(246 kb), which you can download and open on your computer. Try to solve all the problems yourself and only then compare your answers with ours. We wish you success!)

9.1. A horizontal disc rotates around vertical axis with frequency n = 10 rpm(picture on the left). At what distance from the center of the disk can something lying on it remain? small body if the coefficient of friction is μ = 0.2

9.2. A block is placed on a rotating horizontal disk. The same bar is placed on top of it, tied with a thread to the axis of the disk. At what angular velocity of rotation of the disk will the lower bar slip out if, when it lies alone, it begins to slide at an angular velocity w o? The coefficients of friction between all surfaces are the same. [ w = w o √3 ]

9.3. Load of mass m, attached by a stiffening spring k to the vertical axis, moves around this axis along a horizontal circle with a radius R with angular velocity w. What is the length of the undeformed spring? [see answer in general file]

9.4. A coupling of mass m is mounted on a smooth horizontal rod of length 2L about and fastened with two identical springs with the axis OO 1 and stop at the end of the rod. In the absence of rotation, the springs are unloaded, and their stiffnesses are equal k. The system is spun around the axis OO 1 . Find the dependence of the distance from the axis to the coupling on the angular velocity of rotation. Ignore the dimensions of the coupling

9.5. mass man m = 70 kg swinging on swings. Rope length l = 8 m. A person passes the equilibrium position at a speed v = 6 m/s. What is the tension in the ropes at this moment? [see answer in general file]

9.6. A ball suspended from a thread of length l, rotates in the horizontal plane so that the thread makes an angle α vertical (conical pendulum). Determine the speed of the ball. [see answer in general file]

9.7. On a horizontal disk lies a small bar tied with a thread of length l to the axis of the disk. The thread is stretched and makes an angle with the vertical α . The disc starts spinning slowly. At what angular velocity of rotation of the disk will the block come off from it? What will be the tension in the thread? The mass of the bar is m. [see answer in general file]

9.8. Vehicle mass m = 1000 kg drove onto a convex bridge long l = 156 m with speed v o = 36 km/h. On the bridge he moves with acceleration a = 1 m/s 2. Determine the pressure force of the car on the bridge in the middle of the bridge, where the radius of curvature R = 200 m.

9.9. Two bodies of mass m, connected by a thread of length l, moving at a speed v, directed perpendicular to the thread (figure on the left), on a horizontal table. The middle of the thread comes across a nail driven into the table. What is the tension in the thread immediately after this? [see answer in general file]

9.10. Two identical bodies of mass m tied with a thread of length 2L and lie on a smooth table (picture on the left). For the middle of the thread begin to pull from constant speed v in a direction perpendicular to the initial direction of the thread. How does the magnitude of the force that must be applied to the thread depend on the angle α between the velocity vector v and thread? [see answer in general file]

9.11. A car moving along a horizontal road at a speed v, enters a horizontal turn with a radius of curvature R. What is the maximum tangential acceleration can develop a car on a turn if the coefficient of friction between the wheels and the road is equal to μ . Both axles of the car are leading. [see answer in general file]

9.12. On a horizontal disk at a distance R = 1 m from its axis lies a small block. The disk begins to spin with angular acceleration ε = 4 s −2. After what time does the block begin to slide on the disk if the coefficient of friction is μ = 0.5? [see answer in general file]

9.13. bushing mass m can slide without friction on a horizontal rod (figure on the left). A thread is threaded through the bushing ring, one end of which is fixed, and a load of mass m. Determine the angle between the lower section of the thread and the vertical in the steady motion mode of the system. The thread is smooth and weightless, its upper end is horizontal. [see answer in general file]

9.14. At point A of the disk (figure on the left), one end of the spring is fixed, the stiffness of which k = 100 N/m. Attached to the other end of the spring is a mass m = 20 g. Distance OA=5cm, own length of the spring l = 10 cm. What will be the length of the spring if the disc rotates at an angular velocity w = 100 s −1? There is no friction. [Hooke's law will not survive such a regime]

