Irodov – Problems in General Physics

(Joyce) #1

the plank when the amplitude of oscillation of the plank becomes
less than T = 1.0 s.
4.33. Find the time dependence of the angle of deviation of a
mathematical pendulum 80 cm in length if at the initial moment the
pendulum
(a) was deviated through the angle 3.0° and then set free without
push;
(b) was in the equilibrium position and its lower end was imparted
the horizontal velocity 0.22 m/s;
(c) was deviated through the angle 3.0° and its lower end was im-
parted the velocity 0.22 m/s directed toward the equilibrium position.
4.34. A body A of mass m 1 = 1.00 kg and a body B of mass m 2 =
4.10 kg are interconnected by a spring as shown in Fig. 4.9. The
body A performs free vertical harmonic oscilla-
tions with amplitude a = 1.6 cm and frequency
= 25 s-1. Neglecting the mass of the spring,
find the maximum and minimum values of force
that this system exerts on the bearing surface.
4.35. A plank with a body of mass m placed
on it starts moving straight up according to
the law y = a (1 — cos cot), where y is the

displacement from the initial position, co = (^) Fig. 4.9.
= =- 11 s-1. Find:
(a) the time dependence of the force that the body exerts on the
plank if a = 4.0 cm; plot this dependence;
(b) the minimum amplitude of oscillation of the plank at which
the body starts falling behind the plank;
(c) the amplitude of oscillation of the plank at which the body
springs up to a height h = 50 cm relative to the initial position (at
the moment t = 0).
4.36. A body of mass in was suspended by a non-stretched spring,
and then set free without push. The stiffness of the spring is x.
Neglecting the mass of the spring, find:
(a) the law of motion y (t) , where y is the displacement of the body
from the equilibrium position;
(b) the maximum and minimum tensions of the spring in the pro-
cess of motion.
4.37. A particle of mass in moves due to the force F = — amr,
where a is a positive constant, r is the radius vector of the particle
relative to the origin of coordinates. Find the trajectory of its motion
if at the initial moment r = roi and the velocity v = voj, where i
and j are the unit vectors of the x and y axes.
4.38. A body of mass m is suspended from a spring fixed to the
ceiling of an elevator car. The stiffness of the spring is x. At the mo-
ment t = 0 the car starts going up with an acceleration w. Neglecting
the mass of the spring, find the law of motion y (t) of the body rela-
tive to the elevator car if y (0) = 0 and y (0) = 0. Consider the fol-
lowing two cases: