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  1. J

    Shm question -- a mass hanging on a spring vertically set into motion

    A mass on the end of a spring which is hanging vertically is raised up and let go. It then oscillates between 2m and 1.5m above the floor and completes 32 cycles in one minute. The height, h metres, of the mass above the floor after t seconds can be modelled by the function h=acos(pi t / 180)...
  2. J

    Centroid question

    7) Pile foundations are the part of a structure used to carry and transfer the load of the structure to the bearing ground located at some depth below ground surface. A concrete pile for a domestic dwelling has a radius of 1000 mm at its base, and 2000 mm at the top. It is 2000 mm deep and...
  3. J

    Second moment of area

    Find the second moment of area about the vertical axis for the cross-section of the follwing shape. i cant get the pic to paste so will describe it: it is a rectangle of horizontal length 8 and vertical height 6. if we let (0,0) be at the lhs bottom corner, then a circle has been cut...
  4. J

    Centre of mass question

    a triangle ABC with AB=BC=2a and AC=2a rt(2) is drawn on a uniform lamina. A semi-circle is drawn on BC as diameter,on the opposite side of BC from A and the area enclosed by the triangle and the semi-circle is cut out. The resulting lamina is suspended freely from B,show that AB makes an angle...
  5. J

    Motorboat relative motion

    a motorboat moving at 8km/h relative to the water travels from A to a point B 10km whose bearing from A is 150. it then travels to C,10km from B and due west of B. if there is a current of constant speed 4km/h from north to south,find the 2 courses to be set. having a bit of trouble with...
  6. J

    General motion of a particle

    a particle moves in the xy plane such that at a time t it is at a point (x,y) where x=2cos(at) y=2sin(at) prove particle moves in a circular path with constant angular velocity. prove that the acceleration of the particle at time t is in the direction of the radius from the particle to...
  7. J

    Relative motion

    a ship A is travelling due east at a speed of 8m/s and a ship B is travelling due south at 10m/s. At an instant when A is 3km from B in a direction 060 a motor boat leaves A and travels in a straight line to B with speed 14m/s 1) show it reacges B in 500 seconds 2)if upon reaching B the...
  8. J

    My answers seem ok but differ from book.

    1) a car moves along a straight road against a resistance to motion which is 10 times the speed of the car. the car has a mss of 800kg and the engine is working at the constant rate 5kw. find an expression for the acceleration of the car. my attempt: P=driving force.v => 5000/v=driving...
  9. J

    Work done by engine pulling up a mass

    just a query about last part of a question. a mass m hangs at end of light string and is raised vertically by an engine working at a constant rate kmg.at t=o,velocity =0 x=0 and x is measured in upwards direction. now i have shown increase in total energy of the mass, when moved up a...
  10. J

    Hopefully last question on circular motion (on a cone)

    a smooth hollow circular cone of semi-angle y is fixed with its axis vertical and its vertex A downwards. A particle P,of mass m,moving with constant speed V describes a horizontal circle on the inner surface of the cone in a plane which is at a distance b above A. show V^2=gb...done b)...
  11. J

    More circular motion questions:

    these are only short queries so i put them in the same thread. 1) one end of a light inelastic string of length a is attached to a fixed point A and a particle of mass m is attached to the other end,B. The particle is held at the same level as A,at a distance of asin x away from A,and...
  12. J

    Circular motion questions 2

    2) a particle P of mass m moves in a vertical circle along the smooth inner surface of a fixed hollow sphere of internal radius a and centre O,the plane of the circle passing through O. The particle is projected from the lowest point of the sphere with a horizontal velocity u. when OP makes an...
  13. J

    Circular motion questions

    a bead of mass m can slide without friction along a circular hoop of radius a which is fixed in a vertical plane. the bead is connected to the highest point of the hoop by a light elastic string of natural length a and modulus 3mg. initially the bead is moving with speed u through the lowest...
  14. J

    Circular motion/conical pendulum?

    one end of a light inelastic string is attached to a point A vertically above a point O on a smooth horizontal plane and at a height h above it. The string carries a particle P of mass m at its other end. WHEN JUST TAUT the string is inclined to the vertical at an angle S if P moves in a...
  15. J

    3 particles A,B,C of masses m,2m,3m lie at rest in that order on

    long questions but only need a little help i think: 1) 3 particles A,B,C of masses m,2m,3m lie at rest in that orderon smooth horizontal table.the distance between each particle is a> A slack light inelastic string of length 2a connects A and B and an exactly similar slack string connects...
  16. J

    Energy problems part (2)

    2 identical strings of length 1 metres and modulus of elasticity are each fastened to a particle of mass .5 kg. their othe ends are fixed to 2 points 4 metres apart in a vertical line. Find the height of the particle above the lower fixed point A in the equilibrium position. the particle is now...
  17. J

    Trouble understanding energy concepts

    a particle of weight W is attached by 2 light inextensible strings each of length a to 2 fixed points,A and B, distant a apart in a horizontal line. write down tension in either string. one of the strings is now replaced by an elastic string of the same natural length and it is found that in...
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