1. As shown in Figure 1, two tanks of different cross-sectional areas are connected by a pipe. The tanks are filled with water, and openings A and B are tightly sealed with pistons that can move without friction. Initially, both pistons are in equilibrium at the same height. The cross-sectional area of B is n times larger than that of A.
As shown in Figure 2, a force of magnitude F is applied vertically downward to the piston at A, causing it to move downward by distance h. As a result, the piston at B moves upward by distance h'. Next, a force of magnitude F' is applied vertically downward to the piston at B. As a result, both pistons return to their original positions shown in Figure 1. From 1-9 below choose the combination that correctly expresses h' and F'.
Answer: 5
2. Block A have weight 100 N tied with ropes horizontally in C (see figure). Block B have weight 500 N. Coefficient of friction between A and B = 0.2 and the coefficient of friction between the floor and B = 0.5. The magnitude of the force F at least to shift the beam B is. ..
Answer: 320 N
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2. Block A have weight 100 N tied with ropes horizontally in C (see figure). Block B have weight 500 N. Coefficient of friction between A and B = 0.2 and the coefficient of friction between the floor and B = 0.5. The magnitude of the force F at least to shift the beam B is. ..
Answer: 320 N
3. Bullet with a mass 50 gram is fired in the direction of the block mass 0.95 kg, which is located on the flat areas of the slick is associated with spring, as in the picture on the side. It causes the spring depressed 20 cm Calculation indicates that the style of 1 N may cause the spring depressed 1 cm. Magnitude initial velocity is. ..
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Answer: 40 m/s
4. Two stationary particles of masses M1 and M2 are a distance d apart. A third particle, lying on the line joining the particles, experiences no resultant gravitational force. What is the distance of this particle from M1?
5.A particle of mass 4 kg moves with simple harmonic motion and its potential energy U varies with position x as shown in the figure below. What is the period of oscillation of the mass?
6. A mass m on a smooth horizontal table is attached by two light springs to two fixed supports as shown in the diagram below. The mass executes linear simple harmonic motion of amplitude a and period T. The energy associated with this simple harmonic motion is
5.A particle of mass 4 kg moves with simple harmonic motion and its potential energy U varies with position x as shown in the figure below. What is the period of oscillation of the mass?
6. A mass m on a smooth horizontal table is attached by two light springs to two fixed supports as shown in the diagram below. The mass executes linear simple harmonic motion of amplitude a and period T. The energy associated with this simple harmonic motion is
Answer: 2π2ma2/T2
7. Mountain bikes often have a suspension system built into the front and rear wheels in order to cushion impacts when riding on tough terrains. The figure below shows one such bike. A study of the suspension system of this bike is made by applying a force on the seat and measuring the compression x. The graph shows the results of the study.
(a) Calculate the effective spring constant of this suspension system
(b) Calculate the mass of a cyclist who produces a compression of 50 mm when seated on this bike
(c) Calculate the elastic potential energy stored the suspension system when the cyclist is seated on the bike
Answer: (a) 17142 N/m
(b) 85.7 kg
(c) 21.427 J
8. A molecule collides with another, stationary molecule of the same mass. Demonstrate that the angle of divergence:
(a) equals 90° when the collision is ideally
elastic;
(b) differs from 90° when the collision
is inelastic.
9. In a nuclear collision, an alpha particle A of mass 4 unit is incident with velocity v on a stationary helium nucleus B of 4 mass unit. After collision, A moves in the direction BC with velocity v/2, where BC makes angle 600 with the initial direction AB, and the helium nucleus moves along BD. Calculate the velocity of rebound of the helium nucleus along BD and the angle θ made with the direction AB.
Answer: 0,866v ; θ = 300
10. The velocity of a particle moving in the positive direction of the x axis varies as v = ax1/2 where a is a positive constant. Assuming that at the moment t = 0 the particle was located at the point x = 0, find:
(a) the time dependence of the velocity and the acceleration of the particle;
(b) the mean velocity of the particle averaged over the time that the particle takes to cover the first s metres of the path
11. A point moves rectilinearly with deceleration whose modulus depends on the velocity v of the particle as w = av1/2, where a is a positive constant. At the initial moment the velocity of the point is equal to vo. What distance will it traverse before it stops? What time will it take to cover that distance?
12. car starts moving rectilinearly, first with acceleration a =5.0 m/s2 (the initial velocity is equal to zero), then uniformly, and finally, decelerating at the same rate a, comes to a stop. The total time of motion equals t = 25 s. The average velocity during that time is equal to (v) = 72 km per hour. How long does the car move uniformly?
Answer: 15 s
13. A disc rolls without slipping along a horizontal surface with velocity u. The disc then encounters a smooth drop of height h, after which it continues to move with velocity v. At all times the disc remains in a vertical plane (figure)
14. In the arrangement shown in Fig. 6.10, the radius of the pulley is r , its moment of inertia about the rotation axis is I and k is the spring constant. Assuming that the mass of the thread and the spring is negligible and that the thread does not slide over the frictionless pulley, calculate the angular frequency of small oscillations.
15. A U-tube is filled with a liquid, the total length of the liquid column being h. If the liquid on one side is slightly depressed by blowing gently down, the levels of the liquid will oscillate about the equilibrium position before finally coming to rest.
(a) Show that the oscillations are SHM.
(b) Find the period of oscillations.
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