1. Aim: What is the parallelogram of forces?
Do Now:
One soccer player can kick a ball 40 feet and another player can kick the ball 30 feet. If both players kick the ball at the same time, how far will the ball travel?
HW: Worksheet

2. The angles formed by the two players can be:
180° 0°
90°
60°
100°
and much more······

3. How do we find the combined forces acting on a certain object?
We need to draw a parallelogram based on the two forces
Parallelogram of forces Q P
object
resultant S R
PQ and RQ are vectors that represent two forces
applied to an object at point Q. The resultant (is the diagonal of the parallelogram) of these two forces is represented by the vector SQ.
The amount of resultant is called magnitude.

4. Example:
Two forces of 25 and 15 pounds act on a body so that the angle between them measures 75°. Find the magnitude of the resultant to the nearest pound.
25 lb
75°
15 lb
resultant
15 lb
25 lb
105°
R2 = – 2(25)(15) cos105°
R2 = – 750 cos105°
R2 =
R = 32

5. Exercise: Two forces of 12 pounds and 20 pounds act on
a body with an angle of 60° between them. Find to
the nearest pound, the magnitude of the resultant.
20 lb
60°
12 lb
resultant
12 lb
20 lb
28 lb

6. 2. A resultant force of 143 pounds is needed to
move a heavy box. Two applied forces act at
angles of 35° and 47° with the resultant. Find to
the, nearest pound, the magnitude of the larger
force. L
Box
35° S
47°
143 S L
106 lb

7. 3. Two forces of 25 pounds and 38 pounds act on a
body at an angle of 70°. Find, to the nearest tenth
of a pound, the magnitude of the resultant force.
38 lb
70°
resultant
25 lb
25 lb
38 lb
52.1 lb