The system in Fig. 12-38 is in equilibrium. A concrete block of mass hangs from the end of the uniform strut of mass. A cable runs from the ground, over the top of the strut, and down to the block, holding the block in place. For angles and , find (a) the tension T in the cable and the (b) horizontal and (c) vertical components of the force on the strut from the hinge.
a)The tension in the cable is.
b)Horizontal component of the force is
c) Vertical component of the force is
Theconcrete block of mass
Strut of mass
In the free body diagram of the given situation, we notice the acting torques on the body both horizontally and vertically.Here, the acting torque results from the applied force along the length of the cable hanging from the strut and along the weight of the block to balance it at the strut.The vertical force acting on the body about the hinge is due to the tension resulting from the hanging to the strut, also the downward pull due to the weight of the block, and the downward pull due to the weight of the strut that acts at the center of the strut. Then using Newton's laws of motion, we balance the acting torques in an equation separately for both the horizontal and the vertical directions. Then, accordingly, calculate the required values as per the problem
We note that the angle between the cable and the strut is
The angle between the strut and any vertical force(like the weights in the problem) is
Denotingand as the length of the boom, we compute torques about the hinge and find
The unknown lengthcancels out and we obtain
The tension in the cable is.
Since the cable is at from horizontal, then horizontal equilibrium of forces requires that the horizontal hinge force be
Horizontal component of the force is
Vertical equilibrium of forces gives the vertical hinge force component
Vertical component of the force is
A uniform ladder whose length is and whose weight is leans against a frictionless vertical wall. The coefficient of static friction between the level ground and the foot of the ladder is . What is the greatest distance the foot of the ladder can be placed from the base of the wall without the ladder immediately slipping?
Figure 12-59 shows the stress versus strain plot for an aluminum wire that is stretched by a machine pulling in opposite directions at the two ends of the wire. The scale of the stress axis is set by , in units of . The wire has an initial length of and an initial cross-sectional area of . How much work does the force from the machine do on the wire to produce a strain of?
Question: Figure 12-29 shows a diver of weight 580 N standing at the end of a diving board with a length of L =4.5 m and negligible v mass. The board is fixed to two pedestals (supports) that are separated by distance d = 1 .5 m . Of the forces acting on the board, what are the (a) magnitude and (b) direction (up or down) of the force from the left pedestal and the (c) magnitude and (d) direction (up or down) of the force from the right pedestal? (e) Which pedestal (left or right) is being stretched, and (f) which pedestal is being compressed?
A makeshift swing is constructed by making a loop in one end of a rope and tying the other end to a tree limb. A child is sitting in the loop with the rope hanging vertically when the child’s father pulls on the child with a horizontal force and displaces the child to one side. Just before the child is released from rest, the rope makes an angle of with the vertical and the tension in the rope is .
(a) How much does the child weigh?
(b) What is the magnitude of the (horizontal) force of the father on the child just before the child is released?
(c) If the maximum horizontal force the father can exert on the child is , what is the maximum angle with the vertical the rope can make while the father is pulling horizontally?
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