A uniform rod with mass M and length L is attached to a horizontal cable at one

Question

A uniform rod with mass M and length L is attached to a horizontal cable at one end and a wall at the other as shown in the figure. The tension, T, exerted by the cable holds the rod in place tilted at an angle as shown. Use the variables listed (in red) above, for symbolic input, along with g. Rod and Wall no extra weight 1. HORIZONTAL FORCES. (a) The net horizontal force on the rod must be equal to because it's . (b) Write a symbolic expression for the horizontal force exerted on the rod by the wall. FH = 2. VERTICAL FORCES. (a) The net vertical force on the rod must be equal to because it's . (b) Write a symbolic expression for the vertical force exerted on the rod by the wall. FV = 3. MOMENT ARMS AND TORQUES. For each force, write symbolic expressions for length of the moment arm and the corresponding torque, assuming the hinge is the pivot point and CCW rotation is positive. (a) Weight of Rod. rperpendicular = cm = (b) Tension in Cable. rperpendicular = cable = (c) Horizontal Force exerted by Hinge. rperpendicular = H = (d) Vertical Force exerted by Hinge. rperpendicular = V = (e) Torque Equation. Sum the torques and apply Newton's Laws for Rotational Motion to obtain a torque equation. = = 4. APPLICATION. What is the angle, , if the hinge exerts a horizontal force of 50 N and a vertical force of 78.5 N? = °

Explanation / Answer

net horizontal forces on the rod,

Fx=T*sin(alpa)

net vertical forces on the rod,

Fy=w+T*cos(alpa)

if length of the rod is l

torque on the rod is,

W*l/2+(T*sin(theta)*l*sin(theta))=T*cos(theta)*l*cos(theta)

and

Fx=50 N

Fy=78.5 N

tan(alpa)=Fy/Fx

tan(alpa)=78.5/50

===> alpa=57.5 degrees

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