Pulleys and connected objects Knowledge-Based Practice

Questions

1. 1.

   A light, inextensible cord has one end anchored to the ceiling, wraps underneath a light, frictionless movable pulley supporting a 2 kg load, and then passes over a light, fixed pulley to a hanging 2 kg counterweight. Taking $g = 10\text{ m/s}^2$, what is the magnitude of the acceleration of the counterweight as it descends?

   • A) $2\text{ m/s}^2$
   • B) $4\text{ m/s}^2$
   • C) $5\text{ m/s}^2$
   • D) $8\text{ m/s}^2$
2. 2.

   Two blocks of masses 3 kg and 2 kg resting on a frictionless horizontal tabletop are connected to each other by a light cord, and a second light cord connects the 2 kg block over a massless, frictionless pulley to a hanging 5 kg block. Taking $g = 10\text{ m/s}^2$, what is the tension in the cord between the 3 kg block and the 2 kg block while the system accelerates?

   • A) 10 N
   • B) 25 N
   • C) 15 N
   • D) 50 N
3. 3.

   A light, inextensible cord passing over a frictionless, massless pulley connects a 3 kg block on one side to two 1 kg blocks suspended one beneath the other on the opposite side. Taking $g = 10\text{ m/s}^2$, what is the tension in the cord connecting the two 1 kg blocks while the system accelerates?

   • A) 10 N
   • B) 12 N
   • C) 8 N
   • D) 24 N
4. 4.

   Two blocks of masses 4 kg and 1 kg are connected by a light, inextensible cord passing over a frictionless, massless pulley at the apex of a double incline. If both inclines make an angle of $30^\circ$ with the horizontal and are frictionless, what is the magnitude of the acceleration of the system? (Take $g = 10\text{ m/s}^2$.)

   • A) 3 m/s²
   • B) 5 m/s²
   • C) 6 m/s²
   • D) 1.5 m/s²
5. 5.

   A 5 kg block resting on a horizontal tabletop is connected by a light, inextensible cord passing over a massless, frictionless pulley to a hanging 2 kg block. What is the minimum coefficient of static friction between the 5 kg block and the tabletop required to keep the system at rest? (Take $g = 10\text{ m/s}^2$.)

   • A) 0.40
   • B) 0.29
   • C) 0.50
   • D) 0.67
6. 6.

   A load of mass 4 kg is supported by a light, frictionless movable pulley. One end of a light, inextensible cord is fixed to the ceiling, while the other end is pulled vertically upward with a constant force $F$. If the load accelerates upward at $2\text{ m/s}^2$, what is the magnitude of $F$? (Take $g = 10\text{ m/s}^2$.)

   • A) 16 N
   • B) 20 N
   • C) 48 N
   • D) 24 N
7. 7.

   A frictionless, massless pulley suspended from a fixed ceiling supports two masses of 3 kg and 1 kg connected by a light, inextensible string. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the magnitude of the force exerted by the ceiling on the pulley while the masses are accelerating?

   • A) 15 N
   • B) 30 N
   • C) 40 N
   • D) 20 N
8. 8.

   A 2 kg block resting on a frictionless incline tilted at $30^\circ$ above the horizontal is connected by a light, inextensible cord passing over a frictionless, massless pulley to a hanging 3 kg block. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the magnitude of the acceleration of the system?

   • A) $2\text{ m/s}^2$
   • B) $4\text{ m/s}^2$
   • C) $5\text{ m/s}^2$
   • D) $6\text{ m/s}^2$
9. 9.

   A 4 kg block resting on a frictionless horizontal tabletop is connected by a light, inextensible cord passing over a massless, frictionless pulley to a hanging 1 kg block. Assuming $g = 10\text{ m/s}^2$, what is the magnitude of the acceleration of the system when released from rest?

   • A) 2 m/s²
   • B) 2.5 m/s²
   • C) 6 m/s²
   • D) 10 m/s²
10. 10.

    Two blocks with masses of 3 kg and 2 kg are connected by a light, inextensible cord passing over a frictionless, massless pulley. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the magnitude of the tension in the cord while the blocks are accelerating?

    • A) 10 N
    • B) 20 N
    • C) 24 N
    • D) 30 N

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