Reference no: EM133030666

Question 1. Design of Machine Elements

A fatigue test was conducted in which the mean stress was 70 MPa (10150 psi), and the stress amplitude was 210 MPa (30460 psi).
(a) Compute the maximum stress level. c) Compute the stress ratio.
(b) Compute the minimum stress level. d) Compute the magnitude of the stress range.

Question 2. Mechanics (Statics/ Dynamics)
The uniform slender bar of mass m is released from rest in the horizontal position as shown in solid lines. Determine the force exerted on the bar by the support A as the bar passes the position as shown in dotted lines. Friction at pivot A is negligible. (Mass moment of inertia of slender bar about its mass center is ml²/12

Question 3. Strength of materials/ Mechanics of materials

A beam ABC is simply supported at A and C as shown in Figure 1. It is subjected to uniformly distributed load of intensity w along AB. A concentrated load P is applied at D of a rigid member which is firmly fixed to the beam at B. The beam has constant EI. Ignore the weight of the beam.
(a) Determine the magnitude and orientation of the reaction force at supports A and C.
(b) Express the elastic curve of the beam in terms of E, 1, w, a and x. The origin of x is at support A.
(c) Determine the allowable beam length if the deflection at B is limited to 2 mm. Given: E= 200 GPa, I = 2x106 mm4 and w = 2 kN/m.

Question 4. Theory of machines

a) Draw the free body diagrams.

b) Analytical expression of torque T required for the mechanism to remain in static equilibrium, Write it down depending on the position variables and the pointed outer P.

c) Calculate the T torque whepte following numerical values of the mechanism are given. θ = 30 *, Φ = 45 °, r = 30 mm. l= 70 mm. P= 40 N.

Question 5. Material Science

Determine Miller indices for the planes A and B shown in the figures

Question 6. Manufacturing Science
A single start screw extruder of an Injection-molding machine that has a pitch of 3 cm rotates at 5 revolutions per minute. Calculate the volume and mass flow rate inside the barrel, given that the barrel diameter is 140 mm, H, the thickness of the ribbon is 20 mm. The density of the material is 1.2 g/cm3. State two important advantages of injection molding process in manufacturing.

Question 7. Engineering Economics

What is the equivalent values of the shown cash diagram (use i=15% per year).

Question 8. Vibration Engineering

Given that k -1 Wm and m -1 Kg and that the middle spring has a stiffness of nk.

The first natural frequency is 1 rad/5 . and the second natural frequency is 4.6 rad/s.

The first modal vector of the system is {1 1}. The second modal vector is of the form{1 A}j, what is A?

Question 9. Engineering Controls

Compare the responses of
5v + v = g + g
And
5v +v = g
If v(0) = 5 and g=10 for -∞≤t≤∞

Question 10. Electrical Machines

The core of a 300-kVA, 15000/650 V, 50-Hz, 1-ph, core type transformer has across-section of 30 cm x 30 cm. Find (1) the number of H.V. and L.V. turns per phase and (ii) the e.m.f. per turn if the maximum core density is not to exceed 1.5 Tesla. Assume a stacking factor of 0.75.What will happen if its primary voltage is increased by 15% on no-load ?

Question 11. Physics

In the system in the figure, find (a) the equivalent resistance between points A and B (b) the total current in the following circuit and the current in the 18 ohm, 40 ohm and 60 ohms

Question 12. Basic Mathematics

1) Find the coordinates of the vertices, foci, and co-vertices and the equations of the oblique asymptotes of the following hyperbola: y2/16 - x3/9 =1. Then sketch the graph of the hyperbola and its asymptotes.

2. Write the equation of a hyperbola in standard from with its center at the origin vertices at(±2,0) and point (5,3) on the graph of the hyperbola.

3. Find the equation of the hyperbola whose graph is shown below:

Question 13.Engineering Mathematics

Find the inverse Laplace Transform of 1/(s2-2s+2)(s+1)