Problem S12007 (4 points)

A homogeneous cylinder with weight G and radius R lay on a rough horizontal floor and adjoins to a rough vertical wall. What conditions must be satisfied by the force F enclosed to a point A of the cylinder to keep it in equilibrium. The coefficient of friction between the cylinder and the floor is f. The coefficient of friction between the cylinder and the wall is f too.


Problem S22007 (6 points)

Cube 1 of weight G1 and edge length a is put on homogeneous cores 2 and 3 hinged together at C, as shown in figure. Rods each of weight G2 stand on a smooth horizontal floor. AC =   CD = =  = l. The system is kept in equilibrium with the help of spring KL connecting the middle of pieces AC and . Determine the force of the spring tension.


Problem K12007 (6 points)

There is slider crank mechanism with OA = AB. Crank OA rotates with angular velocity w. Its position determined by a angle j. Find the size and a direction of angular acceleration of crank OA, when vectors of speed and acceleration of the center point M of the connecting rod AB of the slider crank mechanism are mutually perpendicular.

Problem K22007 (8 points)

Crank 1 rotates with angular velocity w1. Point B is the center of the connecting rod AC. OA = l (Fig.). Determine the velocities and accelerations of the sliders 2 and 3 in relation to a crank for this position.

Problem D12007 (5 points)

Initially a particle of mass m = 1 kg is in position A; its velocity is v0 = 10 m/sec and it is directed to the point B along an inclined plane. Force F changes in accordance with the law F = 20 t .

Neglecting friction, determine rising height H of the particle through t = 2 sec, if a = 30.

Problem D22007 (6 points)

The wheel presents a homogeneous disk with mass m and radius r. The axiss C acceleration is connected to the velocity by dependence . Initially the velocity of the axis is v0. The wheel rolls without sliding. Determine force expression P(t) which acting on wheel.

Problem D32007 (7 points)

The load 1 with mass m1 = m is on the rough surface inclined at angle a = 45 to the horizontal (coefficient of friction f = 0,25). Unstretched cord passes over the pulley 2 mass m2 = m. The pulley 2 is homogeneous circular cylinder. Other end of the cord is wound on a drum and makes the wheel 3 roll without sliding on a horizontal surface. There radiuses are , mass m3 = 1,5m and radius of gyration about horizontal axis, passing through the wheel center .

Determine the velocity of the load 1 to the time when it will pass on the inclined plane distance s, if cord is at the angle b = 30 to the horizontal this time. Initially the system was in equilibrium.

Problem D42007 (8 points)

Loads 2 and 3 with m2 = 2m, m3 = m connected to a rod 1 of length l and mass m1 = m. Inextensible string passing over the pulley 4 of the mass m4 = 2m. String connects centres of gravity of the rod 1 and wheel 5 with radius r. The wheel rolls without sliding on the inclined plane at angle a = 30 to the horizontal. The wheels 4 and 5 are homogeneous cylinders.

Initially the system was in equilibrium and objects 1 and 5 have equal angular acceleration. At that time cos φ = 0,8. Determine mass of the wheel 5.


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