Forces with magnitudes of 2000 newtons and 900 newtons act on a machine part at angles of 10° and 85° respectively, with the x-axis. find the direction and the magnitude of the resultant of these forces. round to the nearest tenth place.
First, you need to find the components of each force:
F₁x = 2000 cos10 = 1969.6 N F₁y = 2000 sin10 = 347.3 N F₂x = 900 cos85 = 78.4 N F₂y = 900 sin85 = 896.6 N
Then, you have to sum up the same components of the two forces: Rx = F₁x + F₂x = 1969.6 + 78.4 = 2048.0 N Ry = F₁y + F₂y = 347.3 + 896.6 = 1243.9 N
In order to find the magnitude of the resultant, you need to apply the Pythagorean theorem: R = √(Rx² + Ry²) = √ 2048.0² + 1243.9² = 2396.2 N
Now, in order to find the direction (angle), you need to use a bit of trigonometry: α = tan⁻¹ (Ry / Rx) =tan⁻¹ (1243.9 / 2048) = tan⁻¹ (0.60737) =31.3°
Therefore, the answer is: the resultant has a magnitude of 2396.2N with an angle of 31.3° with respect to the x-axys.
