Reference no: EM13549710

For my project I constructed a trebuche. A trebuche is an ancient device used for launching projectiles. It acheives this by harnessing potential energy and allowing this potential energy to convert into kenetic energy. This potential energy is stored in the form of a raised weight held in place once raised by a latch or a hook. This tpye of stored energy works because of the effects of gravity on mass. This potential energy of an object can be determined by multiplying the mass of the object by the acceleration acheived by the force of gravity on the object multiplied by the height of object. Once the latch or hook is taken away from holding the weight in position the force of gravity accelerates the weight causing it to traverse the given height of the object and thus converts the potential energy into kenetic energy. In this scenario the lever arm to which the weight is attached is put into motion by these principles and the object we wish to project across a distance is able to acheive a trajectory from the potential energy being converted into kenetic energy. For this model a weight of aprox 9.1 Kg (9.8) with weight of board) raised to a height of aproximately 1.3 meters. Due to the acceleration of gravity at approximately 9.8m/s^2, this correlates to about 124.8 joules of potetial energy. The tpye of force being inacted upon the lever to propel it into having kenetic enery in this scenario is torque. Torque is a measure of force calculated by the perpendicular force on an axis multiplied by the distance of the radius by which is rotates. In this situation however my torque is ever changing. Prior to launch my weight is not perpendicular to my lever arm but sits at aprocmiately a 60 degree angle from horizontal. This means my torque right when i release the latch or hook mechanism is gravity multiplied my mass multiplied by the cosine of 60 degrees minus the torque created in the opposite direction from the lever arm that hangs over the opposite side of the rotational center. Because the opposite side of the lever is about 2 meters in length and is fairly uniform throughout the center of mass would be at 1 meter. Its mass being about 3kg the opposite torque created would be acceleration due to gravity times mass times 1 meter times cos of 60 degrees (14.7newtons). The length of lever on the weighted end is about 2/3 meters and weighs about 2/3kg. So the torque on weighted end would equate to aprox. 31.9 newtons. This creates a net force of 22.1 newtons at the start of launch. This number will vary however with the position of the lever arm is it rotates through the launch cycle. This is because the angle of the lever arm changes at is rotates. About halfway through the launch the weight will be perfectly perpendicular to the rotational axis where torque will reach its largest magnitude before it begins to diminish again as the angle varies away from this position. With the projectile on about 1 meter of string and attached to the unweighted end that is by iteself 3 times the length of the weighted end, the projectile obtains a velocity 4.5 times greaters than the endpoint of the weight end. However because torque is always varying and the wighted and unweighte arms are not equal length im finding it dificult to calculate the velocity of the projectile before release. Would I have been able to calculate veloctiy my trajectory could be determined by mutiplying that velocity by the cosine of the angle of release (aprox 45-50 degrees) multipled by the time of flight. The time of flight could be determined by finding velocity in the y-plane by taking the sine(45-50 degrees) and then by divinding this number by the acceleration due to gravity. this would give me time to reach max height where velocity is 0. That height would be determined by the equation D = v(t) - .5at^2. We could then calculate the time it would take for the object to freefall from this height by using the same equation only pluggin in max height for distance and solving for time. Add the two times together and we have the total time for flight which we would multiply by the previously calculated x-plane velocity to find distance.