular to the step, which have equal magnitudes because constant-velocity motion requires zero net force.
6. 6.

   A small steel sphere suspended from the ceiling by a light, inextensible cord swings along a vertical circular arc. A student constructs an inertial free-body diagram for the sphere at the precise moment it passes through the lowest point of its trajectory while moving toward the right. Which statement correctly identifies all forces that belong on the diagram and describes their directions and relative magnitudes?

   • A) The diagram must include only two forces: a downward gravitational force and an upward tension force, with the tension force having a greater magnitude than the gravitational force.
   • B) The diagram must include three forces: a downward gravitational force, an upward tension force of equal magnitude, and a rightward horizontal force representing the sphere's motion.
   • C) The diagram must include three forces: a downward gravitational force, an upward tension force, and a separate upward centripetal force that maintains the circular path.
   • D) The diagram must include only two forces: a downward gravitational force and an upward tension force, with both forces having equal magnitudes because the cord is vertical.
7. 7.

   In a physics laboratory investigation, a glider of mass $M$ rests on a level, frictionless air track and is connected by a light, taut string passing over an ideal pulley to a hanging mass $m$. When the system is released from rest, both objects accelerate together under the influence of gravity. In constructing a standard free-body diagram for the isolated glider during this acceleration, which statement correctly identifies all external forces acting directly on it and describes their physical relationships?

   • A) The diagram must include four forces: a downward gravitational force, an upward normal force, a forward tension force, and an additional forward net force representing the glider's acceleration.
   • B) The diagram must include three forces: a downward gravitational force, an upward normal force, and a horizontal tension force directed toward the pulley whose magnitude is equal to the full weight of the hanging mass ($m g$).
   • C) The diagram must include three forces: a downward gravitational force, an upward normal force equal in magnitude to the glider's weight, and a horizontal tension force directed toward the pulley whose magnitude is strictly less than $m g$.
   • D) The diagram must include four forces: a downward gravitational force, an upward normal force, a horizontal tension force directed toward the pulley, and an additional downward gravitational force transferred directly from the hanging mass.
8. 8.

   A student holds a heavy textbook completely stationary by pressing it directly upward against a flat, horizontal ceiling with their hand. When constructing a standard free-body diagram for the textbook, which statement correctly identifies all external forces acting directly on the textbook and explains their directions and magnitudes?

   • A) An upward contact force from the hand, a downward gravitational force from Earth, and a downward normal force from the ceiling, with the hand's upward force having a magnitude equal to the sum of the other two forces.
   • B) An upward contact force from the hand, an upward normal force from the ceiling, and a downward gravitational force from Earth, with the two upward forces together balancing the downward gravitational force.
   • C) An upward contact force from the hand and a downward gravitational force from Earth only, with the hand's upward force having a magnitude exactly equal to the textbook's weight because the object is in equilibrium.
   • D) An upward contact force from the hand, a downward gravitational force from Earth, and an upward contact force exerted by the textbook on the ceiling, with all forces canceling symmetrically.
9. 9.

   A commuter train travels along a straight, horizontal track while accelerating forward at a constant rate. Inside a train car, a small sphere suspended by a light string hangs at a fixed angle, tilted backward relative to the vertical. An observer standing on the ground outside the train constructs an inertial free-body diagram to represent all forces acting directly on the sphere. Which statement correctly identifies every force that must be drawn on this free-body diagram and provides the correct physical justification?

   • A) Three forces: the downward gravitational force, the tension directed along the string, and a separate forward force of acceleration, because an accelerating object requires an applied forward force to sustain its acceleration.
   • B) Three forces: the downward gravitational force, the tension directed along the string, and a backward inertial force, because the sphere stays stationary relative to the train car and must be in static equilibrium.
   • C) Exactly two forces: the downward gravitational force exerted by Earth and the tension directed along the string upward and forward, whose unbalanced horizontal component provides the forward net force.
   • D) Exactly two forces: the downward gravitational force and a purely vertical tension force, because the backward tilt of the string is caused by the sphere's velocity rather than an unbalanced horizontal force.
10. 10.

    An automobile travels at a constant speed around a flat, unbanked horizontal curve without skidding. A student constructs an inertial free-body diagram to represent all external forces acting directly on the vehicle during this turn. Which statement correctly identifies every force that must be drawn on this free-body diagram and provides the correct physical justification?

    • A) Downward gravitational force, upward normal force, inward static friction, and an outward centrifugal force, because an outward force is required to balance the inward force during steady circular motion.
    • B) Downward gravitational force, upward normal force, a forward applied engine force, and an independent inward centripetal force, because centripetal acceleration requires a distinct centripetal force vector drawn on the body.
    • C) Downward gravitational force, upward normal force, and radially inward static friction, because the vertical forces balance while static friction acts as the sole horizontal interaction providing the net inward acceleration.
    • D) Downward gravitational force, upward normal force, and radially outward kinetic friction, because the tires slide against the pavement away from the center of the turn as the car negotiates the curve.
11. 11.

