Free-body diagrams Transitional Reasoning Practice

Questions

1. 1.

   A maintenance technician holds a portable sensor of weight $W$ stationary against a flat, horizontal ceiling by exerting a steady upward force of magnitude $F$ perpendicular to the ceiling. The sensor remains completely at rest, and air resistance is negligible. Which statement correctly identifies the forces acting on the free-body diagram of the sensor and compares the magnitude of the applied force $F$ to the sensor's weight $W$?

   • A) The free-body diagram contains only an upward applied force $F$ and a downward gravitational force $W$, where $F = W$.
   • B) The free-body diagram contains an upward applied force $F$, an upward normal force from the ceiling, and a downward gravitational force $W$, where $F < W$.
   • C) The free-body diagram contains an upward applied force $F$, an upward normal force from the ceiling, and a downward gravitational force $W$, where $F + F_N = W$.
   • D) The free-body diagram contains an upward applied force $F$, a downward gravitational force $W$, and a downward normal force from the ceiling, where $F > W$.
2. 2.

   In a physics laboratory, a cart of mass $M$ on a frictionless, horizontal track is connected by a taut, light string passing over an ideal pulley to a hanging block of weight $W$. When the system is released from rest, the cart accelerates along the track while the hanging block accelerates downward. Assuming air resistance and pulley friction are negligible, which statement correctly identifies the forces acting on the free-body diagram of the hanging block alone and compares their magnitudes?

   • A) The free-body diagram includes only an upward tension force and a downward gravitational force, with the tension force equal in magnitude to the weight ($T = W$).
   • B) The free-body diagram includes an upward tension force, a downward gravitational force, and a downward contact force transmitted from the cart, with the tension force exceeding the weight ($T > W$).
   • C) The free-body diagram includes only an upward tension force and a downward gravitational force, with the downward gravitational force exceeding the upward tension force in magnitude ($W > T$).
   • D) The free-body diagram includes only an upward tension force and a downward gravitational force, with the upward tension force exceeding the downward gravitational force in magnitude ($T > W$).
3. 3.

   A parcel rests on a flat horizontal conveyor belt in a logistics facility. The belt moves horizontally to the right at a constant velocity, and the parcel travels along with it without slipping. Assuming air resistance is negligible, which statement correctly identifies all forces that must appear on the parcel's free-body diagram?

   • A) The free-body diagram contains only two forces: a downward gravitational force and an upward normal force of equal magnitude, with zero horizontal force acting on the parcel.
   • B) The free-body diagram contains three forces: a downward gravitational force, an upward normal force, and a forward static friction force exerted by the belt to maintain the rightward motion.
   • C) The free-body diagram contains three forces: a downward gravitational force, an upward normal force, and a forward kinetic friction force produced because the conveyor belt is moving.
   • D) The free-body diagram contains four forces: a downward gravitational force, an upward normal force, a forward applied force of motion, and a backward static friction force that balance each other.
4. 4.

   A wooden block of weight $W_1$ rests on a flat horizontal table, and a brass weight of magnitude $W_2$ is placed on top of the block so that both objects remain stationary. When constructing a free-body diagram for the wooden block alone, which statement correctly identifies the forces acting on the block and relates their magnitudes?

   • A) Two forces act on the block: a single downward gravitational force of combined magnitude $W_1 + W_2$ and an upward normal force from the table of magnitude $W_1 + W_2$.
   • B) Two forces act on the block: the downward gravitational force on the block of magnitude $W_1$ and an upward normal force from the table of magnitude $W_1$, because the weight of the brass object acts only on itself.
   • C) Three forces act on the block: the downward gravitational force of the Earth ($W_1$), a downward normal contact force from the brass weight (magnitude $W_2$), and an upward normal force from the table of magnitude $W_1 + W_2$.
   • D) Four forces act on the block: the downward gravitational force on the block ($W_1$), the downward gravitational force on the brass weight ($W_2$), a downward normal contact force from the brass weight, and an upward normal force from the table.
5. 5.

