Pulleys and connected objects Transitional Reasoning Download PDF

Questions

1. 1.

   A vertical pulley system consists of a massless, frictionless pulley suspended from a fixed ceiling. A light, inextensible main cord passes over the pulley, supporting a 2.0 kg block on the left side and a 2.0 kg upper block on the right side. A 1.0 kg lower block is attached directly beneath the upper block by a second light, inextensible cord. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the tension in the cord connecting the two blocks on the right as the system accelerates freely from rest?

   • A) 6.0 N
   • B) 8.0 N
   • C) 10 N
   • D) 12 N
2. 2.

   A physics student investigates how the inertia of a counterweight affects system dynamics. In Trial 1, a cart of mass 3.0 kg on a frictionless horizontal track is accelerated by a suspended 1.0 kg block connected by a light cord passing over an ideal pulley. In Trial 2, the suspended block is removed, and the student pulls the cord vertically downward with a constant force equal to the block's weight of 10 N (taking $g = 10\text{ m/s}^2$). What is the ratio of the cart's acceleration in Trial 2 to its acceleration in Trial 1 ($a_2 / a_1$)?

   • A) $4/3$
   • B) $1$
   • C) $3/4$
   • D) $3/2$
3. 3.

   A technician of mass 60 kg stands on a 20 kg lightweight inspection platform suspended in a warehouse. A light, inextensible cable attached securely to the platform passes upward over an ideal, frictionless pulley fixed to the ceiling, and the technician grips the free end of the cable. By pulling down on the cable, the technician causes both the platform and themselves to accelerate vertically upward at $1.0\text{ m/s}^2$. Taking $g = 10\text{ m/s}^2$, what is the magnitude of the normal force exerted by the platform on the technician?

   • A) 160 N
   • B) 440 N
   • C) 660 N
   • D) 220 N
4. 4.

   A student sets up an Atwood machine consisting of two blocks of masses 0.55 kg and 0.45 kg connected by a light, inextensible cord passing over a frictionless, massless pulley to determine the local acceleration due to gravity. The system is released from rest, and an optical sensor measures that the heavier block descends 0.72 m in 1.2 s. What experimental value for the acceleration due to gravity does this measurement yield?

   • A) 5.0 m/s²
   • B) 10 m/s²
   • C) 12 m/s²
   • D) 15 m/s²
5. 5.

   To investigate the kinetic friction between a wooden block and a horizontal track, a student connects a 2.0 kg block to a 3.0 kg hanging mass using a light, inextensible cord routed over a frictionless pulley. When the system is released from rest, an electronic motion sensor records that the blocks accelerate at $4.0\text{ m/s}^2$. Assuming the cord remains taut and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the coefficient of kinetic friction between the block and the track?

   • A) 0.33
   • B) 0.50
   • C) 0.65
   • D) 0.80
6. 6.

   A student designs an experiment to investigate how tension is distributed through a series of connected bodies. Two identical blocks, 1 and 2, each of mass $m$, rest on a frictionless horizontal table and are joined by a light, inextensible cord labeled A. A second light, inextensible cord labeled B connects block 2 over an ideal pulley at the edge of the table to a third identical block of mass $m$ hanging freely. When the system is released from rest and accelerates, what is the ratio of the tension in cord A to the tension in cord B ($T_A / T_B$)?

   • A) $1/3$
   • B) $2/3$
   • C) $1/2$
   • D) $1$
7. 7.

   A laboratory cart of mass 2.0 kg rests on a frictionless track inclined at $30^\circ$ above the horizontal and connects to a suspended cylinder of mass 3.0 kg by a light, inextensible cord passing over an ideal pulley at the top of the incline. The system is held at rest and then released, allowing the cylinder to descend freely under gravity. Taking $g = 10\text{ m/s}^2$, what is the magnitude of the tension in the connecting cord during the motion?

   • A) 12 N
   • B) 18 N
   • C) 20 N
   • D) 24 N
8. 8.

   In an experiment investigating mechanical advantage and constrained motion, a block of mass 1.0 kg rests on a frictionless horizontal tabletop and is attached to a light, inextensible cord. The cord extends horizontally over an ideal fixed pulley at the edge of the table, loops under an ideal movable pulley supporting a suspended cylinder of mass 6.0 kg, and has its remaining end firmly anchored to the ceiling. Taking $g = 10\text{ m/s}^2$ and neglecting all friction as well as the masses of the cord and pulleys, what is the magnitude of the tension in the cord after the system is released from rest?

   • A) 6.0 N
   • B) 15 N
   • C) 20 N
   • D) 12 N
9. 9.

   In a laboratory demonstration, two blocks of masses 3.0 kg and 1.0 kg are connected by a light, inextensible cord passing over a frictionless, massless pulley that is suspended from the ceiling by a vertical support rod. When the blocks are released from rest and accelerate freely under gravity (taking g = 10 m/s²), what magnitude of downward force is exerted on the support rod by the pulley?

   • A) 15 N
   • B) 20 N
   • C) 40 N
   • D) 30 N
10. 10.

    A student sets up an experiment where a cart of mass 3.0 kg on a frictionless horizontal track is connected by a light cord over an ideal pulley to a hanging 1.0 kg mass. To study how shifting mass affects the motion without changing the total system mass, the student moves a 1.0 kg load from the cart into the hanging mass, resulting in a 2.0 kg cart and a 2.0 kg hanging mass. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what are the acceleration of the system and the tension in the cord after this transfer?

    • A) $a = 2.5\text{ m/s}^2$ and $T = 7.5\text{ N}$
    • B) $a = 5.0\text{ m/s}^2$ and $T = 10\text{ N}$
    • C) $a = 5.0\text{ m/s}^2$ and $T = 20\text{ N}$
    • D) $a = 10\text{ m/s}^2$ and $T = 20\text{ N}$