1. Engineering
  2. Mechanical Engineering
  3. ball mo ball 2450 min figure 4 catapult system e...

Question: ball mo ball 2450 min figure 4 catapult system e...

Question details

Ball Mo Ball 2450 min Figure 4: Catapult system. (e) System with spring extended, (b) system at launch point4. [10 marks in total] In Workshop 10, you will need to model the launch velocity of a catapult system shown in Fig. 4. The way the catapult works is as follows The arm is pulled back, putting potential energy into the spring(s) (see Fig. 4(a) Note that even though only one spring is shown in Fig. 4, there could be more than 1 spring in the actual system. When the springs are extended sufficiently the arm is released converting the po- tential energy stored in the springs into kinetic energy by contracting and hence accelerating the arm and ball forward. (Note: Not all the energy is going into the ball) . The arm is stopped by a bar (not shown in Fig. 4) such that the angle in which the ball is release, θ is 45° (Fig. 4(b)). You are required to write a MATLAB function that predicts the launch com- ponent of velocity, uo & vo, given properties of the spring configurations. But before you do that, you will need a bit of theory. Even though the theory given below might seem long, the MATLAB function that you are required to write should not take more than one A4 page.where Tmax the maximum extension and Tmin is the minimum extension. If the length of the spring at maximum and minimum extensions are denoted by lmax and Imin re- spectively, then Tmax Imax-rest. min min rest Note that if you have more than one spring in the setup, then you can just add up the energy of each individual spring, i.e. the total energy in the springs is given by Etotal-Σ E spring,i where Espring, is the energy of each individual spring given by Eq. (5) and N is the number of springs in the system. For example, if N -2, Eq. (8) will expand to total - E spring,1Spring,2 1maX,l min,iSince we will assume that the total potential energy, Etotal, is completely converted into kinetic energy, we will need to express kinetic energy in terms of velocity. Kinetic energy is related to the angular velocity by 2 K Etotal2 where (10) dt and I is the moment of inertia and w is the angular velocity. The moment of inertia is a function of the object and the axis of rotation. It is a fairly complex process to determine the formula for I, so we will just give them to you hereIarmmarmarm 3 an 2 ballballball (12) where m is the mass of the arm or ball, larm is the length of the arm and lball is the distance of the ball from the pivotal point. Note that the arm is modeled as an infinitely thin rod of evenly distributed mass rotating about its end, and the ball is modeled as a point mass. You will learn more about moment of inertia in later years of your course. The total moment of inertia for a system is merely the sum of the parts of the system, (13) The magnitude of the launch velocity (V%) of the ball can now be calculated using the following formula Vo-wlball- (14)The r and y component of velocity can now be determine by 10-0 cos(45°) (15) vo Vo sin(45) (16) Your task You are required to write a function that takes as its input, lrest, Imax, min k and L for each spring. All these parameters must be arrays because there could be more than 1 spring in the system. The output of your function should be the uo and vo component of the launch velocity of the ball. The function declaration and the first few lines of your MATLAB function should look likefunction [u0, vO]-GetVelocityFromSetup(lrest,lmax,lmin,k,L) N-length(k); xmax = zeros ( 1 , N) ; xmin = zeros( 1 , N) ; Etotal-0; % Fill in the rest of the function here!! !! Note that the MATLAB function must be called GetVelocityFromSetup() to work cor- rectly with the catapult simulator in Workshop 10. The flow chart of your function would look something like Fig. 5. The parameters that you will need to use in your program are given in the last section entitled Constants. To ensure that your program is working properly, the solution for one set of parameters is shown below >> lrest (1)-0.149;lmax (1)-0.247;lmin(1)-0.177;k(1)-287.5;L(1)-6.903; >> lrest (2)-0.149; lmax(2)-0.250;lmin(2)-0.180;k (2)-308.9;L(2)-9.617; >> [u0, v0]-GetVelocityFromSetup(lrest,lmax,lmin,k,L) 5.3923no 5.3923 5.3923Calculate the total moment of inertia, I, using Eq. (13) and use Eq. (9) to calculate the angular velocity, w Use Eqs. (14), (15) and (16) to calculate u and v uo and va 0* Figure 5: Flowchart

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution