The 125-kg homogeneous rectangular solid is held in the arbitrary position shown by the

The rack for storing automobile wheels consists of two parallel rods A and B. Determine the magnitude of the force P required to begin extracting the wheel. The mass of the wheel is m. Neglect all friction.

The positioning device locks the sliding panel C into place relative to the fixed panel D, to which the device is attached. Pressing at E rotates the moving part of the device clockwise about O, retracting the pin AB from the hole in panel C. If a force P = 40 N is required to begin clockwise rotation of the device, determine the moment M about point O exerted by the internal coiled spring S.

The light bracket ABC is freely hinged at A and is constrained by the fixed pin in the smooth slot at B. Calculate the magnitude R of the force supported by the pin at A under the action of the \(80-N \cdot m\) applied couple.

The uniform bar with end rollers weighs 60 lb and is supported by the horizontal and vertical surfaces and by the wire AC. Calculate the tension T in the wire and the reactions against the rollers at A and at B.

The mass of the uniform right-triangular tabletop is 30 kg, and that of each of the vertical legs is 2 kg. Determine the normal reaction force exerted by the floor on each leg. The mass center of a right triangular body can be obtained from Table D/3 in Appendix D.

The device shown in the figure is useful for lifting drywall panels into position prior to fastening to the stud wall. Estimate the magnitude P of the force required to lift the 25-kg panel. State any assumptions.

Magnetic tape under a tension of 10 N at D passes around the guide pulleys and through the erasing head at C at constant speed. As a result of a small amount of friction in the bearings of the pulleys, the tape at E is under a tension of 11 N. Determine the tension T in the supporting spring at B. The plate lies in a horizontal plane and is mounted on a precision needle bearing at A.

The tool shown is used for straightening twisted members as wooden framing is completed. If the force P = 30 lb is applied to the handle as shown, determine the normal forces applied to the installed stud at points A and B. Ignore friction.

A freeway sign measuring 12 ft by 6 ft is supported by the single mast as shown. The sign, supporting framework, and mast together weigh 600 lb, with center of gravity 10 ft away from the vertical centerline of the mast. When the sign is subjected to the direct blast of a 75-mi/hr wind, an average pressure difference of \(17.5 \mathrm{lb} / \mathrm{ft}^2\) is developed between the front and back sides of the sign, with the resultant of the wind-pressure forces acting at the center of the sign. Determine the magnitudes of the force and moment reactions at the base of the mast. Such results would be instrumental in the design of the base.

A slender rod of mass \(m_1\) is welded to the horizontal edge of a uniform semi cylindrical shell of mass \(m_2\). Determine an expression for the angle with the horizontal made by the diameter of the shell through \(m_1\). (Consult Table D/3 in Appendix D to locate the center of gravity of the semicircular section.)

The curved arm BC and attached cables AB and AC support a power line which lies in the vertical y-z plane. The tangents to the power line at the insulator below A make \(15^{\circ}\) angles with the horizontal y-axis. If the tension in the power line at the insulator is 1.3 kN, calculate the total force supported by the bolt at D on the pole bracket. The weight of the arm BC can be neglected compared with the other forces, and it can be assumed that the bolt at E supports horizontal force only.

The device shown in section can support the load L at various heights by resetting the pawl C in another tooth at the desired height on the fixed vertical column D. Determine the distance b at which the load should be positioned in order for the two rollers A and B to support equal forces. The weight of the device is negligible compared with L.

A large symmetrical drum for drying sand is operated by the geared motor drive shown. If the mass of the sand is 750 kg and an average gear-tooth force of 2.6 kN is supplied by the motor pinion A to the drum gear normal to the contacting surfaces at B, calculate the average offset \(\bar{x}\) of the center of mass G of the sand from the vertical centerline. Neglect all friction in the supporting rollers.

Determine the force P required to begin rolling the uniform cylinder of mass m over the obstruction of height h.

The small tripod-like stepladder is useful for supporting one end of a walking board. If F denotes the magnitude of the downward load from such a board (not shown), determine the reaction at each of the three feet A, B, and C. Neglect friction.

Each of the three uniform 1200-mm bars has a mass of 20 kg. The bars are welded together into the configuration shown and suspended by three vertical wires. Bars AB and BC lie in the horizontal x-y plane, and the third bar lies in a plane parallel to the x-z plane. Compute the tension in each wire.

The uniform 15-kg plate is welded to the vertical shaft, which is supported by bearings A and B. Calculate the magnitude of the force supported by bearing B during application of the \(120-N \cdot m\) couple to the shaft. The cable from C to D prevents the plate and shaft from turning, and the weight of the assembly is carried entirely by bearing A.

A vertical force P on the foot pedal of the bell crank is required to produce a tension T of 400 N in the vertical control rod. Determine the corresponding bearing reactions at A and B.

The drum and shaft are welded together and have a mass of 50 kg with mass center at G. The shaft is subjected to a torque (couple) of \(120-N \cdot m\) and the drum is prevented from rotating by the cord wrapped securely around it and attached to point C. Calculate the magnitudes of the forces supported by bearings A and B.

Determine and plot the tension ratio T/mg required to hold the uniform slender bar in equilibrium for any angle \(\theta\) from just above zero to just under \(45^{\circ}\). The bar AB of mass m is uniform.

Two traffic signals are attached to the 36-ft support cable at equal intervals as shown. Determine the equilibrium configuration angles \(\alpha, \beta\), and \(\gamma\), as well as the tension in each cable segment.

The two traffic signals of Prob. 3/119 are now repositioned so that segment BC of the 36-ft support cable is 10 ft in length and is horizontal. Specify the necessary lengths AB and CD and the tensions in all three cable segments.

In executing the biceps-curl exercise, the man holds his shoulder and upper arm stationary and rotates the lower arm OA through the range \(0 \leq \theta \leq 105^{\circ}\). The detailed drawing shows the effective origin and insertion points for the biceps muscle group. Determine and plot the tension \(T_B\) in this muscle group over the specified range. State the value of \(T_B\) for \(\theta = 90^{\circ}\). Neglect the weight of the forearm, and assume slow, steady motion.

The basic features of a small backhoe are shown in the illustration. Member BE (complete with hydraulic cylinder CD and bucket-control links DF and DE) weighs 500 lb with mass center at \(G_1\). The bucket and its load of clay weigh 350 lb with mass center at \(G_2\). To disclose the operational design characteristics of the backhoe, determine and plot the force T in the hydraulic cylinder AB as a function of the angular position \(\theta\) of member BE over the range \(0 \leq \theta \leq 90^{\circ}\). For what value of \(\theta\) is the force T equal to zero? Member OH is fixed for this exercise; note that its controlling hydraulic cylinder (hidden) extends from near point O to pin I. Similarly, the bucket-control hydraulic cylinder CD is held at a fixed length.

The mass center of the 1.5-kg link OC is located at G, and the spring of constant k = 25 N/m is unstretched when \(\theta = 0\). Plot the tension T required for static equilibrium over the range \(0 \leq \theta \leq 90^{\circ}\) and state the values of T for \(\theta = 45^{\circ}\) and \(\theta = 90^{\circ}\).

The system of Prob. 3/60 is repeated here, but now the crank OA has mass \(m_C = 3 kg\) with mass center at G. Determine and plot the moment M which must be applied to the crank in order to hold the cylinder of mass m = 5 kg in equilibrium. Use the range \(0 \leq \theta \leq 180^{\circ}\) and neglect all friction. State the value of \(\theta\) for which M = 0.

The 125-kg homogeneous rectangular solid is held in the arbitrary position shown by the tension T in the cable. Determine and plot the following quantities as functions of \(\theta\) over the range \(0 \leq \theta \leq 60^{\circ}\) : \(T, A_y, A_z, B_x, B_y\), and \(B_z\). The hinge at A cannot exert an axial thrust. Assume all hinge force components to be in the positive coordinate directions. Friction at D is negligible.