9.15. The vertical shaft rotates (figure on the left). A weightless rod of length l = 10 cm, at the other end of which there is a small massive ball. At what angle from the vertical will the rod deviate at the angular speeds of rotation of the shaft: w 1 = 14 c −1 and w 2 \u003d 7 c -1? [α 1 = 60°; α 2 = 0]

9.16. The thread and the homogeneous rod attached to it rotate at a constant speed around the vertical axis. Will the thread and the rod be directed along the same straight line? [will not]

9.17. Space station rotates around its axis (figure on the left), due to which an artificial gravity force is created on it. The astronaut releases the object at point A. Will the object fall to point B? [No]

9.18. A mathematical pendulum consists of a ball of mass m = 50 g suspended on a thread of length l = 1 m. Define least force thread tension if the ball passes the equilibrium position with a speed v = 1.4 m/s. [see answer in general file]

9.19. The mathematical pendulum oscillates. In the position of greatest deviation, the acceleration of the load in 20 times less than when passing through the equilibrium position. Find the angle of maximum deviation. [see answer in general file]

9.20. On a rotating horizontal table at a distance R=50cm from the axis of rotation lies a load weighing P = 10 N. Coefficient of friction between load and table surface μ = 0.25. What is the friction force holding the load if the speed of rotation of the table n = 12 rpm? At what angular speed wmax the load will slide on the table? [see answer in general file]

9.21. Small ball of mass m = 100 g suspended on a long thread from the ceiling of the car, which moves uniformly along curved section paths at speed 72 km/h. With what force T the thread is taut if the radius of curvature of the path section R = 200 m? [T=1H]

2.101. A weight of mass m = 50 g, tied to a thread of length l = 25 cm, describes a circle in the horizontal plane. Weight rotation frequency n = 2 rpm. Find the tension in the string T.
2.102. The disk rotates around a vertical axis with a frequency of n = 30 rpm. A body lies on the disk at a distance r = 20 cm from the axis of rotation. What should be the coefficient of friction k between the body and the disk so that the body does not roll off the disk?

2.103. An airplane flying at a speed v = 900 km/h makes a "dead loop". What should be the radius of the "dead loop" R, so that greatest strength F, pressing the pilot to the seat, was equal to: a) five times the force of gravity acting on the pilot; b) ten times the force of gravity acting on the pilot?

2.104. A motorcyclist rides along a horizontal road with a speed v = 72 km/h, making a turn with a radius R = 100 m. At what angle a must he lean so as not to fall when turning?

2.105. A ball is suspended on a thread from the ceiling of a tram car. The car moves at a speed v = 9 km/h along a curve with a radius R = 36.4 m. At what angle a will the thread with the ball deviate?

9 . 11 . A car moving along a horizontal road at a speed v, enters a horizontal turn with a radius of curvature R. What is the maximum tangential acceleration that a car can develop on a turn if the coefficient of friction between the wheels and the road is m. Both axles of the car are leading.

9 . 12 . On a horizontal disk at a distance R= 1 m from its axis lies a small bar. The disk begins to spin up with an angular acceleration e = 4 s–2. After what time does the bar begin to slide on the disk if the coefficient of friction is m = 0.5?

9 . 13 . bushing mass m can slide without friction along a horizontal rod (Fig. 9.4). A thread is threaded through the bushing ring, one end of which is fixed, and a load of mass m. Determine the angle between the lower section of the thread and the vertical in the steady motion mode of the system. The thread is smooth and weightless, its upper end is horizontal.

9.14 . At the point A disk (Fig. 9.5) one end of the spring is fixed, the stiffness of which k= 100 N/m. Attached to the other end of the spring is a mass m= 20 g. Distance OA= 5 cm, own length of the spring l\u003d 10 cm. What will be the length of the spring if the disk rotates with an angular velocity w \u003d 100 s–1? There is no friction. [Hooke's law will not survive such a regime]

9.15 . The vertical shaft rotates (Fig. 9.6). A weightless rod of length l\u003d 10 cm, at the other end of which there is a small massive ball. At what angle from the vertical will the rod deviate at the angular speeds of rotation of the shaft: w1 = 14 s–1 and w2 = 7 s–1?

