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← Unit 2 Handouts

Topic 2.8: Practice Sheet — Spring Forces

Name: _______________________________ Date: _______________ Period: ______

Directions: For every problem, start from Hooke's Law ($F_s = k\Delta x$, magnitude only) and solve symbolically before substituting numbers.

  1. A spring has a spring constant of $k = 400\text{ N/m}$. Find the force it exerts when compressed $0.05\text{ m}$ from its relaxed length.
  2. A spring stretches $0.15\text{ m}$ when a $3.0\text{ kg}$ mass hangs from it at rest. Find the spring constant $k$.
  3. A different spring has $k = 180\text{ N/m}$. What mass, hung at rest, would stretch it $0.10\text{ m}$?

Comparison Reasoning

  1. A spring with $k = 300\text{ N/m}$ holds a $4.0\text{ kg}$ mass at rest. A second, identical spring instead holds an $8.0\text{ kg}$ mass at rest. a) Find the stretch for each spring. b) Without recalculating from scratch, explain how you could have predicted the ratio between the two stretches just from the ratio of the masses.

Progress Check Style

  1. The graph below (sketch it yourself, or imagine it) shows applied force (N) on the y-axis vs. stretch (m) on the x-axis for a spring, plotted from lab data of five different hanging masses. The best-fit line is straight, passes through the origin, and has a slope of $60\text{ N/m}$. a) What is the spring constant of this spring? b) A student says: "Since the graph is a straight line, this must mean the spring's force doesn't depend on how far it's stretched." Explain what is wrong with this reasoning.

Conceptual

  1. Two identical springs are attached to a cart from opposite sides — one stretched, one compressed by the same amount, as shown below.

    wall |~~~~~[cart]~~~~~| wall
     (stretched)  (compressed)

    Explain, using the restoring-force idea, why both springs push/pull the cart in the SAME direction, even though one is stretched and the other is compressed.

AP Classroom-Style Questions

(Modeled directly on the real Topic 2.8 AP Classroom quiz question styles — multi-spring reasoning, ranking across scenarios, and conceptual "why" justifications.)

  1. Two Springs, One Block. A block on a horizontal surface is attached to two horizontal springs (spring constants $k_1$ and $k_2$), one on each side. Both springs are compressed a distance $\Delta x$ from their unstretched length, and the block remains at rest due to static friction between the block and the surface. Write a symbolic expression for the magnitude of the static friction force acting on the block.
  2. Ranking Across Scenarios. Three identical vertical springs each hold up a hanging block at equilibrium: Scenario A holds mass $m$, Scenario B holds mass $2m$, and Scenario C uses TWO of these identical springs side by side (each sharing the load equally) to hold up mass $2m$. Rank the stretch distances $\Delta x_A$, $\Delta x_B$, and $\Delta x_C$ from smallest to largest, and justify your ranking.
  3. Conceptual: The Submerged Spring. A block hangs at rest from a vertical spring, stretching it to length $L$. The block is then completely submerged in a tank of water and comes to rest again — and the new spring length is LESS than $L$. A student claims the spring constant $k$ must have decreased because of the water. Explain why this reasoning is incorrect, and give the actual explanation for why the spring's length decreased.

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.