Problem S1–2007 (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 S2–2007 (6 points) 


Cube 1 of weight G_{1} and edge
length a is put on homogeneous cores 2
and 3 hinged together at C, as shown in
figure.
Rods
each of weight G_{2} stand on a smooth horizontal
floor. AC = ÑÅ = ÂÑ = CD =
= ÀÂ = l. The system is
kept in equilibrium with the help of spring KL connecting the
middle of pieces AC and ÂÑ. Determine the force of the
spring tension. 
Problem K1–2007 (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
K2–2007 (8 points) 


Crank 1 rotates with angular velocity w_{1}. 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 D1–2007 (5 points) 


Initially a
particle of mass m = 1 kg is in position A; its velocity is v_{0} = 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
D2–2007 (6 points) 


The wheel presents a homogeneous disk with mass m and radius r. The axis’s C acceleration is connected to the velocity by dependence _{}. Initially the velocity of the axis is v_{0}. The wheel rolls
without sliding. Determine force expression P(t)
which acting on wheel. 
Problem
D3–2007 (7 points) 


The load 1 with mass m_{1} = 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 m_{2} = 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 m_{3} = 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
D4–2007 (8 points) 


Loads 2 and 3 with m_{2} = 2m, m_{3} = m
connected to a rod 1 of length l and mass m_{1} = m. Inextensible
string passing over the pulley 4 of the mass m_{4} = 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. 