1. Design and check for stability for a square and ground end helical spring subjected to a maximum force of 1300 N supported between flat surfaces. The deflection of the spring corresponding to the maximum force should be approximately 25mm. The material used for the spring is cold drawn steel wire with ultimate tensile strength, modulus of elasticity and rigidity of 1090, 207000 and 81730 MPa, respectively. Assume and state relevant parameters.

A spring was compressed by varying load from 100N to 350N. If the spring material is music wire, design the spring specifications and indicate its factor of safety against fluctuating stresses.Assume and state relevant parameters.

A rock is dropped from the top of a tall tower. Half a second later another rock, twice as massive as the first, is dropped. Ignoring air resistance,

15.33 A spur gear reducer has an 18-tooth pinion driven 1500 rpm by an electric motor and a 36-tooth gear that drives a load involving “moderate shock.” A life of 106 pinion revolutions is required, and the transmitted load, Ft, is 100 lb (this figure includes a
safety factor of 2). Conditions are such that Km = 1.8 and kt = 1. It is proposed that standard 20° full-depth gears be used, with both pinion and gear teeth being cut with a low-cost, average-quality, form-cutting process from steel of 235 Bhn for the gear and 260 Bhn for the pinion. Diametral pitch is to be 10, and face width 1.0 in. Estimate the reliability with respect to bending fatigue failure.

What is the aluminum profile? What is the manufacturing method of aluminum profile? What are the materials used in the manufacture of the product? Describe them all in detail. Please keep the explanations long!!!

Explain the meaning and usefulness of the equivalent diameter, for the annular region in a double pipe heat exchanger.

Hydrogen, acting as a van der Waals gas (EOS shown below), is compressed in an isothermal closed system process from 6.236m3/kg to 0.629m3/kg at 300K. What is the change in specific entropy of the gas? (use the entropy change relation in chapter 12)

P = RT/( v − b) − a/( v^2) (1)

a = 27R^2Tcrit^2/(64Pcrit) (2)

b = RTcrit/ (8Pcrit) (3)

Following example 12-7 in the book the change in internal energy of a van der Waals gas for an isothermal process can be derived (the result is shown below). Using the definition of boundary work (wb = R P dv) and conservation of energy what is the amount of heat which is rejected by the compression process?

u2 − u1 = a (1/v1 − 1/v2)

a tapered surface is to be turned on an automatic lathe the work piece is 750 mm long with minimum and maximum diameter of 100 & 200 mm at opposite ends the automatic controls on the lathe permit to surface speed to

be maintained at a constant value of 200 m/min by

adj Listing the rotational speed as a function of workpiece
diameter. Feed = 0. 25 mm/rev and depth of cut · 3. 0 m.
The rough geometry of the piece has already been formed,
and this operation will be the final cut. Determine (a) the

time required to turn the taper and (b) the rotational speeds
at the beginning and end of the cut.

Determine the carburizing time (in s) necessary to achieve a carbon concentration of 0.44 wt% at a position 1.8 mm into an iron-carbon alloy that initially contains 0.031 wt% C. The surface concentration is to be maintained at 1.2 wt% C, and the treatment is to be conducted at 1090°C. Assume that D0 = 5.1 x 10-5 m2/s and Qd =154 kJ/mol. You will find the table below useful.

In line-shaft driven product machinery, torsional deflections and vibrations of the camshaft due to the time-varying torque of various cams can cause synchronization problems between the various stations on the machine. We need to design a testing machine that will measure the torsional vibration effects of dynamic torque loading on a camshaft. This machine will accommodate two cams, each of which will drive its own spring-loaded translating roller follower on a slider mechanism at speeds up to 300 rpm. These cams will be designed to give approximately opposite torque-time functions to one another. They can be used singly or in pairs to investigate the effectiveness of the addition to a production machine of a torque-balancing cam that drives a dummy load. The cams will be split to allow removal and installation without disassembling the shaft. The torque-time and follower force time functions for the primary cam are provided as an excel file P09-20 on the books website. The secondary cam will be a mirror image of the primary cam to approximately balance the torque. The camshaft in this test fixture must be designed to have torsional deflections that are large enough to be measured by 5000 count per revolution, optical shaft encoders attached at each end of the camshaft, but not so large as to fatigue fail the shaft. At the same time, we want the camshaft to be stiff in bending and have a bending natural frequency at least 10 times its torsional natural frequency to minimize any coupling effects between bending and torsional modes. Stated another way: what should the shaft diameter be to give sufficient torsional deflections to be measurable under the designed loading conditions, but not to create undesirable bending deflections or vibrations. Plain bearings should be used to avoid vibrations that would come from rolling element bearings. The test machine will be driven by a speed controlled PM DC motor through a gear reduction unit of your design. Motor selection is also your responsibility. What is required is a detailed design of a camshaft torsional vibration test machine including the camshaft, keys, follower trains, bearings, couplings, gearbox, frame and mounting hardware. infinite life is desired.

Assume a dimension that a customer is interested in is given by R = x0.5+y. The variables x and y are determined using standard calibration gage pins, where the nominal value of x is 0.9” and the nominal value of y is 0.2”. The manufacturer of the gage pins states that the pins have error bounds of +0.0002” with a quality rate of 95.45%. Assume that the gage pin diameter follows a normal distribution. What is the expanded uncertainty with a 99.73% coverage probability? Use an appropriate estimate of the standard uncertainties of y and z in your calculation.

Determine the roots of f (x) = −12 − 21x + 18x2 − 2.75x3 graphically. In addition, determine the first root of the function with (b) bisection and (c) false position.

For (b) and (c) use initial guesses of xl = −1 and xu = 0 and a stopping criterion of 1%.

For questions 1, 2, and 3, walk through each question by hand, then use the “disp” command in your MATLAB script to display your answer to the screen.
1. What is the final value of x? x = 10; if round(x/5) == x/5 x = 2 * x + 4; elseif x == 10 x = 4 * x; else x = 0; end
2. What is the final value of x? x = 10; if round(x/3) == x/3 x = 2 * x + 4; elseif x == 10 x = 4 * x; else x = 0; end
3. What is the final value of x? x = 9; if round(x/4) == x/4 x = 2 * x + 4; elseif x == 4 x = 4 * x; else x = 0; end
4. Write a MATLAB script that calculates the total cost for Giant Slinkys: • Ask the user to input the quantity of Giant Slinkys they wish to have shipped. • Make sure the user's input is a positive integer. • 10 or fewer Giant Slinkys cost $21.99 each. • 11 to 50 Giant Slinkys are $19.99 each • 51 to 100 Giant Slinkys are $17.99 each • More than 100 Giant Slinkys cost $15 each. • Sales tax is 9.5% • Shipping is $10 for each group of 10 Giant Slinkys. For example: ◦ Shipping for 1 Giant Slinky is $10; Shipping for 8 is also $0; Shipping for 10: $10. ◦ Shipping for 11 Giant Slinkys is $20; Shipping for 15, also $20; Shipping for 20: $20. • Shipping is free for orders of 50 or more Giant Slinkys