two forces of 62N and 95N are acting on an object at an angle of30 degree and 60 degree from horizontal in opposite direction . find out total force experienced by the object in horizontal and vertical planes?
F1 = 62N @ 30 Deg., CCW.
F2 = 95N @ 240 Deg., CCW.
X = hor. = 62cos30 + 95cos240 = 6.19 N.
Y = ver. = 62sin30 + 95sin240=-51.3 N.
To find the total force experienced by the object in the horizontal and vertical planes, we need to resolve the given forces into their horizontal and vertical components.
Let's start with the force of 62N at an angle of 30 degrees from the horizontal:
Horizontal component = 62N * cos(30°)
Vertical component = 62N * sin(30°)
Now, let's calculate the force of 95N at an angle of 60 degrees from the horizontal:
Horizontal component = 95N * cos(60°)
Vertical component = 95N * sin(60°)
Adding up the horizontal and vertical components of both forces will give us the total force experienced by the object in each plane.
Horizontal force = (62N * cos(30°)) - (95N * cos(60°))
Vertical force = (62N * sin(30°)) + (95N * sin(60°))
Calculating these values will give us the total force experienced by the object in the horizontal and vertical planes.
To find the total force experienced by the object in the horizontal and vertical planes, we can break down the given forces into their respective horizontal and vertical components.
Let's start with the force of 62N acting at an angle of 30 degrees from the horizontal. We can find its horizontal component by multiplying the magnitude of the force (62N) by the cosine of the angle (30 degrees):
Horizontal component = 62N * cos(30°) ≈ 53.5N
Similarly, we can find its vertical component by multiplying the magnitude of the force (62N) by the sine of the angle (30 degrees):
Vertical component = 62N * sin(30°) ≈ 31N
Now let's move on to the force of 95N acting at an angle of 60 degrees from the horizontal. We can use the same trigonometric functions to find its horizontal and vertical components:
Horizontal component = 95N * cos(60°) ≈ 47.5N
Vertical component = 95N * sin(60°) ≈ 82.4N
Since the two forces are in opposite directions in the horizontal plane, we subtract the horizontal components to find the total horizontal force felt by the object:
Total horizontal force = 47.5N - 53.5N = -6N
Note that the negative sign indicates that the force is in the opposite direction.
Now we can add the vertical components of the two forces to find the total vertical force felt by the object:
Total vertical force = 31N + 82.4N ≈ 113.4N
Therefore, the total force experienced by the object in the horizontal plane is -6N and in the vertical plane is 113.4N.