Forces

The Head-to-Tail Method

Adding Vectors Graphically, Tip to Tail

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Do Now warm-up prompt

Head-to-Tail Method — draw vectors tip-to-tail; the resultant runs from the first tail to the last tip.

Given

Two forces, 3 N and 4 N, act at an angle of 90° to each other.
Find: the resultant of these forces.

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Monster Shoot Out Game

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Vector Resultants Simulation

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Finding Resultants

“Head to Tail”

Head-to-tail vector diagram, step 1
Head-to-tail vector diagram, step 2
↓

R = 5 N, 37° N of E

Head-to-tail vector diagram
Head-to-tail resultant diagram
↓

R = 13 N, 22.6° N of W

Head-to-tail vector diagram
Head-to-tail resultant diagram
↓

R = 45 N, 63° S of W

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The Coanda Effect

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When a fluid moves in a single direction, it exerts very little pressure perpendicular to the direction of its flow. The external air pressure keeps the ball in place.

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. In the head-to-tail method, where is the resultant drawn?

2. Forces of 3 N and 4 N act at 90° to each other. What is the magnitude of their resultant?

3. A 4 N east force and a 3 N north force are added head-to-tail. What is the direction of the resultant?

4. A 12 N force west and a 5 N force north are added head-to-tail. What is the magnitude of the resultant?

5. A hair dryer blowing upward can hold a ping pong ball in its stream. Why does the ball stay in place?

NYSSLS Regents Practice · Forces · Vector Models

Forces on an Air-Hockey Puck

Three students blow through straws at an air-hockey puck on a nearly frictionless table. At one instant, the three horizontal forces on the puck are 6.0 N east, 8.0 N north, and 6.0 N west.

What is the resultant force on the puck?

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Multiple choice

C1. Does the order in which the three vectors are drawn head-to-tail change the resultant?

Substitute values

C2. The students change their forces to 11.0 N east, 12.0 N north, and 6.0 N west. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the new resultant. Then calculate the resultant.

R = √((Feast − Fwest)2 + Fnorth2) = √(( N − N)2 + ( N)2) = N
Support or Refute · Justify

C3. A student makes the following claim.

Claim: An object acted on by three forces can never be in equilibrium, because three forces cannot cancel the way two equal and opposite forces do.

Place a check mark in either the Support or Refute box. Justify your response.

Draw the vector · Determine the magnitude

C4. The student blowing north stops, and the student blowing west blows harder, now 9.0 N west. The 6.0-N east force is unchanged. Taking east as to the right, choose the direction of the resultant force on the puck, and determine its magnitude.

puck
●
R = N
Multiple choice

C5. One student stops blowing, so only the 6.0-N east and 8.0-N north forces remain. What is the resultant?

Constructed response

C6. Describe how to use the head-to-tail method to find the resultant of the original three forces on the puck (6.0 N east, 8.0 N north, 6.0 N west), and state what the diagram shows.

Equilibrium →