Thursday, October 22, 2009
physics teacher was briefing us about the exam today, and he told us there would be qns that combine the sem1 stuff with stuff from this sem. so..., we thought of a qns that includes everything, ever single topic, from Mechanics. Heres the basic idea(WARNING, IF YOU DUN WANNA DIE, DO NOT READ, if you want to explode into 10^16 pieces, attempt solving the problem)
A light ball, 0.5kg is thrown at a bigger ball, 2kg, that is attached to a pole, which is stuck to a engine and is suspended like a pendelum. The light ball collides elastically with the bigger ball and bounces back at 2m/s. The light ball was in contact with the bigger ball for 0.23s. Suspose the velocity of the ball jus before it hit the bigger ball is 5m/s. The bigger ball swings upwards and just barely hits a switch, which turns on the engine.
(a) Find the force by the light ball, and find out at what height is the switch at.
The engine starts and applys a torque to the pole and the ball in varying magnitudes so that it would have an constant angular acceleration in the clockwise direction. After turning for 10 rounds, the ball turns an additional 137(degrees), before it breaks free. Suspose the length of the pole is 0.5m and the system has a angular acceleration of 1.7rad/s^2,
(b) Find the angular velocity, tangential velocity of the ball just before its release. Also find the torque by the engine(assume pole is massless). Draw a free body force diagram of the ball at that time too.
(c)If the pole breaks at a tension of (*some close enough number*), did the ball break free due the the pole breaking or due to another mechanism?
The ball now travels in a parabola and lands in a rubber funnel with water some distance away, where the water level is at the same level as point of launch.
(d)How far is the funnel away from the point of launch? What is the maxium height of the parabola? What is the speed in which the ball lands?
(e)What is the height of the ball from the ground when its 3/4 to the funnel? What is its velocity then?
The density of the ball is 477.465kg/m^3, and thus it floats on the water.
(f)Find the amount of water displaced.
The water is leaking out from the funnel at 2m/s and the radius of the narrow part of the funnel is 0.09m. The length of that part is 0.5m and the length from the narrow part to the point where the water level is is 0.4m. The diameter of the funnel 0.1m below the surface of the water is 0.2m.
(g)Find the speed in which the ball falls into the funnel.
When the water is drained the ball with a radius of 0.1m is bigger than the funnel but manages to slip through as the funnel is made of rubber. If the funnel squeezes the ball with a force of 5N and the ball falls through in 2 sec,
(h)Find the coefficient of friction of the rubber funnel. Also find the exit velocity of the ball, the acceleration of the ball in the funnel and the work done by friction.
The ball exits the funnel and falls 1m onto a spring on a platform, which moves towards ground level at a acceleration of 2m/s^2. If the collision is totally inelastic and the spring compresses by 0.075m
(i)Find the spring constant and the height which the ball will spring back up to(assume platform is on ground as spring decompresses and a(platform)=0m/s^2 at that moment.)Also draw a free body force diagram of the ball as the spring compresses.
As the ball reaches its highest point, a ultra dense sphere is manipultaed to and released from beside it and falls at the same speed. The ultra dense material is also controlled in such a way that the distance between it and the ball remains constant, at 0.1m. If the mass of the material is 10^6 kg
(j)How much would the ball move towards the direction of the material as it falls?
The ball lands outside of the spring, doesn't bounce and rolls down a frictionless ramp 0.75m high with a angle of 35(degree) to the ground and onto a frictionless conveyer belt and moves relavtive to the belt at(*some speed lower than the ball*).
(l)Find the speed of : the ball relavtive to earth, the conveyer belt relative to earth
The ball rows into the middle of 4 marbles arranged in the shape of a squarewith length 0.4m(still on belt). The mass of marbles from top right clockwise is : 0.2kg, 0.5kg, 1.5kg, 0.1kg
(m)Find the velocity of the center of gravity of the ball and the marbles.
The ball finally rolls pass the finish line 10m from the ramp.
(FINALE)Find the time it took since the engine was switched on. (LOLOL)
If that comes out in the exam, I'll conceit defeat and walk out. Luckly it was me who cme up with it, and not some teacher from the physics department. I'm not even sure it can be solved, but its the gheyest qns ever, i'm sure. If you can do, gratz, you totally pwned non-calculus based mechanics.