Three forces are acting on a large boulder. The first force is pulled with a force of 550 N due North while the second force is being pulled with a force of 325 N at an angle of 30° North of West. The third rope is being pulled with a force of 475 N due South. (a) Draw the vector diagram of theses vectors. (b) Calculate Rx of the resultant force acting on the boulder. (c) Calculate Ry of the resultant force acting on the boulder. (d) What is the magnitude of the resultant force? (e) What is the direction of the resultant force? (f) Draw the vector diagram of the magnitude and direction of the resultant force showing its horizontal and vertical components.
Answers
Given : Three forces are acting on a large boulder.
To Find : Calculate Rx of the resultant force acting on the boulder. Calculate Ry of the resultant force acting on the boulder.
Solution:
in North = 550 N
in South = 475 N = -475 N in North
325 N at an angle of 30° North of West
=> 325Cos30° in West and 325Sin30° in North
=> 281.46 N in West and 162.5 in North
281.46 N in West = -281.46 N in East
Hence
Rx = -281.46 N
Ry = 550 - 475 + 162.5 = 237.5N
Magnitude = √(-281.46)² + (237.5)² = 368.273 N
Direction of resultant vector = 180° - tan⁻¹(237.5 / 281.46) = 180 - 40.16°
Hence 40.16° North of West.
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