1. Calculate the period of small oscillations of a hydrometer (Figure.1) which was slightly pushed down in the vertical direction. The mass of the hydrometer is m = 50 g, the radius of its tube is r = 3.2 mm, the density of the liquid is p = 1.00 g/cm3. The resistance of the liquid is assumed to be negligible.
Answer: 2,477 s
2. Find the frequency of small oscillations of the arrangement illustrated in Fig. 2. The radius of the pulley is R, its moment of inertia relative to the rotation axis is I, the mass of the body is m, and the spring stiffness is x. The mass of the thread and the spring is negligible, the thread does not slide over the pulley, there is no friction in the axis of the pulley.
3. A vessel contains a mixture of nitrogen (m1 = 7.0 g) and carbon dioxide (m2 = 11 g) at a temperature T = 290 K and pressure po, = 1.0 atm. Find the density of this mixture, assuming the gases to be ideal.
Answer: 1,51 g/l
4. A spool with thread wound on it, of mass m, rests on a rough horizontal surface. Its moment of inertia relative to its own axis is equal to I = γmR2, where y is a numerical factor, and R is the outside radius of the spool. The radius of the wound thread layer is equal to r. The spool is pulled without sliding by the thread with a constant force F directed at an angle a to the horizontal (Fig. 3). Find:
(a) the projection of the acceleration vector of the spool axis on the x-axis;
(b) the work performed by the force F during the first t seconds after the beginning of motion.
5. A uniform cylinder of radius R is spinned about its axis to the angular velocity ωo and then placed into a corner (Fig. 4). The coefficient of friction between the corner walls and the cylinder is equal to k. How many turns will the cylinder accomplish before it stops?
Answer: 2,477 s
2. Find the frequency of small oscillations of the arrangement illustrated in Fig. 2. The radius of the pulley is R, its moment of inertia relative to the rotation axis is I, the mass of the body is m, and the spring stiffness is x. The mass of the thread and the spring is negligible, the thread does not slide over the pulley, there is no friction in the axis of the pulley.
3. A vessel contains a mixture of nitrogen (m1 = 7.0 g) and carbon dioxide (m2 = 11 g) at a temperature T = 290 K and pressure po, = 1.0 atm. Find the density of this mixture, assuming the gases to be ideal.
Answer: 1,51 g/l
4. A spool with thread wound on it, of mass m, rests on a rough horizontal surface. Its moment of inertia relative to its own axis is equal to I = γmR2, where y is a numerical factor, and R is the outside radius of the spool. The radius of the wound thread layer is equal to r. The spool is pulled without sliding by the thread with a constant force F directed at an angle a to the horizontal (Fig. 3). Find:
(a) the projection of the acceleration vector of the spool axis on the x-axis;
(b) the work performed by the force F during the first t seconds after the beginning of motion.
5. A uniform cylinder of radius R is spinned about its axis to the angular velocity ωo and then placed into a corner (Fig. 4). The coefficient of friction between the corner walls and the cylinder is equal to k. How many turns will the cylinder accomplish before it stops?
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untuk pembahasan rincinya nda ada kak
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