    Two crates, crate 1 and crate 2, rest in static equilibrium stacked vertically on a horizontal floor, with crate 1 placed directly on top of crate 2. A student isolates crate 2 to construct its standard free-body diagram. Which statement correctly identifies every force that must be drawn on this free-body diagram and provides the correct physical justification?

    • A) Four forces: the downward gravitational force on crate 2, the downward gravitational force on crate 1 transmitted through the stack, the downward contact force from crate 1, and the upward normal force from the floor.
    • B) Two forces: the downward gravitational force on crate 2 and the upward normal force from the floor, because crate 1 only alters the magnitude of the floor support rather than applying an independent contact force.
    • C) Four forces: the downward gravitational force on crate 2, the downward normal force from crate 1, the upward normal force from the floor, and the upward reaction force exerted by crate 2 on crate 1.
    • D) Three forces: the downward gravitational force on crate 2, the downward normal force exerted by crate 1, and the upward normal force exerted by the floor, because only external forces acting directly on crate 2 belong on its diagram.
12. 12.

    A heavy display sign of weight $W$ hangs motionless in static equilibrium beneath a ceiling, supported symmetrically by two light cables that each make an angle $\theta$ with the horizontal. A student constructs a free-body diagram to analyze the forces acting directly on the sign. Which statement correctly identifies the forces that must be drawn on the free-body diagram and their relationship to the sign's weight?

    • A) Exactly two forces must be drawn: the downward gravitational force and a single net upward tension, because opposing horizontal cable components cancel out and are omitted from free-body diagrams.
    • B) Exactly three forces must be drawn: the downward gravitational force and two tension forces pulling upward along each cable, where each tension magnitude equals $\frac{W}{2}$ regardless of the angle $\theta$.
    • C) Exactly three forces must be drawn: the downward gravitational force and two tension forces pulling upward and inward along each cable, where each tension magnitude equals $\frac{W}{2\sin\theta}$.
    • D) Four forces must be drawn: the downward gravitational force, two upward tension forces along each cable, and a downward reaction force exerted by the sign to balance the cable pulls.
13. 13.

    A small steel bob attached to a light string swings in a horizontal circle at a constant speed, forming a conical pendulum. A student constructs a free-body diagram to analyze the forces acting directly on the bob during this steady circular motion. Which statement correctly identifies the forces that must be drawn on the free-body diagram and explains how they relate to the bob's acceleration?

    • A) Three forces must be drawn: downward gravity, tension along the string, and an outward centrifugal force that prevents the bob from falling inward.
    • B) Exactly two forces must be drawn: downward gravity and tension along the string, because the horizontal component of the tension supplies the net inward acceleration.
    • C) Three forces must be drawn: downward gravity, tension along the string, and an inward centripetal force that actively turns the bob along the circular path.
    • D) Exactly two forces must be drawn: downward gravity and a purely horizontal centripetal force, because the tension in the string is replaced by the net radial force.
14. 14.

    A passenger stands on a platform scale inside an elevator cab that is moving upward while steadily slowing down to a stop. In constructing a standard free-body diagram for the passenger during this deceleration, which statement correctly identifies all external forces acting directly on the passenger and their relative magnitudes?

    • A) Only two forces act on the passenger: a downward gravitational force and an upward normal force from the scale, with the gravitational force having a greater magnitude than the normal force.
    • B) Only two forces act on the passenger: a downward gravitational force and an upward normal force from the scale, with the normal force having a greater magnitude than the gravitational force because the elevator is traveling upward.
    • C) Three forces act on the passenger: an upward normal force from the scale, a downward gravitational force of equal magnitude, and an additional downward force of deceleration.
    • D) Three forces act on the passenger: an upward cable tension transmitted through the cab, an upward normal force from the scale, and a downward gravitational force.
15. 15.

    An apparatus uses a frictionless horizontal rod to press a wooden block firmly against a rough vertical wall, keeping the block completely stationary. When drawing a standard free-body diagram for the block, which statement correctly identifies all external forces acting on the block and explains how they achieve static equilibrium?

    • A) Three forces act on the block: downward gravity is balanced by an upward normal force from the wall, while the horizontal applied push is balanced by static friction directed into the wall.
    • B) Four forces act on the block: downward gravity and the horizontal push from the rod are each balanced by equal and opposite internal reaction forces acting within the block.
    • C) Four forces act on the block: downward gravity is balanced by an upward static friction force from the wall, and the horizontal push is balanced by a horizontal normal force directed outward from the wall.
    • D) Three forces act on the block: downward gravity is balanced directly by the horizontal push transmitted along the contact boundary, while the wall exerts only an outward normal force.
16. 16.

