Consider the two forces, F1 and F2. Assume that these forces are applied on an object in the xy-plane. The first force has a magnitude F1 = 15 N and is applied in a direction that makes an angle α = 30° with the positive x axis, and the second force has a magnitude F2 = 10 N and is applied in a direction that makes an angle β = 45° with the negative x axis. (a) Calculate the scalar components of F1 and F2 along the x and y directions.

To calculate the scalar components of F1 and F2 along the x and y directions, we can use trigonometry.

For F1: The x-component of F1 can be calculated using the formula: F1x = F1 * cos(α) F1x = 15 N * cos(30°) = 15 N * √3/2 ≈ 12.99 N

The y-component of F1 can be calculated using the formula: F1y = F1 * sin(α) F1y = 15 N * sin(30°) = 15 N * 1/2 = 7.5 N

For F2: The x-component of F2 can be calculated using the formula: F2x = F2 * cos(β) F2x = 10 N * cos(45°) = 10 N * √2/2 = 5√2 N ≈ 7.07 N

The y-component of F2 can be calculated using the formula: F2y = F2 * sin(β) F2y = 10 N * sin(45°) = 10 N * √2/2 = 5√2 N ≈ 7.07 N

So, the scalar components of F1 are approximately F1x = 12.99 N and F1y = 7.5 N. The scalar components of F2 are approximately F2x = 7.07 N and F2y = 7.07 N.