Problem Sheet No. 1
1. Determine the tension in cables CA and CB.
Ans. TCA = 2870 N, TCB = 3520 N.
2. The uniform bar has a mass per unit length of 60 kg/m. Determine the reactions at the supports. Ans. Ay = 3060 N, By = 2060 N.
3. The uniform angle bar with equal legs has a mass of 20 kg and is supported in the vertical plane as shown. Calculate the force FA supported by the pin at A. Ans. FA = 277 N.
4. Determine the reactions at A and E if P=500 N. What is the maximum value that P may have for static equilibrium? Neglect the weight of the structure compared with the applied loads. Ans. Ax = -1290 N, Ay = 2960 N, E x= 3290 N, P=1732 N.
A man pushes the 40 kg machine with mass centre at G up an incline at a steady speed. Determine the required force magnitude P and the normal reaction forces at A and B. Neglect the small effects of friction. Ans. P = 112.1 N, NB = 219 N, NA = 207 N.
During an engine test, a propeller thrust T = 3000 N is generated on the 1800-kg airplane with mass centre at G. The main wheels at B are locked and do not skid; the small tail wheel at A has no brake. Compute the percent change n in the normal forces at A and B as compared with their “engine-off” values. Ans. nA = -32.6%, nB = 2.28%
What fraction n of the weight W of a jet airplane is the net thrust (nozzle thrust T minus air resistance R) in order for the airplane to climb with a constant speed at an angle ( with the horizontal? Ans. n = sin (
The three cables are secured to a ring at B, and the turnbuckle at C is tightened until it supports a tension of 1.6 kN. Calculate the moment M produced by the tension in cable AB about the base of the mast at D. Ans. M = 8 kN.m
The uniform bar AB has a mass of 50 kg and supports the 200-kg load at A. Calculate the tension in the supporting cable and the magnitude FB of the force supported by the pin at B. Ans. T = 7650 N, FB = 5660 N
A uniform ring of mass m and radius r carries an eccentric mass m0 at a radius b and is in an equilibrium position on the incline, which makes an angle ( with the horizontal. If the contacting surfaces are rough enough to prevent slipping, write the expression for the angle ( which defines the equilibrium position.
The two planks are connected by a large spike. If a force P = 120 N is required on the handle of each crowbar to loosen the spike, calculate the corresponding tension T in the spike. Also find the value of b which will eliminate any tendency to bend the spike. State any assumptions which you make. Ans. T = 1560 N, b = 53.8 mm
Two light pulleys are fastened together and form an integraL unit. They are prevented from turning about their bearing at O by a cable wound securely around the smaller pulley and fastened to point A. Calculate the magnitude R of the force supported by the bearing O for the applied 2-kN load. Ans. R = 4.38 kN
A former student of mechanics wishes to weigh himself but has access only to a scale A with capacity limited to 400 N and a small 80-N spring dynamometer B. With the rig shown he discovers that when he exerts a pull on the rope so that B registers 76 N, the scale A reads 268 N. What are his correct weight and mass m? Ans. W= 648 N, m= 66.1 kN
The exercise machine consists of a lightweight cart which is mounted on small rollers so that it is free to move along the inclined ramp. Two cables are attached to the cart – one for each hand. If the hands are together so that the cables are parallel and if each cable lies essentially in a vertical plane, determine the force P which each hand must...
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