1. A mathematical pendulum with length 1 m with coefficients of moving both linear 1, 1 x 10-5/° C are brought from other regions on the surface of Earth. If the period of the pendulum is getting bigger 0.01% of period features in place of the old. Determine the temperature difference of the second place!
(Answer: 18,18 K)
5. A rod homogeneous mass m fastened with ropes A and B, the chemical equilibrium in the position as shown with rope B horizontal. Specify value tanθ!
7.A vessel of volume V= 30 liter contains ideal gas at the temperature 0oC. After a portion of the gas has been let out, the pressure in the vessel decreased by ∆p = 0.78 atm (the temperature remaining constant). Find the mass of the released gas. The density under the normal conditions ρ = 1.3g/L.
Answer: m = 30,4 g
8.A smooth vertical tube having two different sections is open from both ends and equipped with two pistons of different areas (figure). Each piston slides within a respective tube section. One mole of ideal gas is enclosed between the pistons tied with a non-stretchable thread. The cross-sectional area of the upper piston is ∆S=10cm2 greater than that of the lower one. The combined mass of the two pistons is equal to m = 5.0kg. The outside air pressure is po = 1.0 atm. By how many kelvins must the gas between the pistons be heated to shift the pistons through l = 5.0 cm?
Answer: 0,91 K
9.Two inclined plane intersect on a horizontal field. Its tilt toward horizontal is α and β. If a thrown particle perpendicular from a point P in the plane which left such that a particle collides with other fields also are perpendicular, find the initial velocity! (see picture)
10.Determine the period of oscillations of mercury of mass m =200g poured into a bent tube (figure) whose right arm forms an angle θ =30o with the vertical. The cross-sectional area of the tube is S=0,50cm2 . The viscosity of mercury is to be neglected.
Answer: 0,788 s
11.A uniform cylinder of radius R is spinned about its axis to the angular velocity ωo and then placed into a corner. The coefficient of friction in all surface is equal to μ. How many turns will the cylinder accomplish before it stops?
12. A small bar A resting on a smooth horizontal plane is attached by threads to a point P (figure) and, by means of a weightless pulley, to a weight B possessing the same mass as the bar itself. Besides, the bar is also attached to a point O by means of a light nondeformed spring of length lo = 50 cm and stiffness x = 5mg/ lo,where m is the mass of the bar. The thread PA having been burned, the bar starts moving. Find its velocity at the moment when it is breaking off the plane.
Answer: 1,7 m/s
13. A marble bounces down stairs in a regular manner, hitting each step at the same place and bouncing the same height above each step (see figure). The stair height equals its depth (tread = rise) and the coefficient of restitution e is given. Find the necessary horizontal velocity and bounce height. (The coefficient of restitution is defined as e = -vf/vi, where vf and vi are the vertical velocities just after and before the bounce. respectively).
14. Two steel spheres, the lower of radius 2a and the upper of radius a are dropped from a height h (measured from the center of the larger sphere) above a steel plate as shown. Assume that the centers of the spheres always lie on a vertical line and all collisions are elastic, what is the maximum height of the upper sphere will reach?
15. As shown in the figure below, a ball is launched diagonally upward from a horizontal ground. The time at launch is 0. After passing through a point at height h at time t, the ball lands at time T.
(Answer: 18,18 K)
2. An object with mass m experiencing vibration in tune. Suppose that vibration is angular frequency ω. When it is at x = a, the momentum of the objects it is α, what is the momentum of the thing when it is at x = b?
3.The bullet is fired with the angle of elevation of a = 60o in the bottom of the inclinewith a slope angle b = 30o as on the image. If the initial speed of the bullet 29.4 m/s and acceleration of gravity 9, 8 m/s2 ,so great a distance d is. .. (Answer:A)
A. 58,80 m B.29,40 m C.26,13 m
D. 36,28 m E. 49,80 m
4.The ball is at the apex of the building half a ball with a radius of 100 m. The ball was given the initial velocity of the ball so that it is never about the building. Specify the minimum value of z!
Answer: 41,42 m
5. A rod homogeneous mass m fastened with ropes A and B, the chemical equilibrium in the position as shown with rope B horizontal. Specify value tanθ!
Answer: tanθ = 3/4
6.Above the semicircular areas with rough surface that has a radius of 1 m is placed the ball with a radius of 10 cm pejal mass 1 kg as in the picture. If the angle θ = 60o, the angular velocity of the ball at the lowest point is .... (g = 9,8 m/s2)
Answer: 25,1 rad/s
7.A vessel of volume V= 30 liter contains ideal gas at the temperature 0oC. After a portion of the gas has been let out, the pressure in the vessel decreased by ∆p = 0.78 atm (the temperature remaining constant). Find the mass of the released gas. The density under the normal conditions ρ = 1.3g/L.
