Pulleys and connected objects Knowledge-Based Download PDF

Questions

1. 1.

   Two blocks of masses 3 kg and $M$ (where $M > 3\text{ kg}$) are connected by a light, inextensible string passing over a frictionless, massless pulley. If the magnitude of the acceleration of each block is $2.5\text{ m/s}^2$, what is the value of $M$? (Take $g = 10\text{ m/s}^2$.)

   • A) 4 kg
   • B) 4.5 kg
   • C) 6 kg
   • D) 5 kg
2. 2.

   Two blocks of masses 7 kg and 3 kg rest on opposite frictionless surfaces of a fixed triangular wedge, each inclined at $30^\circ$ to the horizontal, and are connected by a light, inextensible string passing over an ideal pulley at the apex. Taking $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.5$, what is the magnitude of the acceleration of the system?

   • A) 1 m/s²
   • B) 2 m/s²
   • C) 3.5 m/s²
   • D) 4 m/s²
3. 3.

   A 4 kg block on a rough horizontal surface with a coefficient of kinetic friction $\mu_k = 0.25$ is connected by a light, inextensible string passing over an ideal pulley to a hanging block of mass 6 kg. Taking $g = 10\text{ m/s}^2$, what is the magnitude of the acceleration of the system once released from rest?

   • A) 3 m/s²
   • B) 4 m/s²
   • C) 5 m/s²
   • D) 6 m/s²
4. 4.

   A load of mass 12 kg is suspended from an ideal, massless movable pulley. A light, inextensible string passes under the pulley, with one end anchored to a rigid ceiling and the other end pulled vertically upward with a constant force of 90 N. Taking g = 10 m/s², what is the magnitude of the upward acceleration of the load?

   • A) 5 m/s²
   • B) 2.5 m/s²
   • C) 7.5 m/s²
   • D) 15 m/s²
5. 5.

   Two blocks, A of mass 2 kg and B of mass 3 kg, rest on a frictionless horizontal table and are connected by a light string, while a second light string connects block B over an ideal pulley at the edge of the table to a hanging block C of mass 5 kg. Taking $g = 10\text{ m/s}^2$, what is the magnitude of the tension in the string connecting block A and block B while the system is in motion?

   • A) 25 N
   • B) 20 N
   • C) 15 N
   • D) 10 N
6. 6.

   A 3 kg block resting on a frictionless horizontal table is connected by two light strings passing over ideal pulleys at opposite edges of the table to hanging blocks of masses 5 kg and 2 kg. Taking $g = 10\text{ m/s}^2$, what is the tension in the string attached to the 2 kg block while the system is in motion?

   • A) 14 N
   • B) 20 N
   • C) 26 N
   • D) 35 N
7. 7.

   A 2 kg block resting on a frictionless ramp inclined at 30° to the horizontal is connected by a light, inextensible string passing over an ideal pulley at the top of the ramp to a hanging 3 kg block. Taking g = 10 m/s² and sin 30° = 0.5, what is the magnitude of the acceleration of the system when released from rest?

   • A) 2 m/s²
   • B) 3 m/s²
   • C) 4 m/s²
   • D) 6 m/s²
8. 8.

   Two blocks with masses of 1 kg and 3 kg are connected by a light, inextensible string passing over a frictionless, massless pulley suspended from a rigid ceiling. Taking $g = 10$ m/s², what is the magnitude of the force exerted by the pulley on the ceiling while the blocks are accelerating?

   • A) 15 N
   • B) 20 N
   • C) 40 N
   • D) 30 N
9. 9.

   A 4 kg block resting on a frictionless horizontal table is connected by a light, inextensible string over an ideal pulley to a hanging 1 kg block. What is the magnitude of the acceleration of the system when released from rest, taking g = 10 m/s²?

   • A) 10 m/s²
   • B) 2.5 m/s²
   • C) 1.6 m/s²
   • D) 2.0 m/s²