A heavy concrete panel is being lifted into position in a building by means of a crane (see figure below). The tension of 2.52 104 N in the supporting cable produces a torque with respect to point O. (Let L = 41.0 m.)
(a) Does this torque tend to rotate the panel clockwise or counterclockwise about an axis through point O?
counterclockwise
clockwise
(b) Find the torque.
2
(a) clockwiûe.
(b)
Torque =T•L•cosα- mg•(L/2) •cosα=
=(T - mg/2) •L•cosα
To determine the direction of rotation, we can use the right-hand rule for torque. If we curl the fingers of our right hand in the direction of the rotation, the thumb will point in the direction of the torque vector.
In this case, the thumb points counterclockwise, indicating that the torque tends to rotate the panel counterclockwise about an axis through point O.
To find the torque, we can use the formula:
Torque = Tension * Lever Arm
Given:
Tension (T) = 2.52 * 10^4 N
Lever Arm (L) = 41.0 m
Using the above values, we can calculate the torque:
Torque = 2.52 * 10^4 N * 41.0 m = 1.03 * 10^6 N*m
So, the torque exerted on the concrete panel is 1.03 * 10^6 N*m.
To determine the direction of the torque, we need to consider the right-hand rule. If we imagine gripping the cable with our right hand and curling our fingers in the direction that the cable "winds" around the axis through point O, then our thumb will point in the direction of the torque.
Since the cable is wrapped clockwise around the axis through point O, the torque will be counterclockwise. Therefore, the answer to part (a) is counterclockwise.
To find the torque, we can use the formula:
Torque = Force x Distance
The force in the supporting cable is given as 2.52 x 10^4 N. To find the distance, we need to know the perpendicular distance between the line of action of the force and point O. Since this distance is not given, we cannot calculate the torque without further information.