Figure 12-49a shows a vertical uniform beam of length L that is hinged at its lower end. A horizontal force is applied to the beam at distance y from the lower end. The beam remains vertical because of a cable attached at the upper end, at angle with the horizontal. Figure 12-49a gives the tension T in the cable as a function of the position of the applied force given as a fraction y/L of the beam length. The scale of the T axis is set by . Figure gives the magnitude Fh of the horizontal force on the beam from the hinge, also as a function of y/L. Evaluate (a) angle and (b) the magnitude of .
The scale of the T axis is set by .
If net torque acting on the system is zero, the object is said to be in equilibrium. This can happen when there are more than one torque acting on the object in a different direction such that the vector sum of all the torques acting on the object is zero. As per Newton’s first law, if there is no torque acting on the system, the object will continue its state of rest or state of angular motion.
With the pivot at the hinge, the net torque zero. It can be written as,
This leads to,
It can be interpreted as the slope on the tension graph. To get use,
Substitute equation (ii), the result implies that the slope on the graph is equal to -fa or fa =300. Thus substituting this value we get,
The magnitude of the slope of Fh graph is equal to the magnitude of .
Consider point A and point B on Fh graph as shown in figure below.
The slope is calculated as,
Thus, the magnitude of
A uniform cube of side length rests on a horizontal floor.The coefficient of static friction between cube and floor is m. A horizontal pull is applied perpendicular to one of the vertical faces of the cube, at a distance above the floor on the vertical midline of the cube face. The magnitude of is gradually increased. During that increase, for what values of will the cube eventually (a) begin to slide and (b) begin to tip? (Hint: At the onset of tipping, where is the normal force located?)
In Fig. 12-68, an 817 kg construction bucket is suspended by a cable A that is attached at O to two other cables B and C, making angles and with the horizontal. Find the tensions in (a) cable A, (b) cable B, and (c) cable C. (Hint: To avoid solving two equations in two unknowns, position the axes as shown in the figure.)
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