Spring forces and Hooke's law Transitional Reasoning Download PDF

Questions

1. 1.

   In an Atwood machine apparatus, an ideal, massless pulley is suspended from a rigid ceiling by an ideal vertical spring with a spring constant of $600\text{ N/m}$. A light, inextensible cord passes over the pulley, connecting a $3.0\text{ kg}$ block on one side to a $1.0\text{ kg}$ block on the other. If the blocks are released from rest and accelerate freely without cord slippage, what is the steady elongation of the supporting spring during this motion? (Assume $g = 10\text{ m/s}^2$ and neglect friction.)

   • A) 5.0 cm
   • B) 6.7 cm
   • C) 2.5 cm
   • D) 3.3 cm
2. 2.

   A lower block of mass 3.0 kg rests on a frictionless horizontal floor, and an upper block of mass 1.0 kg is placed on top of it. An ideal horizontal spring with a force constant of 200 N/m connects the upper block to a fixed vertical wall, while the lower block is free of any direct connection. The coefficient of static friction between the two blocks is 0.30. If the upper block is pulled away from the wall to stretch the spring and the entire system is released from rest, what is the maximum extension of the spring such that the lower block accelerates together with the upper block without slipping immediately after release? (Assume $g = 10\text{ m/s}^2$).

   • A) 1.5 cm
   • B) 3.0 cm
   • C) 6.0 cm
   • D) 2.0 cm
3. 3.

   A laboratory apparatus consists of a block of mass 3.0 kg on a smooth, frictionless horizontal bench, connected by a light cord passing over an ideal pulley to a hanging block of mass 2.0 kg. A light spring with a force constant of 400 N/m is spliced into the horizontal segment of the cord. The system is released from rest and accelerates freely without spring oscillations. What is the steady extension of the spring during this motion? (Assume $g = 10\text{ m/s}^2$).

   • A) 3.0 cm
   • B) 5.0 cm
   • C) 2.0 cm
   • D) 8.0 cm
4. 4.

   An optical calibration sled of mass 2.0 kg rests on a frictionless horizontal rail between two rigid end supports. The sled is attached to the left support by an ideal spring of force constant 120 N/m and to the right support by an ideal spring of force constant 180 N/m, with both springs unstretched at the central neutral position. A mechanism displaces the sled 5.0 cm to the right of its neutral position and releases it from rest. What is the magnitude of the sled's initial acceleration immediately after release?

   • A) 7.5 m/s²
   • B) 4.5 m/s²
   • C) 3.0 m/s²
   • D) 1.5 m/s²
5. 5.

   A robotic positioning system holds a 4.0 kg crate stationary on a horizontal floor by pressing it against an ideal horizontal spring fixed to a vertical wall. The spring has a force constant of 500 N/m and is maintained at a steady compression of 12 cm. The coefficient of static friction between the crate and the floor is 0.35. What is the minimum horizontal force the robotic system must apply to the crate to keep it stationary at this compression? (Assume g = 10 m/s²).

   • A) 14 N
   • B) 46 N
   • C) 60 N
   • D) 74 N
6. 6.

   An automated transport rover pulls a 50 kg supply cart along a straight horizontal track using an elastic hitch spring with a force constant of 500 N/m. A constant kinetic friction force of 40 N opposes the cart's motion. If the rover and cart accelerate forward together at 1.2 m/s², what is the steady elongation of the hitch spring?

   • A) 0.04 m
   • B) 0.08 m
   • C) 0.12 m
   • D) 0.20 m
7. 7.

   An automated inspection device uses a horizontal spring with a force constant of 200 N/m to hold a 2.0 kg instrument module firmly against a vertical wall. The coefficient of static friction between the module and the wall is 0.50. What is the minimum compression of the spring required to prevent the module from sliding down under its own weight? (Assume g = 10 m/s²).

   • A) 0.05 m
   • B) 0.20 m
   • C) 0.10 m
   • D) 0.40 m
8. 8.

   A testing apparatus holds a 4.0 kg cart on a frictionless track inclined at 30° above the horizontal, secured to a top anchor by an ideal spring with a force constant of 250 N/m. An actuator applies a constant 30 N force pulling the cart parallel to and down the incline, resulting in an acceleration of 2.5 m/s² down the ramp. What is the elongation of the spring during this motion? (Assume g = 10 m/s²).

   • A) 0.16 m
   • B) 0.20 m
   • C) 0.08 m
   • D) 0.24 m
9. 9.

   A laboratory setup consists of Block A of mass 3.0 kg and Block B of mass 2.0 kg resting on a frictionless horizontal track, connected to each other by an ideal spring with a force constant of 240 N/m. A technician pulls Block B horizontally with a constant force of 20 N, causing both blocks to accelerate together along the track without relative oscillation. What is the steady elongation of the spring during this acceleration?

   • A) 2.5 cm
   • B) 3.3 cm
   • C) 8.3 cm
   • D) 5.0 cm
10. 10.

    A student designs an experiment to monitor the motion of an elevator carrying sensitive research equipment. A test package of mass 2.0 kg is suspended from a vertical ideal spring with a force constant of 100 N/m. When the elevator accelerates upward from rest at a constant rate of 2.5 m/s2, what is the total elongation of the spring? (Assume g = 10 m/s2).

    • A) 5 cm
    • B) 15 cm
    • C) 20 cm
    • D) 25 cm