(a)
The tension in the cable.
(a)
Answer to Problem 4.152RP
The tension in the cable is
Explanation of Solution
The free-body diagram is shown in figure 1.
Write the expression for the tension in the cable.
Here,
Write the expression of the vector
Find the magnitude of the vector
Put equations (II) and (III) in equation (I).
Write the expressions for the position vectors.
Here,
Sum of the moments of the forces about the point A must be zero.
Here,
Write the expression for the sum of the moments about the point A.
Here,
Put the above equation in equation (VI) and use determinants.
Conclusion:
Equate the coefficient of
Thus, the tension in the cable is
(b)
The reactions at A and B.
(b)
Answer to Problem 4.152RP
The reaction at A is
Explanation of Solution
Equate the coefficient of
Here,
Substitute
Equate the coefficient of
Here,
Substitute
Write the expression for
Substitute
Refer figure 1.
The net force must be equal to zero.
Here,
Write the expression for the net force.
Here,
Put the above equation in equation (VIII).
Equate the coefficient of
Equate the coefficient of
Equate the coefficient of
Write the expression of
Conclusion:
Thus, the reaction at A is
Want to see more full solutions like this?
Chapter 4 Solutions
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
- 4.74 For the frame shown, determine the magnitude of the pin reaction at B.Neglect the weight of the frame.arrow_forward4.174 The weight W = 6 kN hangs from the cable which passes over the pulley at F. Neglecting the weights of the bars and the pulley, determine the magnitude of the pin reaction at D.arrow_forwardThe rectangular plate shown weighs 75 lb and is held in the position shown by hinges at A and Band by cable EF . Assuming that the hinge at B does not exert any axial thrust, determine (a) the tension in the cable, (b) the reactions at A and B.arrow_forward
- The spanner shown is used to rotate a shaft. A pin fits in a hole at A, while a flat, frictionless surface rests against the shaft at B. If a 60-lb force P is exerted on the spanner at D, find the reactions at A and B.arrow_forwardA 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C . Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at A and B . Assume that the hinge at B does not exert any axial thrust.arrow_forwardA lever AB is hinged at C and attached to a control cable at A . If the lever is subjected to a 75-lb vertical force at B , draw the freebody diagram needed to determine the tension in the cable and the reaction at C.arrow_forward
- The frame shown supports part of the roof of a small building. Knowingthat the tension in the cable is 150 kN, determine the reaction at thefixed end E.arrow_forwardA 10-kg storm window measuring 900 × 1500 mm is held by hinges at A and B. In the position shown, it is held away from the side of the house by a 600-mm stick CD. Assuming that the hinge at A does not exert any axial thrust, determine the magnitude of the force exerted by the stick and the components of the reactions at A and B.arrow_forwardA 200-mm lever and a 240-mm-diameter pulley are welded to the axleBE, which is supported by bearings at C and D. If a 720-N verticalload is applied at A when the lever is horizontal, determine: (a) the tension in the cord, (b) the reactions at C and D. Assume that thebearing at D does not exert any axial thrust.arrow_forward
- The uniform (18 kg) bar OA is held in the position Shown by the pin at o" and the cable AB. Detemine the tension T in the cable and the magnitude of the reactions at pin o". 1.5 m 60° 1.2 marrow_forwardA foldable tray for the paper supply of a photocopy machine is shown. The tray is supported by a single hinge at A and two slotted links (one on each side of the tray). If the stack of paper weighs 14 N and other weights may be neglected, determine the reactions at point B for one of the links when D = 190 mm.arrow_forwardA light rod AD is supported by frictionless pegs at B and C and rests against a frictionless wall at A. A vertical 120-lb force is applied at D. Determine the reactions at A, B, and C.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L