Set Study

Notes, problems and apps put together in sections by a Hub 4 Mech member. Follow them in order.

Notes, problems and apps put together in sections by a Hub 4 Mech member. Follow them in order.

Problem Set

Force Vectors Problem Set

ID: l0abh8pht4

160 force vector problems with step-by-step solutions, from the parallelogram law to the dot product: 6 warm-ups, 10 workouts and 4 challenges on each topic.

1Section
Adding Forces
20 items
1. 1.1ProblemProblemWarm-up
  Resultant of Two Forces 60° Apart
2. 1.2ProblemProblemWarm-up
  Hook on a Wall
3. 1.3ProblemProblemWarm-up
  Pulling a Sled
4. 1.4ProblemProblemWarm-up
  Resultant of Two Perpendicular Forces
5. 1.5ProblemProblemWarm-up
  Difference of Two Forces
6. 1.6ProblemProblemWarm-up
  Pulling Down a Tree
7. 1.7ProblemProblemWorkout
  Two Tugboats on a Ship
8. 1.8ProblemProblemWorkout
  Two Tractors on a Stuck Truck
9. 1.9ProblemProblemWorkout
  Moving a Pallet Down an Aisle
10. 1.10ProblemProblemWorkout
  Cable Angle for a Required Resultant
11. 1.11ProblemProblemWorkout
  The Missing Force on a Bracket
12. 1.12ProblemProblemWorkout
  Three Ropes, Two Triangles
13. 1.13ProblemProblemWorkout
  How Big Can the Resultant Be?
14. 1.14ProblemProblemWorkout
  Pulling a Car Out of a Ditch
15. 1.15ProblemProblemWorkout
  Second Force for a Vertical Resultant on a Hook
16. 1.16ProblemProblemWorkout
  Two Dogs and a Sled
17. 1.17ProblemProblemChallenge
  Pulling a Car Out of a Gap
18. 1.18ProblemProblemChallenge
  Dragging a Log
19. 1.19ProblemProblemChallenge
  Three Winches on a Guide Rail
20. 1.20ProblemProblemChallenge
  Moving a Boulder
2Section
Components Along Two Axes
20 items
1. 2.1ProblemProblemWarm-up
  Force Components on Oblique Axes
2. 2.2ProblemProblemWarm-up
  A Force on the Bisector
3. 2.3ProblemProblemWarm-up
  Perpendicular Axes as a Special Case
4. 2.4ProblemProblemWarm-up
  Components and Projections
5. 2.5ProblemProblemWarm-up
  A Lamp on Two Wires
6. 2.6ProblemProblemWarm-up
  A Wall Bracket
7. 2.7ProblemProblemWorkout
  Pulling Out a Stump
8. 2.8ProblemProblemWorkout
  Two Cranes, One Panel
9. 2.9ProblemProblemWorkout
  A Sign on Two Chains
10. 2.10ProblemProblemWorkout
  One Component Is Given
11. 2.11ProblemProblemWorkout
  Choosing the Second Rope
12. 2.12ProblemProblemWorkout
  Components Bigger Than the Force
13. 2.13ProblemProblemWorkout
  Crane Jib
14. 2.14ProblemProblemWorkout
  Setting a Component
15. 2.15ProblemProblemWorkout
  Bicycle Frame
16. 2.16ProblemProblemWorkout
  Components Versus Projections
17. 2.17ProblemProblemChallenge
  Equal Components Along Two Axes
18. 2.18ProblemProblemChallenge
  One Component Twice the Other
19. 2.19ProblemProblemChallenge
  Felling a Tree Safely
20. 2.20ProblemProblemChallenge
  From Components Back to the Force
3Section
Rectangular Components in 2D
20 items
1. 3.1ProblemProblemWarm-up
  A Force in the First Quadrant
2. 3.2ProblemProblemWarm-up
  A Force in the Second Quadrant
3. 3.3ProblemProblemWarm-up
  Direction by a Slope
4. 3.4ProblemProblemWarm-up
  Magnitude and Direction from Components
5. 3.5ProblemProblemWarm-up
  Pulling a Suitcase
6. 3.6ProblemProblemWarm-up
  Components of a Tow Rope Force
7. 3.7ProblemProblemWorkout
  Weight on an Incline
8. 3.8ProblemProblemWorkout
  Pulling Up a Ramp
