Forces F\(_1\)(10N, 090°) and F\(_2\)(20N, 210\(^o\)) and (4N,330°) act on a particle, Find, correct to one decimal place, the magnitude of the resultant fo...

Answer Details

To find the magnitude of the resultant force, we need to first calculate the x and y components of each force.

For F1:

• The magnitude is 10 N
• The angle is 90 degrees
• The x component is 10 cos(90) = 0 N
• The y component is 10 sin(90) = 10 N

For F2:

• The magnitude is 20 N
• The angle is 210 degrees
• The x component is 20 cos(210) = -17.3 N (negative because it points to the left)
• The y component is 20 sin(210) = -10 N (negative because it points downwards)

For F3:

• The magnitude is 4 N
• The angle is 330 degrees
• The x component is 4 cos(330) = 3.5 N (positive because it points to the right)
• The y component is 4 sin(330) = -2 N (negative because it points downwards)

To find the total x and y components, we can add up the individual x and y components:

• The total x component is 0 - 17.3 + 3.5 = -13.8 N
• The total y component is 10 - 10 - 2 = -2 N

To find the magnitude of the resultant force, we can use the Pythagorean theorem:

resultant force = sqrt((-13.8)^2 + (-2)^2) = 13.9 N

Therefore, the magnitude of the resultant force is 13.9 N.