   A laboratory cart of weight $W$ is held stationary on a smooth, frictionless ramp inclined at an angle $\theta$ ($0^\circ < \theta < 90^\circ$) relative to the horizontal by a light cord aligned parallel to the incline surface. The upper end of the cord is anchored to a fixed support at the top of the ramp, and air resistance is negligible. Which statement correctly identifies the forces acting on the cart's free-body diagram and relates the cord tension $T$ to the cart's weight $W$?

   • A) Exactly four forces act on the cart (weight vertically downward, a normal force perpendicular to the ramp, cord tension directed up the incline, and a separate downhill gravity force), and the tension magnitude satisfies $T = W$.
   • B) Exactly three forces act on the cart (weight vertically downward, a normal force directed vertically upward, and cord tension directed up the incline), and the tension magnitude satisfies $T = W$.
   • C) Exactly three forces act on the cart (weight vertically downward, a normal force perpendicular to the ramp, and cord tension directed horizontally), and the tension magnitude satisfies $T > W$.
   • D) Exactly three forces act on the cart (weight vertically downward, a normal force perpendicular to the ramp, and cord tension directed up the incline), and the tension magnitude satisfies $T < W$.
6. 6.

   A tetherball of weight $W$ is tied to the top of a vertical pole by a light cord and swings in a horizontal circle at a constant speed. The cord remains taut and makes a constant non-zero angle with the vertical throughout the motion, while air resistance is negligible. When analyzed from an inertial frame of reference, which statement correctly identifies the forces on the ball's free-body diagram and compares the tension magnitude $T$ in the cord to the ball's weight $W$?

   • A) Three forces act on the ball: the downward weight, the tension directed along the cord, and an inward centripetal force; the tension magnitude $T$ is equal to $W$.
   • B) Three forces act on the ball: the downward weight, the tension directed along the cord, and an outward centrifugal force; the tension magnitude $T$ is greater than $W$.
   • C) Exactly two forces act on the ball: the downward weight and the tension directed along the cord; the tension magnitude $T$ is greater than $W$.
   • D) Exactly two forces act on the ball: the downward weight and the tension directed along the cord; the tension magnitude $T$ is equal to $W$.
7. 7.

   A child rides a playground swing moving along a vertical circular arc. As the swing passes through the lowest point of its path while moving forward at maximum speed, air resistance is negligible. Which statement correctly identifies the forces that must appear on the child's free-body diagram in an inertial reference frame and compares their magnitudes?

   • A) An upward normal force from the seat, a downward gravitational force, and a forward force of motion; the upward normal force is equal in magnitude to the downward gravitational force.
   • B) Only an upward normal force from the seat and a downward gravitational force; the upward normal force is equal in magnitude to the downward gravitational force.
   • C) Only an upward normal force from the seat and a downward gravitational force; the upward normal force is greater in magnitude than the downward gravitational force.
   • D) Only an upward normal force from the seat and a downward gravitational force; the upward normal force is less in magnitude than the downward gravitational force.
8. 8.

   A robotic rover navigates a flat, unbanked circular track on a horizontal testing floor at a constant speed without skidding. Air resistance is negligible, and the rover maintains uniform circular motion solely through tire-ground interactions. Which statement correctly identifies the forces that must be included on the rover's free-body diagram when analyzed from an inertial reference frame and describes the direction of the net force?

   • A) Four forces must be included: downward gravity, an upward normal force, an inward static friction force, and an outward centrifugal force that keeps the net force equal to zero.
   • B) Three forces must be included: downward gravity, an upward normal force, and an outward static friction force directed away from the center of curvature, resulting in a net force pointing radially outward.
   • C) Three forces must be included: downward gravity, an upward normal force, and an inward static friction force directed toward the center of the curve, resulting in a net force directed horizontally inward.
   • D) Two forces must be included: downward gravity and a contact normal force tilted inward toward the center of the curve, where the horizontal component of the normal force produces the inward net force.
9. 9.