Answer: m = 30,4 g
8.A smooth vertical tube having two different sections is open from both ends and equipped with two pistons of different areas (figure). Each piston slides within a respective tube section. One mole of ideal gas is enclosed between the pistons tied with a non-stretchable thread. The cross-sectional area of the upper piston is ∆S=10cm2 greater than that of the lower one. The combined mass of the two pistons is equal to m = 5.0kg. The outside air pressure is po = 1.0 atm. By how many kelvins must the gas between the pistons be heated to shift the pistons through l = 5.0 cm?
Answer: 0,91 K
9.Two inclined plane intersect on a horizontal field. Its tilt toward horizontal is α and β. If a thrown particle perpendicular from a point P in the plane which left such that a particle collides with other fields also are perpendicular, find the initial velocity! (see picture)
10.Determine the period of oscillations of mercury of mass m =200g poured into a bent tube (figure) whose right arm forms an angle θ =30o with the vertical. The cross-sectional area of the tube is S=0,50cm2 . The viscosity of mercury is to be neglected.
Answer: 0,788 s
11.A uniform cylinder of radius R is spinned about its axis to the angular velocity ωo and then placed into a corner. The coefficient of friction in all surface is equal to μ. How many turns will the cylinder accomplish before it stops?
12. A small bar A resting on a smooth horizontal plane is attached by threads to a point P (figure) and, by means of a weightless pulley, to a weight B possessing the same mass as the bar itself. Besides, the bar is also attached to a point O by means of a light nondeformed spring of length lo = 50 cm and stiffness x = 5mg/ lo,where m is the mass of the bar. The thread PA having been burned, the bar starts moving. Find its velocity at the moment when it is breaking off the plane.
Answer: 1,7 m/s
13. A marble bounces down stairs in a regular manner, hitting each step at the same place and bouncing the same height above each step (see figure). The stair height equals its depth (tread = rise) and the coefficient of restitution e is given. Find the necessary horizontal velocity and bounce height. (The coefficient of restitution is defined as e = -vf/vi, where vf and vi are the vertical velocities just after and before the bounce. respectively).
14. Two steel spheres, the lower of radius 2a and the upper of radius a are dropped from a height h (measured from the center of the larger sphere) above a steel plate as shown. Assume that the centers of the spheres always lie on a vertical line and all collisions are elastic, what is the maximum height of the upper sphere will reach?
Hint: Assume that the larger sphere collides with the plate and recoils before it collides with the smaller sphere
15. As shown in the figure below, a ball is launched diagonally upward from a horizontal ground. The time at launch is 0. After passing through a point at height h at time t, the ball lands at time T.
What is the height h? From 1-5 below choose the correct answer.
1.½ gt2 3. ½ gT(T-t) 5.½ g(T-t)2
2.½ gtT 4. ½ gt(T-t)
Answer: 4
16. An elastic ball is dropped on a long inclined plane. It bounces, hits the plane again, bounces, and so on. Let us label the distance between the points of the first and the second hit d12 and the distance between the points of the second and the third hit d23 . Find the ratio d12/d23.
Answer: 1/2
17. As shown in Figure 1, two people of the same height are holding up a box attached to a pole. The center of gravity of the pole and the box is located at point G. The pole is supported at points A and B. The pole and the box do not change form.
As shown in Figure 2, the two people are now standing on a slope inclined by angle (θ < π/4) from the horizontal. The person supporting the upper end at A exerts a force of magnitude of FA vertically upward. The person supporting the lower end at B exerts a force of magnitude of FB vertically upward. What is the value of the ratio FA/FB ? From 1-6 below choose the correct answer.
Answer: 6
18. As shown in the figure below, an artificial satellite is travelling in a circular orbit around the earth. The radius of the orbit from earth's center is r. Assume that the earth is uniform sphere with a radius of R. The magnitude of acceleration due to gravity at the earth's surface is g.
What is the period of the satellite's orbital motion? From 1-4 below choose the correct answer.
Answer: 3
19.A horizontally flying bullet of mass m gets stuck in a body of mass M suspended by two identical threads of length l (figure). As a result, the threads swerve through an angle θ. Assuming m << M, find:
(a) the velocity of the bullet before striking the body;
(b) the fraction of the bullet's initial kinetic energy that turned into heat.
Answer: h = h/2 ; Smax = H
(Irodov I.E Problem In General Physics)
(a) the velocity of the bullet before striking the body;
(b) the fraction of the bullet's initial kinetic energy that turned into heat.
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20. A small disc A slides down with initial velocity equal to zero from the top of a smooth hill of height H having a horizontal portion (figure). What must be the height of the horizontal portion h to ensure the maximum distance s covered by the disc? What is it equal to?
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| (figure) |
(Irodov I.E Problem In General Physics)
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