You are to program a robotic arm on an assembly line to move in the xy-plane. It

Question

You are to program a robotic arm on an assembly line to move in the xy-plane. Its first displacement is A ; its second displacement is B , of magnitude 6.42 cm and direction 63.5 measured in the sense from the +x-axis toward the -y-axis. The resultant C =A +B of the two displacements should also have a magnitude of 6.42 cm , but a direction 22.4 measured in the sense from the +x-axis toward the +y-axis.

A) Find the component Ax of A

B) Find the component Ay of A .

C) Find the magnitude of A .

D) Find the direction of A  measured in the sense from +x - axis toward the +y - axis.

Explanation / Answer

B = 6.42 Cos63.5 i^ - 6.42 Sin63.5 j^

A = Ax i^ + Ay j^

C = 6.42 Cos22.4 i^ + 6.42 Sin22.4 j^

Given

C = A + B

6.42 Cos22.4 i^ + 6.42 Sin22.4 j^ = Ax i^ + Ay j^ + 6.42 Cos63.5 i^ - 6.42 Sin63.5 j^

comparing the X-components

6.42 Cos22.4 = Ax + 6.42 Cos63.5

Ax = 3.1

comparing the Y-components

6.42 Sin22.4 = Ay - 6.42 Sin63.5

Ay = 8.2

A = sqrt(Ax2 + Ay2) = sqrt(3.12 + 8.22) = 8.77

angle = tan-1(Ay/Ax) = tan-1(8.2/3.1) = 69.33

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.