9. 3.9ProblemProblemWorkout
  Components from Coordinates
10. 3.10ProblemProblemWorkout
  A Known Horizontal Component
11. 3.11ProblemProblemWorkout
  Magnitude and One Component
12. 3.12ProblemProblemWorkout
  Components on Rotated Axes
13. 3.13ProblemProblemWorkout
  Hydraulic Cylinder
14. 3.14ProblemProblemWorkout
  Wind on a Roof Panel
15. 3.15ProblemProblemWorkout
  Three Ways to Give a Direction
16. 3.16ProblemProblemWorkout
  The Calculator Trap
17. 3.17ProblemProblemChallenge
  Choosing the Axes
18. 3.18ProblemProblemChallenge
  From a Component to the Force
19. 3.19ProblemProblemChallenge
  Where to Anchor a Guy Rope
20. 3.20ProblemProblemChallenge
  Components in Two Systems
4Section
Resultant of Coplanar Forces
20 items
1. 4.1ProblemProblemWarm-up
  Two Forces by Components
2. 4.2ProblemProblemWarm-up
  Three Forces on an Eyebolt
3. 4.3ProblemProblemWarm-up
  Three-Way Tug of War
4. 4.4ProblemProblemWarm-up
  Nearly Opposite Forces
5. 4.5ProblemProblemWarm-up
  Adding Cartesian Vectors
6. 4.6ProblemProblemWarm-up
  Wires on a Utility Pole
7. 4.7ProblemProblemWorkout
  Belt on a Pulley
8. 4.8ProblemProblemWorkout
  Slings on a Crane Hook
9. 4.9ProblemProblemWorkout
  Third Force on a Bracket
10. 4.10ProblemProblemWorkout
  Two Unknown Magnitudes
11. 4.11ProblemProblemWorkout
  Gusset Plate
12. 4.12ProblemProblemWorkout
  Making the Resultant Horizontal
13. 4.13ProblemProblemWorkout
  Direction for a Vertical Resultant
14. 4.14ProblemProblemWorkout
  A Robot Gripper
15. 4.15ProblemProblemWorkout
  Two Cables and a Load
16. 4.16ProblemProblemWorkout
  Third Force on a Ring
17. 4.17ProblemProblemChallenge
  The Smallest Resultant of Three Forces
18. 4.18ProblemProblemChallenge
  Two Winches and a Known Pull
19. 4.19ProblemProblemChallenge
  Designing a Member Force
20. 4.20ProblemProblemChallenge
  Two Directions for a Vertical Resultant
5Section
Cartesian Vectors in 3D
20 items
1. 5.1ProblemProblemWarm-up
  Magnitude and Direction Angles
2. 5.2ProblemProblemWarm-up
  The Third Direction Angle
3. 5.3ProblemProblemWarm-up
  Unit Vector of a 3D Vector
4. 5.4ProblemProblemWarm-up
  From Two Angles
5. 5.5ProblemProblemWarm-up
  Drone Thrust
6. 5.6ProblemProblemWarm-up
  A Cable Pulling Down
7. 5.7ProblemProblemWorkout
  The Missing z Component
8. 5.8ProblemProblemWorkout
  Angles with a Sign
9. 5.9ProblemProblemWorkout
  Pointing an Antenna
10. 5.10ProblemProblemWorkout
  Angles from Components
11. 5.11ProblemProblemWorkout
  A Robot Arm
12. 5.12ProblemProblemWorkout
  Rope on a Flagpole
13. 5.13ProblemProblemWorkout
  Elevation and Bearing
14. 5.14ProblemProblemWorkout
  Can These Angles Exist?
15. 5.15ProblemProblemWorkout
  Writing F = F u
16. 5.16ProblemProblemWorkout
  Mooring Chain of a Buoy
17. 5.17ProblemProblemChallenge
  Magnitude from One Component
18. 5.18ProblemProblemChallenge
  Equal Direction Angles
19. 5.19ProblemProblemChallenge
  Half the Force Is Vertical
20. 5.20ProblemProblemChallenge
  A Crane Boom in Space
6Section
Resultant of Forces in 3D
20 items
1. 6.1ProblemProblemWarm-up
  Resultant of Two Cartesian Forces
2. 6.2ProblemProblemWarm-up
  Direction Angles Plus Components
3. 6.3ProblemProblemWarm-up
  Forces Along the Axes
4. 6.4ProblemProblemWarm-up
  Subtracting Vectors
5. 6.5ProblemProblemWarm-up
  Hook in a Ceiling
