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

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

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.

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 = 252 + 152 – 2(25)(15) cos105° R2 = 625 + 225 – 750 cos105° R2 = 1044.1143 R = 32

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

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

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