Spring forces and Hooke's law Transitional Reasoning Practice

Questions

1. 1.

   In an optical alignment mechanism, a small 0.50 kg slider is positioned on a frictionless horizontal track between two rigid end supports. The slider is connected to the left support by Spring 1 with a spring constant of 300 N/m and to the right support by Spring 2 with a spring constant of 500 N/m, such that both springs are relaxed at the central position. A technician applies a horizontal force to hold the slider stationary at a displacement of 4.0 cm to the right of the central position. What is the magnitude of the applied horizontal force?

   • A) 8.0 N
   • B) 20 N
   • C) 32 N
   • D) 12 N
2. 2.

   A 2.0 kg cart rests on a frictionless horizontal track and is connected to a light horizontal spring with a force constant of 240 N/m. The opposite end of the spring is attached to a light, inextensible cord that runs over a frictionless, massless pulley to a 3.0 kg counterweight hanging vertically. When the system is released from rest and accelerates freely, the spring maintains a constant stretch. Taking $g = 10\text{ m/s}^2$, what is the elongation of the spring during this motion?

   • A) 2.5 cm
   • B) 5.0 cm
   • C) 7.5 cm
   • D) 12.5 cm
3. 3.

   A light cord suspends a 2.0 kg block A from a rigid ceiling, and a light ideal spring connects block A to a 3.0 kg block B hanging directly beneath it in static equilibrium. The cord supporting block A is suddenly cut. Taking g = 10 m/s², what is the magnitude of the instantaneous downward acceleration of block A immediately after the cord is cut?

   • A) 5.0 m/s²
   • B) 10 m/s²
   • C) 15 m/s²
   • D) 25 m/s²
4. 4.

   In a friction-testing experiment, a horizontal spring with a force constant of 160 N/m is attached to a 4.0 kg wooden block resting on a rough horizontal surface. When the free end of the spring is slowly pulled horizontally, the block just begins to slip when the spring is stretched by 5.0 cm. Maintaining this 5.0 cm stretch as the block starts to slide, the block accelerates along the surface at $0.50\text{ m/s}^2$. Taking $g = 10\text{ m/s}^2$, what is the coefficient of kinetic friction between the block and the surface?

   • A) 0.10
   • B) 0.15
   • C) 0.20
   • D) 0.25
5. 5.

   In a parts-sorting system, a 2.0 kg package is held stationary against a rough vertical wall by an ideal horizontal spring with a force constant of 500 N/m. The coefficient of static friction between the package and the wall is 0.40, and the acceleration due to gravity is $g = 10\text{ m/s}^2$. What is the minimum compression of the spring required to prevent the package from sliding downward?

   • A) 10 cm
   • B) 4.0 cm
   • C) 16 cm
   • D) 25 cm
6. 6.

   A light ideal spring is suspended vertically from a rigid ceiling, and its lower end supports a light, frictionless pulley. A light string passing over the pulley connects a 3.0 kg block and a 1.0 kg block. When the blocks are released from rest and accelerate, the spring remains stationary and is observed to stretch by 5.0 cm from its relaxed length. Assuming $g = 10\text{ m/s}^2$, what is the spring constant of the spring?

   • A) 300 N/m
   • B) 400 N/m
   • C) 800 N/m
   • D) 600 N/m
7. 7.

   A light ideal spring with a spring constant of 200 N/m is mounted vertically on a floor, and a 1.0 kg platform is attached to its upper end. A 3.0 kg block rests on the platform, and the combined system moves vertically without the block losing contact. At an instant when the spring is compressed by 12 cm from its relaxed length, what is the magnitude of the normal force exerted by the platform on the block? (Take $g = 10\text{ m/s}^2$.)

   • A) 14 N
   • B) 24 N
   • C) 18 N
   • D) 30 N
8. 8.

   A cart with a mass of 1.5 kg is released on a frictionless ramp inclined at $30^\circ$ above the horizontal, attached to a light ideal spring that is anchored at the top of the incline. As the cart moves down the ramp, the spring stretches and exerts an opposing force parallel to the incline. At the instant the spring has stretched by 5.0 cm from its relaxed length, the cart accelerates down the incline at $2.0\text{ m/s}^2$. Taking $g = 10\text{ m/s}^2$, what is the spring constant of the spring?

   • A) 240 N/m
   • B) 210 N/m
   • C) 150 N/m
   • D) 90 N/m
9. 9.

   Two blocks with masses of 3.0 kg and 2.0 kg rest on a frictionless horizontal floor and are connected by a light spring with a force constant of 200 N/m. A constant horizontal pulling force of 30 N is applied directly to the 2.0 kg block along the line of the spring, causing both blocks to accelerate together. What is the extension of the spring during this motion?

   • A) 6.0 cm
   • B) 9.0 cm
   • C) 12.0 cm
   • D) 15.0 cm
10. 10.

    A student suspends a 0.50 kg block from an ideal vertical spring inside an elevator that is accelerating downward at $2.0\text{ m/s}^2$, observing that the spring stretches by 5.0 cm from its relaxed length. The student then attaches an additional 0.30 kg block directly below the first block and observes the spring while the elevator travels upward at a constant speed of $3.0\text{ m/s}$. Taking $g = 10\text{ m/s}^2$, what is the new stretch of the spring?

    • A) 6.4 cm
    • B) 8.0 cm
    • C) 12.0 cm
    • D) 10.0 cm

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