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1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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...