As mentioned previously, this tower crane is doing something dangerous. You may
ID: 1847901 • Letter: A
Question
As mentioned previously, this tower crane is doing something dangerous. You may assume that a = 16 m, b = 52 m, c = 7 m, and d = 4 m. If the tension in the cable is 9.5 kN, determine its x, y, and z components. What is the moment caused by this force about the base of the tower crane (point C)? Write it out in vector form. What is the scalar component of the moment about the line connecting point C to point A? What is the vector component of the moment about the line connecting point C to point A? In addition, what is the moment about the rotating point of the boom (where the boom intersects the z axis). Write it out in vector form.
http://web.ics.purdue.edu/~krousgri/me270/?p=3474#comments = picture
Explanation / Answer
position vector of A is 0 i - 16 j + 52k Position vector of B is 4 i - 9j + 0 k Unit vector in the direction of Cable is A- B = (- 4 i - 7j + 52 k) /sqrt(4^2 + 7^2 + 52^2) So force in vector form = 9.5 * (- 4 i - 7j + 52 k) /sqrt(4^2 + 7^2 + 52^2) Force in X direction = 9.5 * 4/sqrt(4^2 + 7^2 + 52^2) = 0.722 KN Force in Y direction = 9.5 * 7/ sqrt(4^2 + 7^2 + 52^2) = 1.264 KN Force in Z direction = 9.5 * 52/ sqrt(4^2 + 7^2 + 52^2) = 9.388 KN Moment = cross product of (position vector, force vector) Moment about point C = position vector of point A x force vector = ( 0 i - 16 j + 52 k) x (9.5 * (-4 i - 7 j + 52 k)/ sqrt(4^2 + 7^2 + 52^2)) By doing cross product we get Moment = - 84.48 i + 0 j + 0 k
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.