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Topic 3.2: Practice Sheet — Work

Name: _______________________________ Date: _______________ Period: ______

Directions: For every calculation, identify the angle $\theta$ between the force and the displacement first (0°, 90°, 180°, or given), write $W=Fd\cos\theta$, then substitute numbers. Show every step.

  1. A $15\text{ N}$ force pushes a box $3.0\text{ m}$ in the same direction as the force. Find the work done.
  2. A person carries a $50\text{ N}$ bag at constant height while walking $10\text{ m}$ horizontally, with the bag's weight always pointing straight down. Find the work done by gravity on the bag during this walk, and explain your reasoning using the angle between force and displacement.

Angles and Ratios

  1. A force of magnitude $F$ pushes a block a distance $d$ at $30°$ above horizontal, doing work $W_1$. An identical force pushes an identical block the same distance $d$, but at $60°$ above horizontal, doing work $W_2$. Find the ratio $W_1:W_2$.

Multiple Forces

  1. A box of mass $0.5\text{ kg}$ with a fan on top slides up a frictionless ramp a distance of $4.0\text{ m}$. The fan exerts a constant $0.5\text{ N}$ force directly opposite the box's motion. The box rises $1.0\text{ m}$ over that distance. Find the total work done on the box. (Use $g=10\text{ m/s}^2$.)

Reading a Graph

  1. A force-vs-position graph shows a force rising linearly from $0\text{ N}$ at $x=0$ to $8\text{ N}$ at $x=3\text{ m}$, then constant at $8\text{ N}$ from $x=3\text{ m}$ to $x=5\text{ m}$. Find the total work done over the full $5\text{ m}$.
  2. Boxes X and Y are each pushed the same total distance by forces with varying magnitude. The force-vs-position graph for Box X is a triangle rising from $0$ to $1\text{ N}$ over $1\text{ m}$ then dropping back to $0$ over the next $1\text{ m}$. The graph for Box Y is that same triangle PLUS an additional constant $1\text{ N}$ rectangle over the same $2\text{ m}$. a) Find the work done on Box X. b) Find the work done on Box Y. c) Find the ratio $W_X:W_Y$.

AP Classroom-Style Questions

(Modeled directly on the real Topic 3.2 AP Classroom quiz question styles — sign of work, multi-force summing, and the work-energy theorem preview.)

  1. A block accelerates from rest until it reaches a maximum speed, then continues at that constant speed with no further acceleration. Assume frictional forces are negligible. Which of the following statements about the net work done on the block is correct? (A) The net work on the block is nonzero the entire time. (B) Nonzero net work is being done on the block only when it is accelerating. (C) Nonzero net work is being done on the block only when it is moving at constant speed. (D) Whether nonzero net work is being done depends on the block's mass, acceleration, and maximum speed.
  2. One end of a rod of negligible mass is attached to a block, and the other end is attached to a pivot. The block is held with the rod horizontal, then released, and swings down through its lowest point before swinging back up. Frictional forces are negligible. Explain which force(s) do work on the block as it swings down, and why — be specific about the direction of the rod's tension relative to the block's velocity at each instant.
  3. Two spheres are connected by a rod of negligible mass, initially vertical, with a $7.0\text{ kg}$ sphere on top and a $5.0\text{ kg}$ sphere on the bottom. The system is rotated about its center until the rod is horizontal; each sphere moves a vertical distance of $3.0\text{ m}$ during the rotation. Find the total work done by gravity on the system as it rotates from vertical to horizontal. (Use $g=10\text{ m/s}^2$, and be careful with signs.)
  4. A person stands at rest on a skateboard (combined mass $m$) and pushes off, exerting an average horizontal force of magnitude $F$ over a distance $\Delta x$. The skateboard and person then travel up a frictionless ramp to a flat section at height $h$, arriving with speed $v$. Using the work-energy theorem and the fact that the system still has nonzero kinetic energy at the top, explain why $F\Delta x$ must be GREATER than $mgh$, rather than equal to it.

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