Weight Block

The component that I am analyzing is the object that will carry the momentum to accomplish the jump of the skateboard. This object will be preloaded on compressible springs. The springs will then be released, propelling the object towards the tower that will be mounted upright on the skateboard. This tower provides a physical constraint to the skateboard. The skateboard is going to jump through the momentum that is transferred when the skateboard and the object collide.  The fundamentals requirements needed to design this object are:

·         What is the mass needed for the object

·         What material can be used

·         At what velocity will this object be traveling

·         The shape should be a rectangular slab and be able to fit within the area of the deck of the skateboard

·         Consider multiple slabs to adjust weight as desired

                To determine these requirements, an analysis of the conservation of momentum is need between the object and the skateboard constrained system, an analysis of the velocity that the object acquires through the energy of the spring, and how the final velocity of the system will affect the height of the jump.. I did these analyses first so that I can get an idea of how fast the object will need to be traveling and at what mass the object should be. Depending on the mass, I can then figure out what the type of material can be used and its dimensions.

                I first analyzed the whole skateboard system to find out what velocity the system needed to get the whole system off the ground to a certain height. I was only considering the height of the jump and not any other dimension. Using the following the kinematic equation, I solved for the initial velocity needed for a certain height.

Kinematic equation:            Vf 2=Vi 2 + 2*a*d

Where Vf is the final velocity of the system. For maximum displacement this would be zero.                                                                            

Vi is the initial velocity where this would be the velocity the system experiences right after the collision and this is what I needed to find                                                             

a = constant acceleration, this would be gravity (-g)

d = total displacement, this would be the height of the jump

Solving the equation, I arrived at the conclusion that the height of the jump of the skateboard is proportional to the square of the velocity the system has after the collision.

d = Vi2 / (2*g)

I thus needed to find this Vi by analyzing the conservation of momentum between the collision of the object and the skateboard. The collision will be assumed to be perfectly inelastic. The object in question will be mass 1 and the tower constrained with the tower will be mass 2. Initially, mass 2 is stationary, and after the collision, mass 1 and mass 2 are moving with the same velocity. Solving for the final velocity after the collision, we get

v2 = (m1*v1)/(m1+m2) = Vi

Thus it can be seen that the final velocity will be dependent on the mass of the object, mass 1, the mass of the skateboard system, mass 2, and the velocity the object has right before it collides with the skateboard system.  I then performed the energy balance on the object and the spring to determine how v1 is related to the mass of the object. I came to the following equation:

v1 = [ (0.5*k*x2 – m1*g*x)/(0.5*m1) ]1/2

where, k is the spring constant, x is the displacement in the spring, g is gravity, and m1 is the mass of the object.  I then created a program that would tell me the mass for the object with the given spring constant and distance the spring can be compressed that my teammate is considering. I came to the conclusion that the mass of the object should be around the range of 8- 15 lbs, but again, that all depends on what final spring constants my teammate chooses.

I then considered the area that we will be using on the skateboard. Taking into consideration the constraints of the length and width of the board, I found that area to consider will be from a minimal 8x8 in2 to a maximum 8x12in2. I then used online resources to find different metals that were ductile. I considered the four different types: aluminum, copper, steel, brass.  I tabulated these to figure out how much weight a slab of 0.125 in thickness will weigh.

I then used ThomasNet.com to find some companies that produced sheets or slabs of the above metals.

In conclusion, although much of the selection of the material is dependent on which spring constant we use, we have narrowed it down to just a few metals that are applicable and we can continue to narrow our searches for compatible mechanics with the simulations that were developed.

Sources: http://www.engineeringtoolbox.com/metal-alloys-densities-d_50.html, http://www.thomasnet.com/

Keywords: copper sheets/plates/bars, brass sheets/plates/bars, aluminum sheets/plates/bars, different metals densities