9 . 16 . The thread and the homogeneous rod attached to it rotate at a constant speed around the vertical axis. Will the thread and the rod be directed along the same straight line? [will not]

9. 17 . The space station rotates around its axis (Fig. 9.7), due to which an artificial gravity force is created on it. The astronaut releases an object at a point A. Will the object fall to the point B? [No]

9. 18. A mathematical pendulum consists of a ball of mass m\u003d 50 g suspended on a thread of length l\u003d 1 m. Determine the smallest tension in the thread if the ball passes the equilibrium position with a speed v= 1.4 m/s.

9 . 19 . The mathematical pendulum oscillates. In the position of greatest deviation, the acceleration of the load is 20 times less than when passing through the equilibrium position. Find the angle of maximum deviation.

9.20. On a rotating horizontal table at a distance R= 50 cm from the axis of rotation lies a load weighing P = 10 N. Friction coefficient between the load and the table surface m = 0.25. What is the friction force holding the load if the speed of rotation of the table n=12 rpm? At what angular velocity w max will the weight begin to slide on the table?.gif" width="61" height="31 src=">]

9.23. A plane with an inclination angle a to the horizon rotates with an angular velocity w around the vertical axis. On the inclined plane the load lies. Determine distance R between the axis of rotation and the center of gravity of the load. Ignore friction.

9.24. How many times will the maximum allowable speed of a cyclist on an inclined track with an angle of inclination a increase compared to maximum speed movement along a horizontal track with the same radii of curvature of the trajectory and coefficients of friction m?.gif" width="127" height="53">]

9.26. Hemispherical bowl with radius R= 1 m rotates around a vertical axis with an angular velocity w =4.4 s–1. The bowl contains a ball that rotates with it. Where is it in the bowl? Place to determine the angle.

9.28. The pendulum thread is deflected to a horizontal position and released. What should be the minimum strength of the thread so that it can withstand the tension when a pendulum of mass 1 kg passes through the equilibrium position?

9.30. Load of mass m, tied to an inextensible thread, rotates in a vertical plane. Find the difference in the thread tension at the lower and upper points of the trajectory..gif" width="347" height="48 src=">]

9.31. A ball suspended on a thread was told some initial speed, after which it began to rotate in a circle in a vertical plane. Determine the mass of the ball m, if it is known that the tension force of the thread at the top point of the trajectory was T 1 = 1 H, and at the lower point of the trajectory T 2 = 2 H. Neglect air resistance, g= 9.8 m/s2..gif" width="161" height="57">]

9.33. Ball mass m suspended on a thread of length l, is set in rotational motion in a horizontal plane. What should be the strength of the thread F, to radius R the circle along which the ball moves became equal to ?

9.35. A circular platform rotates around a vertical axis with an angular velocity w. There is a ball of mass on the platform m attached to the axis by a thread. The angle of inclination of the thread is a, the length of the thread is L. Determine the tension in the thread at the time the ball leaves the platform. [ F = m w2 L]

9.36. A cone with an opening angle of 2a rotates around a vertical axis with an angular velocity w. The cone contains a ball of mass m, attached with a thread to the lateral surface of the cone and rotating with it along a circle of radius R. Find the thread tension. ,"en":["OYZZNEzP9ec","rZHScKqwnpY","OYZZNEzP9ec","jxf7XqvZWWg","OYZZNEzP9ec"],"es":["pEPXnBCmpVc","Y2Lyf8RmtRw"],"pt":["36sY_eRDmBY", null,"5MuRr_CQlQE","36sY_eRDmBY","36sY_eRDmBY","f9eXGicP8R8"],"it":["H1ctkzJCNYM"],"pl":["bLwdPh7DooY"],"ro":["fU1vOcLXDpg","pnoWTEtOM98 "])