    A roller-coaster cart coasts over the crest of a smooth, vertical circular track at a speed $v$ while remaining in contact with the rails. A student draws a standard free-body diagram to analyze the cart at the exact apex of the hill where the track is momentarily horizontal. Which description correctly identifies the forces acting on the cart at this point and their relative magnitudes?

    • A) A downward gravitational force and an upward normal force, where the gravitational force has a greater magnitude than the normal force.
    • B) A downward gravitational force, an upward normal force, and a downward centripetal force that keeps the cart along the curve.
    • C) A downward gravitational force and an upward normal force of equal magnitude, because the cart has no vertical velocity at the apex.
    • D) A downward gravitational force, an upward normal force, and an upward centrifugal force that prevents the cart from falling.
17. 17.

    Two wooden blocks, labeled block A and block B, are placed in contact on a frictionless horizontal table with block A positioned to the left of block B. A student applies a steady horizontal force to the left side of block A, pushing it toward the right and causing both blocks to accelerate together across the table. When drawing a standard free-body diagram for block B alone, which statement correctly identifies the forces acting on it and the physical reasoning for their inclusion?

    • A) Exactly three forces act on block B: the downward gravitational force, the upward normal force from the table, and the rightward contact force from block A, because the hand does not exert a direct contact force on block B.
    • B) Four forces act on block B: the downward gravitational force, the upward normal force from the table, the rightward contact force from block A, and the forward push from the hand transmitted directly onto block B.
    • C) Four forces act on block B: the downward gravitational force, the upward normal force from the table, the rightward contact force from block A, and a forward net force that accounts for its acceleration.
    • D) Exactly two forces act on block B: the downward gravitational force and the upward normal force from the table, because the horizontal contact force from block A is balanced by an opposing reaction force within block B.
18. 18.

    A small wooden block is launched up a rough inclined ramp and coasts upward along the incline while slowing down, with no hands, cords, or external pushers touching it during this motion. A student constructs a free-body diagram to analyze the forces acting on the block during this upward coasting phase. Which set of forces correctly identifies all external forces acting directly on the block and their directions?

    • A) Gravitational force directed vertically downward, normal force directed perpendicular to the ramp surface, and kinetic friction directed down along the ramp.
    • B) Gravitational force directed vertically downward, normal force directed perpendicular to the ramp surface, kinetic friction directed down along the ramp, and an upward motive force directed up along the ramp.
    • C) Gravitational force directed perpendicular into the ramp, normal force directed vertically upward, and kinetic friction directed down along the ramp.
    • D) Gravitational force directed vertically downward, normal force directed perpendicular to the ramp surface, and kinetic friction directed up along the ramp.
19. 19.

    A delivery van travels toward the right along a straight, horizontal street and applies its brakes, causing it to slow down at a constant rate. A sealed crate resting on the flat horizontal floor of the van remains completely stationary relative to the floor throughout this braking period. When drawing a standard free-body diagram for the crate during this motion, which set of forces correctly represents every external force acting on it?

    • A) Four forces: a downward gravitational force, an upward normal force, static friction pointing to the right, and an inertial force pointing to the left.
    • B) Four forces: a downward gravitational force, an upward normal force, kinetic friction pointing to the left, and a forward momentum force pointing to the right.
    • C) Three forces: a downward gravitational force, an upward normal force, and a forward contact force pointing to the right that keeps the crate moving.
    • D) Three forces: a downward gravitational force, an upward normal force from the floor, and static friction pointing to the left.
20. 20.

    A student analyzes a crate being pulled across a rough horizontal floor at a constant velocity by a taut cable angled at 30° above the horizontal. In constructing the free-body diagram for the crate, the student must accurately account for all external forces acting directly on it. Which statement correctly identifies the forces that must be included and their physical relationship?

    • A) Exactly four forces are drawn: downward gravity, upward normal force, tension angled along the cable, and backward kinetic friction, where the normal force is smaller in magnitude than the crate's weight.
    • B) Exactly five forces are drawn: downward gravity, upward normal force, tension angled along the cable, backward kinetic friction, and a forward applied force of motion required to maintain constant velocity.
    • C) Exactly four forces are drawn: downward gravity, upward normal force, tension angled along the cable, and backward kinetic friction, where the normal force has a magnitude equal to the crate's weight.
    • D) Exactly six forces are drawn: downward gravity, upward normal force, backward kinetic friction, tension along the cable, and the separate horizontal and vertical resolved components of the cable tension.