6. 6.6ProblemProblemWarm-up
  Two Drones, One Parcel
7. 6.7ProblemProblemWorkout
  Two Ways to Give a Direction
8. 6.8ProblemProblemWorkout
  Third Force for a Vertical Resultant in 3D
9. 6.9ProblemProblemWorkout
  Guy Wires on a Mast
10. 6.10ProblemProblemWorkout
  Resultant Along an Axis
11. 6.11ProblemProblemWorkout
  Wind and a Stay Cable
12. 6.12ProblemProblemWorkout
  Three Forces, Three Forms
13. 6.13ProblemProblemWorkout
  Two Unknown Pulls and a Vertical Resultant
14. 6.14ProblemProblemWorkout
  Pulling a Tree Three Ways
15. 6.15ProblemProblemWorkout
  The Other Force from a Known Resultant
16. 6.16ProblemProblemWorkout
  Lifting Frame
17. 6.17ProblemProblemChallenge
  Turning a Force to Cancel a Component
18. 6.18ProblemProblemChallenge
  Holding Down a Balloon
19. 6.19ProblemProblemChallenge
  Smallest Force for a Vertical Resultant
20. 6.20ProblemProblemChallenge
  Choosing Two Equal Forces
7Section
Force Along a Line
20 items
1. 7.1ProblemProblemWarm-up
  Head Minus Tail
2. 7.2ProblemProblemWarm-up
  A Force Toward a Point
3. 7.3ProblemProblemWarm-up
  Guy Wire on a Mast
4. 7.4ProblemProblemWarm-up
  Unit Vector Between Two Points
5. 7.5ProblemProblemWarm-up
  Tent Pole
6. 7.6ProblemProblemWarm-up
  Direction Angles of a Cable
7. 7.7ProblemProblemWorkout
  Two Ropes on a Flagpole
8. 7.8ProblemProblemWorkout
  A Plate on Three Cables
9. 7.9ProblemProblemWorkout
  No Sideways Pull
10. 7.10ProblemProblemWorkout
  A Brace That Pushes
11. 7.11ProblemProblemWorkout
  Rope Across a Room
12. 7.12ProblemProblemWorkout
  Two Cables from One Point
13. 7.13ProblemProblemWorkout
  From Points to Two Angles
14. 7.14ProblemProblemWorkout
  Awning Cable
15. 7.15ProblemProblemWorkout
  Which Way Does the Mast Lean?
16. 7.16ProblemProblemWorkout
  Tension from One Component
17. 7.17ProblemProblemChallenge
  Balancing Three Guy Wires
18. 7.18ProblemProblemChallenge
  Placing an Anchor
19. 7.19ProblemProblemChallenge
  Tensions for a Vertical Lift
20. 7.20ProblemProblemChallenge
  Keeping the Resultant in a Plane
8Section
Dot Product and Projection
20 items
1. 8.1ProblemProblemWarm-up
  Dot Product and Angle
2. 8.2ProblemProblemWarm-up
  Two Edges of a Box
3. 8.3ProblemProblemWarm-up
  Projections of a Force on Two Lines
4. 8.4ProblemProblemWarm-up
  Perpendicular or Not?
5. 8.5ProblemProblemWarm-up
  Cart on a Rail
6. 8.6ProblemProblemWarm-up
  Angle Between Two Cables from Coordinates
7. 8.7ProblemProblemWorkout
  Cable on a Pipe
8. 8.8ProblemProblemWorkout
  Trap Door Hinge
9. 8.9ProblemProblemWorkout
  Space Frame Members
10. 8.10ProblemProblemWorkout
  Cable Force Along a Beam
11. 8.11ProblemProblemWorkout
  Wind on a Solar Panel
12. 8.12ProblemProblemWorkout
  Cable and Pole
13. 8.13ProblemProblemWorkout
  Projection on a Line Through Two Points
14. 8.14ProblemProblemWorkout
  Parallel and Perpendicular Components of a Force
15. 8.15ProblemProblemWorkout
  Angle with the Floor
16. 8.16ProblemProblemWorkout
  Resultant from the Dot Product
17. 8.17ProblemProblemChallenge
  Making a Right Angle
18. 8.18ProblemProblemChallenge
  Smallest Force for a Resultant Along a Line
19. 8.19ProblemProblemChallenge
  Where to Anchor the Cable
20. 8.20ProblemProblemChallenge
  Limiting the Axial Pull

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