Question

The cylindrical coordinate robot on a factory’s assembly line is shown in a top view (Figure P4.2). The 50-N force acts on a workpiece being held at the end of the robot’s arm. Express the 50-N force as a vector in terms of unit vectors i and j that are aligned with the x- and y-axes.

 

Figure P4.2

Answer 1

Angle made by the force with the horizontal is,

θ = 70° - 30°

    = 40°

 

Find the force vector using the following relation,

Fi = (-F cos θ)i + (F sin θ)j

 

Here, the force acting is F.

 

Substitute, 50 N for F and 40° for θ in the equation,

F = (-F cos θ)i + (F sin θ)j

   = (-50 × cos 40°)i + (50 × sin 40°)j

   = (38.3 N)i + (32.14 N)j

   = (-38.3i + 32.14j) N

 

Force vector acting on the arm is obtained as (-38.3i + 32.14j)N.

Force vector acting on the arm is obtained as (-38.3i + 32.14j)N.