Graphically solve for the WORK done if
F= 40N @ 30 degrees and d= 12 @ 0 degrees.
To graphically solve for the work done, we need to use vector addition to find the dot product of force and displacement. Here's how you can solve this problem step by step:
Step 1: Draw a diagram to represent the given information. Start by drawing an arrow to represent the force vector F with a magnitude of 40 N and an angle of 30 degrees measured from the positive x-axis. Label it as F.
Step 2: Draw another arrow to represent the displacement vector d with a magnitude of 12 units and an angle of 0 degrees (along the positive x-axis). Label it as d.
Step 3: Start at the initial point of the force vector F and draw a line parallel to the displacement vector d. Find the point where this line intersects with the displacement vector d. Label this point as P.
Step 4: Measure the length of the line segment between the initial point of F and point P. This line segment represents the magnitude of the force component parallel to the displacement vector d. Label it as Fpar.
Step 5: Measure the length of the line segment between point P and the initial point of the displacement vector d. This line segment represents the magnitude of the force component perpendicular to the displacement vector d. Label it as Fperp.
Step 6: Calculate the work done using the formula: Work = Fpar * d
Step 7: Measure the angle between the force component parallel to the displacement vector (Fpar) and the displacement vector d. This angle represents the cosine of the angle between the force and displacement vectors.
Step 8: Calculate the work done using the formula: Work = F * d * cos(theta)
Step 9: Substitute the given values into the formula to find the work done: Work = 40 N * 12 units * cos(30 degrees).
Step 10: Calculate and simplify the expression to find the numerical value of the work done.
Following these steps, you can graphically solve for the work done using the given force and displacement vectors.