   A small decorative ornament hangs from a light string attached to the ceiling of a commuter train. As the train accelerates forward along a straight, horizontal track at a constant rate, the string swings backward and remains tilted at a steady angle relative to the vertical. When analyzed from an inertial reference frame, which statement correctly identifies the forces acting on the ornament's free-body diagram and describes the direction of the net force?

   • A) Three forces: the downward gravitational force, the tension force along the string, and a backward inertial force pushing the ornament, producing a net force of zero.
   • B) Three forces: the downward gravitational force, the tension force along the string, and a forward contact force exerted directly by the train, producing a net force directed diagonally upward and forward.
   • C) Two forces: the downward gravitational force and the tension force pulling upward and backward along the string, producing a net force directed horizontally backward.
   • D) Two forces: the downward gravitational force and the tension force pulling upward and forward along the string, producing a net force directed horizontally forward.
10. 10.

    Two crates, Box 1 and Box 2, rest in contact side by side on a smooth, frictionless horizontal floor. A worker pushes horizontally to the right against the outer side of Box 1 with a constant force $F$, causing both crates to accelerate together to the right across the floor. Which statement correctly identifies the forces that must be included on the free-body diagram of Box 2 alone and explains its horizontal motion?

    • A) The free-body diagram of Box 2 must include the worker's applied force $F$, the downward gravitational force, and the upward normal force from the floor, because the external force is transmitted equally to all objects in the system.
    • B) The free-body diagram of Box 2 must include a rightward contact force from Box 1, an equal leftward reaction force opposing Box 1, the downward gravitational force, and the upward normal force from the floor.
    • C) The free-body diagram of Box 2 must include only its downward gravitational force, the upward normal force from the floor, and a rightward normal force exerted by Box 1, which acts as the unbalanced horizontal force causing its acceleration.
    • D) The free-body diagram of Box 2 must include both the worker's pushing force $F$ and a rightward contact force from Box 1, alongside the downward gravitational force and upward normal force from the floor.
11. 11.

    An illuminated museum display of weight W hangs in static equilibrium from two identical, light cables anchored to a ceiling. Each cable pulls upward and outward, making an angle of 30° with the horizontal. Which statement correctly identifies the forces on the free-body diagram of the display and accurately relates the tension magnitude T in each cable to the display's weight W?

    • A) The free-body diagram includes a downward gravitational force of magnitude W and two tension forces of magnitude T directed upward and outward along each cable; applying vertical equilibrium gives $2T \sin 30^\circ = W$, which results in $T = W$.
    • B) The free-body diagram includes a downward gravitational force of magnitude W and two tension forces of magnitude T directed upward and outward along each cable; assuming the two cables share the weight equally without angular dependence yields $T = W / 2$.
    • C) The free-body diagram includes a downward gravitational force of magnitude W and two tension forces of magnitude T directed upward and outward along each cable; projecting the tension with cosine yields $2T \cos 30^\circ = W$, which results in $T = W / (2 \cos 30^\circ)$.
    • D) The free-body diagram includes a downward gravitational force of magnitude W, two tension forces of magnitude T directed downward along the cables, and an upward normal force exerted by the air to maintain equilibrium.
12. 12.

    An elevator cab suspended by a single steel cable is moving downward toward the ground floor while slowing down at a constant rate. Air resistance and guide-rail friction are negligible. Which statement correctly identifies the forces acting on the free-body diagram of the elevator cab and compares their magnitudes?

    • A) The diagram includes an upward tension force, a downward gravitational force, and a downward force of motion; the upward tension is equal in magnitude to the downward gravitational force.
    • B) The diagram includes only an upward tension force and a downward gravitational force; the magnitude of the tension force is greater than the magnitude of the gravitational force.
    • C) The diagram includes only an upward tension force and a downward gravitational force; the magnitude of the gravitational force is greater than the magnitude of the tension force because the cab is moving downward.
    • D) The diagram includes an upward tension force, a downward gravitational force, and an upward deceleration force; the magnitude of the tension force is less than the magnitude of the gravitational force.
13. 13.

