Resultants at 90°
Finding the Resultant & Equilibrant of Two Perpendicular Forces
Two forces at 90° to each other combine like the legs of a right triangle
Angle = 90°
Two forces act on a body. Rank the angles between the forces below, from largest resultants to smallest.
Video Instruction
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D. Finding Resultants When the Angle Between Forces = 90°
Ex 1) A 5.0 N force pulls an object north while a 12 N force is pulling the object west.
Find: the resultant.
Scale 1 cm = 1 N???
Two Methods
Method One — Graphical Method
(Draw It!!)
1. Draw vectors to scale (1 N = 1 cm)
2. Make a parallelogram
Protractor 101
3. Draw diagonal (resultant)
4. Find magnitude & direction of vector
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Parallelogram Method
Method Two — Trig. and Pythagorean
(More accurate)
1. Use a² + b² = c² (to find magnitude)
5.0 N² + 12 N² = R²
2. Tan θ = Opp./Adj.
Tan θ = 5.0/12 → θ = ?
Name That Direction
50 degrees N of E, 35 degrees N of W
65 degrees S of W, 80 degrees S of E
Video Instruction
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E. Equilibrant — Balancing Force
Show Me The Physics
Video Instruction
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The Equilibrant is always equal in magnitude and opposite in direction to the resultant.
If the Resultant = 5 N, 53° N of W…
Video Instruction
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Ex 2
Concurrent forces (acting together) of 10. nt east and 10. nt south act on an object.
Resultant & Equilibrant using Trig. & Pythagorean Theorem
Let’s go to the Videotape!
Intermolecular bonds between water molecules are very strong
kentchemistry YouTube Channel
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A 5.0 N force pulls north and a 12 N force pulls west on an object. What is the magnitude of the resultant?
2. How does the equilibrant compare to the resultant?
3. A resultant is 5 N, 53° N of W. What is the equilibrant?
4. Forces of 10. N east and 10. N south act on an object. What is the equilibrant?
5. For two perpendicular forces, which trig function finds the direction of the resultant?
Drone Delivery in a Crosswind
A delivery drone flies horizontally while carrying a package. Its propellers produce a horizontal force of 12.0 N north. A steady crosswind pushes on it with a horizontal force of 5.0 N east.
Diagram 1: Horizontal Forces on the Drone (top view)
What is the magnitude of the resultant horizontal force on the drone?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. What is the direction of the resultant force?
C2. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C3. The operator wants to add a force (from tilted propellers) that cancels only the crosswind. In the top view, north is up and east is to the right. Choose the direction of this added force, and determine its magnitude.
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C4. Later, the crosswind increases to 9.0 N east while the propellers still push 12.0 N north. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the resultant horizontal force on the drone. Then calculate the resultant.
C5. The drone’s propellers can produce a total horizontal force of 12.0 N, and the operator wants the drone’s resultant force to point due north. If the propellers aim partly west to cancel the 5.0-N wind, what is the largest northward force that remains?
C6. Describe how an engineer could use a scaled vector diagram (no calculator) to determine the magnitude and direction of the resultant force on the drone.
