Online Engineering Mechanics Test - Engineering Mechanics Test - Random

x – y + z = –1   –x + y + z = –1   x + 2y – 2z = 5

Determine the magnitude and direction of the resultant force.

What is the projection of the force F₂ along the positive axis?

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.

Determine the magnitude of the projection of the moment cause by the force about the aa axis.

Determine the magnitude and direction of the couple shown.

Determine the moment of force F₁ about point A on the beam.

The oil rig is supported on the trailer by the pin or axle at A and the frame at B. If the rig has a weight of 115,000 lb and the center of gravity at G, determine the force F that must de developed along the hydraulic cylinder CD in order to start lifting the rig (slowly) off B toward the vertical. Also compute the horizontal and vertical components of reaction at the pin A.

A 17-kg ladder has a center of mass at G. If the coefficients of friction at A and B are _A = 0.3 and _B = 0.2, respectively, determine the smallest horizontal force that the man must exert of the ladder at point C in order to push the ladder forward.

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.

Locate the centroid of the exparabolic segment of area.

Determine the distance to the centroidal axis of the beam's cross-sectional area.

If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B arises.

A package is dropped from the plane which is flying with a constant horizontal velocity of v_A = 150 ft/s at a height h = 1500 ft. Determine the radius of curvature of the path of the package just before it is released from plane at A.

Each of the three barges has a mass of 30 Mg, whereas the tugboat has a mass of 12 Mg. As the barges are being pulled forward with a constant velocity of 4 m/s, the tugboat must overcome the frictional resistance of the water, which is 2 kN for each barge and 1.5 kN for the tugboat. If the cable between A and B breaks, determine the acceleration of the tugboat.

The coefficient of friction between the 2-lb block and the surface is = 0.2. The block is acted upon by a horizontal force of P. Determine the maximum deformation of the outer spring B at the instant the block comes to rest. Spring B has a stiffness of K_B = 20 lb/ft and the "nested" spring C has a stiffness of k_c = 40 lb/ft.

A hockey puck is traveling to the left with a velocity of v₁ = 10 m/s when it is struck by a hockey stick and given a velocity of v₂ = 20 m/s as shown. Determine the magnitude of the net impulse exerted by the hockey stick on the puck. The puck has a mass of 0.2 kg.

The disk rolls without slipping such that it has an angular acceleration of = 4 rad/s² and angular velocity of = 2 rad/s at the instant shown. Determine the accelerations of points A and B on the link and the link's angular acceleration at this instant. Assume point A lies on the periphery of the disk, 150 mm from C.

If rod CD has a downward velocity of 6in/s at the instant shown, determine the velocity of the gear rack A at this instant. The rod is pinned at C to gear B.

If the 3-lb solid sphere is released from rest when = 30°, determine its angular velocity when = 0°, which is the lowest point of the curved path having a radius of 11.5 in. The sphere does not slip as it rolls.