Pulleys and connected objects Transitional Reasoning Practice

Questions

1. 1.

   In a laboratory investigation of connected bodies, block A of mass 3.0 kg rests on a frictionless horizontal bench, and block B of mass 1.0 kg is placed directly on top of block A. The coefficient of static friction between block A and block B is 0.60. Block A is connected to a suspended block C of mass $m$ by a light, inextensible cord passing over a frictionless, massless pulley at the edge of the bench. Taking $g = 10\text{ m/s}^2$, what is the maximum value of $m$ such that block B moves together with block A without slipping?

   • A) 6.0 kg
   • B) 4.5 kg
   • C) 3.0 kg
   • D) 2.4 kg
2. 2.

   A technician of mass 60 kg stands on a platform of mass 20 kg suspended by a light, inextensible cable that loops over a fixed, frictionless overhead pulley. One end of the cable is anchored to the platform frame, while the technician firmly holds the other end and pulls downward. As a result, the technician and platform accelerate together vertically upward at 1.0 m/s². Taking $g = 10\text{ m/s}^2$, what is the magnitude of the normal force exerted by the platform on the technician?

   • A) 220 N
   • B) 260 N
   • C) 440 N
   • D) 660 N
3. 3.

   A 4.0 kg block rests on a horizontal table where the coefficient of kinetic friction between the surface and the block is 0.20. Light, inextensible cords tied to opposite sides of the block pass over frictionless pulleys at the table's edges to suspended masses of 3.0 kg on the left and 5.0 kg on the right. When the system is released from rest, what is the magnitude of the acceleration of the connected blocks? (Take $g = 10\text{ m/s}^2$.)

   • A) 1.5 m/s²
   • B) 1.0 m/s²
   • C) 2.5 m/s²
   • D) 3.0 m/s²
4. 4.

   In a physics laboratory investigation, a student suspends a light, frictionless pulley from an overhead spring scale calibrated in newtons. A light, inextensible cord is passed over the pulley, connecting a 3.0 kg block to a 1.0 kg block. The system is released from rest so that the blocks accelerate freely under gravity without swinging. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what reading does the spring scale display while the blocks are moving?

   • A) 15 N
   • B) 20 N
   • C) 30 N
   • D) 40 N
5. 5.

   A student designs an experiment to determine the coefficient of kinetic friction between a 5.0 kg block and a horizontal lab bench. The block is connected by a light, inextensible cord passing over an ideal pulley at the edge of the bench to a suspended 5.0 kg counterweight. Upon releasing the system from rest, the counterweight accelerates downward at a constant rate of 3.0 m/s². Taking $g = 10\text{ m/s}^2$ and neglecting air resistance, what is the coefficient of kinetic friction between the block and the bench?

   • A) 0.40
   • B) 0.30
   • C) 0.70
   • D) 0.20
6. 6.

   A student investigates tension transmission in a laboratory apparatus using three connected blocks. Blocks P and Q, with masses of 2 kg and 3 kg respectively, rest on a frictionless horizontal bench and are connected by a taut, light cord 1. A second light cord, cord 2, connects block Q over an ideal pulley at the edge of the bench to a suspended block R of mass 5 kg. When the system is released from rest, what is the tension in cord 1 connecting blocks P and Q? (Take $g = 10\text{ m/s}^2$.)

   • A) 10 N
   • B) 15 N
   • C) 25 N
   • D) 50 N
7. 7.

   In a physics experiment, a load of mass 2 kg is supported by an ideal movable pulley. One end of a light, inextensible cord is anchored to a ceiling, passes around the movable pulley, loops over a fixed overhead pulley, and connects to a suspended block of mass 2 kg. If the system is released from rest and both cord and pulleys have negligible mass and friction, what is the magnitude of the upward acceleration of the movable pulley? (Take $g = 10\text{ m/s}^2$.)

   • A) $1.0\text{ m/s}^2$
   • B) $2.0\text{ m/s}^2$
   • C) $4.0\text{ m/s}^2$
   • D) $5.0\text{ m/s}^2$
8. 8.

   A cart of mass 4 kg rests on a frictionless plane inclined at $30^\circ$ to the horizontal and is connected to a suspended counterweight of mass $M$ by a light, inextensible string running parallel to the incline over an ideal pulley at the top. The system is initially held at rest in static equilibrium. If the counterweight is subsequently replaced with a new suspended mass equal to $3M$ and the system is released, what is the magnitude of the cart's acceleration? (Take $g = 10\text{ m/s}^2$ and $\sin 30^\circ = 0.5$.)

   • A) $2.0\text{ m/s}^2$
   • B) $2.5\text{ m/s}^2$
   • C) $3.0\text{ m/s}^2$
   • D) $4.0\text{ m/s}^2$
9. 9.

   A cart of mass 2 kg rests on a frictionless horizontal table and is attached to a light, inextensible string that passes over an ideal pulley at the edge of the table. In Trial 1, a hanging block of mass 3 kg is suspended from the free end of the string and released from rest. In Trial 2, the block is removed and a student pulls the string vertically downward with a constant force of 30 N, matching the weight of the removed block. Taking $g = 10\text{ m/s}^2$, what are the accelerations of the cart in Trial 1 ($a_1$) and Trial 2 ($a_2$)?

   • A) $a_1 = 15\text{ m/s}^2$ and $a_2 = 15\text{ m/s}^2$
   • B) $a_1 = 15\text{ m/s}^2$ and $a_2 = 6\text{ m/s}^2$
   • C) $a_1 = 6\text{ m/s}^2$ and $a_2 = 6\text{ m/s}^2$
   • D) $a_1 = 6\text{ m/s}^2$ and $a_2 = 15\text{ m/s}^2$
10. 10.

    In a physics laboratory, a student connects block X of mass 3 kg and block Y of mass 1 kg using a light, inextensible cord passed over a fixed, frictionless pulley. The blocks are released from rest simultaneously so that block X descends while block Y ascends freely. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what are the magnitude of the system's acceleration and the tension in the cord?

    • A) Acceleration is 10 m/s² and tension is 30 N
    • B) Acceleration is 5 m/s² and tension is 20 N
    • C) Acceleration is 5 m/s² and tension is 15 N
    • D) Acceleration is 2.5 m/s² and tension is 15 N

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