Online Engineering Mechanics Test - Engineering Mechanics Test - Random
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- Total number of questions: 20.
- Time allotted: 30 minutes.
- Each question carries 1 mark; there are no negative marks.
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Marks : 2/20
Test Review : View answers and explanation for this test.
Determine the magnitude and direction 
of F so that this force has components of 40 lb acting from A toward B and 60lb acting from A toward C on the frame.
= 22.9° = 46.2° = 37.1° = 56.3°
The patella P located in the human knee joint is subjected to tendon forces T1 and T2 and a force F exerted on the patella by the femoral articular A. If the directions of these forces are estimated from an X-ray as shown, determine the magnitudes of T1 and F when the tendon force T2 = 6 lb.. The forces are concurrent at point O.
Replace the force and couple system by an equivalent single force and couple acting at point P.
The bricks on top of the beam and the supports at the bottom create the distributed loading shown in the second figure. Determine the required intensity w and dimension d of the right support so that the resultant force and couple moment about point A of the system are both zero.
There is a ball and socket connection at A. At B there is a roller that prevents motion in the —z direction. Corner C is tied to D by a rope. The triangle is weightless. Determine the unknown force components acting at A, B, and C. Use a scalar analysis.
A uniform beam has a mass of 18 kg and rests on two surfaces at points A and B. Determine the maximum distance x to which the girl can slowly walk up the beam before it begins to slip. The girl has a mass of 50 kg and walks up the beam with a constant velocity.
A passenger in the automobile B observes the motion of the train car
A particle having a mass of 1.5 kg, moves along a three-dimensional path defined by the equations r = 94 + 3t) m, = (t2 + 2) rad, and z = (6 - t3) m, where t is in seconds, and the z-axis is vertical. Determine the r, , and z components of force which the path exerts on the particle when t = 2 s.
A boy twirls a 15-lb bucket of water in a vertical circle. If the radius of curvature of the path is 4 ft, determine the minimum speed the bucket must have when it is overhead at A so no water spills out.
Determine the acceleration of block A when the system is released. The coefficient of friction and the weight of each block are indicated in the figure. Neglect the mass of the pulleys and cords.
When at A the bicyclist has a speed of vA = ft/s. If he coasts without pedaling from the top of the hill at A to the shore of B and then leaps off the shore, determine his speed at B and the distance x where he strikes the water at C. The rider and his bicycle have a total weight of 150 lb. Neglect the size of the bicycle and wind resistance.
The elevator E and its freight have a total mass of 400 kg. Hoisting is provided by the motor M and the 60-kg block C. If the motor has an efficiency of e = 0.6, determine the power that must be supplied to the motor when the elevator is hoisted upward at a constant speed of vE = m/s.
The motor M pulls on the cables with a force F that has a magnitude which varies as shown on the graph. If the 15-kg crate is originally resting on the floor such that the cable tension is zero when the motor is turned on, determine the speed of the crate when t = 6s.
Plates A and B each have a mass of 4 kg and are restricted to move along the frictionless guides. If the coefficient of restitution between the plates is e = 0.7, determine (a) the speed of both plates just after collision and (b) the maximum deflection of the spring. Plate A has a velocity of 4 m/s just before striking B. Plate B is originally at rest.
A girl having a weight of 40 lb slides down the smooth slide onto the surface of a 20-lb wagon. Determine the speed of the wagon at the instant the girl stops sliding on it. If someone ties the wagon to the slide at B, determine the horizontal impulse the girl will exert at C in order to stop her motion. Neglect friction and assume that the girl starts from rest at the top of the slide, A.
The sphere starts from rest at = 0 and rotates with an angular acceleration of 
= (4) rad/s2, where is measured in radians. Determine the magnitudes of the velocity and acceleration of point P on the sphere at the instant = 6 rad.
Due to an engine failure, the missile is rotating at 
= 3 rad/s, while its mass center G is moving upward at 200 ft/s. Determine the magnitude of the velocity of its nose B at this instant.
A clown, mounted on stilts, loses his balance and falls backward from the position, where it is assumed the = 0 when = 07deg;. Paralyzed with fear, he remains rigid as he falls. His mass including the stilts is 80 kg, the mass center is at G, and the radius of gyration about G is kG = 1.2 m. Determine the coefficient of friction between his shoes and the ground at A if it is observed that slipping occurs when = 30°.
= 0.833 = 0.468 = 0.243 = 0.400
The uniform slender rod has a mass of 5 kg. Determine the magnitude of the reaction at the pin O when the cord at A is cut and = 90°
A constant torque or twist of M = 0.4N • m is applied to the center gear A. If the system starts from rest, determine the angular velocity of each of the three (equal) smaller gears in 3 s. The smaller gears (B) are pinned at their centers, and the mass and centroidal radii of gyration of the gears are given in the figure.
B = 1975 rad/sB = 5830 rad/sB = 1520 rad/sB = 1022 rad/s