    A researcher holds a sensor unit stationary against a vertical concrete wall by applying a steady horizontal pushing force perpendicular to the wall. The unit remains completely motionless, and aerodynamic effects are negligible. Which statement correctly identifies the forces acting on the unit's free-body diagram and describes their equilibrium conditions?

    • A) The free-body diagram contains three forces, with the horizontal push balanced by static friction and the downward gravitational force balanced by the wall's normal force.
    • B) The free-body diagram contains four forces, where the upward static friction force equals the maximum possible friction value $\mu_s F_N$ regardless of the unit's actual weight.
    • C) The free-body diagram contains four forces, where the upward static friction force balances the unit's downward gravitational force and the outward normal force balances the horizontal pushing force.
    • D) The free-body diagram contains five forces, requiring the horizontal force exerted by the unit on the wall to be drawn alongside the wall's normal force to maintain horizontal balance.
14. 14.

    A delivery truck carrying a heavy wooden crate accelerates forward along a straight, horizontal highway. The crate remains stationary relative to the truck bed without slipping, and aerodynamic drag on the crate is negligible. Which statement correctly identifies the forces acting on the crate's free-body diagram and explains the horizontal acceleration of the crate?

    • A) Four forces act on the crate: downward gravity, an upward normal force, a forward applied force from the truck's engine, and a backward static friction force opposing motion.
    • B) Three forces act on the crate: downward gravity, an upward normal force, and a forward contact push from the engine, with friction playing no role because the crate does not slide.
    • C) Four forces act on the crate: downward gravity, an upward normal force, a forward static friction force, and an equal backward inertial force that keeps the crate at rest relative to the bed.
    • D) Exactly three forces act on the crate: downward gravity, an upward normal force, and a forward static friction force, which provides the net horizontal force causing the crate to accelerate.
15. 15.

    A testing block is given a brief shove at the bottom of a straight ramp inclined at $25^\circ$ to the horizontal and then released. The block slides upward along the rough ramp surface while slowing down, with no hands or launching mechanisms remaining in contact with it. Assuming air resistance is negligible, which statement correctly identifies the forces that must be included on the block's free-body diagram during this upward slide and describes the direction of the net force?

    • A) Four forces act on the block: gravity directed vertically downward, the normal force perpendicular to the ramp, kinetic friction directed down the ramp, and an applied force directed up the ramp; the net force is directed up the ramp.
    • B) Exactly three forces act on the block: gravity directed vertically downward, the normal force perpendicular to the ramp, and kinetic friction directed up the ramp; the net force is zero.
    • C) Exactly two forces act on the block: the normal force perpendicular to the ramp and the parallel component of gravity down the ramp; the net force is directed down the ramp.
    • D) Exactly three forces act on the block: gravity directed vertically downward, the normal force perpendicular to the ramp, and kinetic friction directed down the ramp; the net force is directed down the ramp parallel to the incline.
16. 16.

    A robotic rover pushes a sample container across a flat horizontal surface at a constant velocity by exerting a contact force directed downward and forward at an angle below the horizontal. Kinetic friction between the container and the horizontal surface is not negligible, and air resistance is negligible. Which statement correctly identifies the forces acting on the container's free-body diagram and compares the magnitude of the normal force $F_N$ to the container's weight $W$?

    • A) Four forces act on the container (gravity, normal force, applied force, and friction), and $F_N < W$ because friction opposes the forward motion.
    • B) Four forces act on the container (gravity, normal force, applied force, and friction), and $F_N > W$ because the applied force has a downward vertical component.
    • C) Five forces act on the container (gravity, normal force, applied force, friction, and forward force of motion), and $F_N = W$ because vertical acceleration is zero.
    • D) Three forces act on the container (gravity, normal force, and net applied force), and $F_N > W$ because the container moves at constant velocity.

Answers and step-by-step solutions appear after you finish the test.