as per attached document

Question 1 Vibration welding is a technique for joining plastic parts. It involves laterally moving one thermoplastic part (shown as the upper part in Figu re 1-1) at a frequency of 200 Hz and an amplitude of 1 mm over a second stationary part. I nitially, solid-solid friction between the two parts heats the interface up to the melting point o f the plastic plates. Once a thin layer (gap) of liquid is formed at the interface, the liquid is sh eared back and forth to generate more heat. The thickness of the melt gap ( h) is estimated to be 100 mm. The vibratory motion of the upper part follows a si ne wave. The position along the x-axis of any point on the upper moving plate relative to its initial position can be described using: )t sin( x x O w = [1-1] Where x O is the amplitude of 1 mm. w is the radial frequency of vibration in rad/s. As I am sure you all will recall from high school, w = 2 p N , where N is the frequency of vibration in Hz ( N =200 Hz). (a) Estimate the maximum shear rate ( g&) in the melt gap.

(b) If the fluid is Newtonian, show that the power diss ipated as heat per unit volume ( P&in units of W/m 3) of liquid in the gap is: (hint Power = force x v elocity) 2gh& &= P [1-2] (c) Estimate the maximum shear stress ( t) in the gap if the Newtonian viscosity ( h) is equal to 100 Pa.s at this temperature and shear rate esti mated in (a).

(d) If the plates have the dimensions shown in figure b elow, calculate the force required to drive the upper plate at this frequency for these c onditions. (e) If the polymer fluid is shear thinning ( K= 400 Pa s 0.8 and n = 0.8), calculate the force required to drive the upper plate.

Gap (h = 100 mm) x-axis 1 mm y-axis 100 mm 3 mm Upper plate Liquid gap Lower plate Question 2 The following dynamic modulii vs temperature curves were obtained for three different materials (A, B and C) using dynamic mechanical analysis or D MA.

(a) Explain how DMA works. Specifically, what does the prime ( ¢) signify on the letter G?

(b) Looking at the graph below, state whether you think that the DMA test was done in tension, compression, flexion or shear. State why.