Mechanical Engineering Answers

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A cantilever beam of cross-section 90 mm. width 120 mm deep carries a UDL of 12 KN/m. over the entire length and a concentrated load of 15 KN at the right end. Find the bending stress in the beam, when the length of beam is 10 m.

Evaluate the integral of 3 dx dy. Use inner limits=y^2 to 9, outer limits 0 to 3.

Determine the integral of xy dx dy. Using limits of x=0 to (y+1) and y=0 to 1.

Find the integral of (2-x-y) dx dy. Using limits of x=0 to (1-y)^0.5, and y=0 to 1.

The engine mechanism shown in Fig. 5 has crank OB = 50 mm and length of connecting rod

AB= 225 mm. The centre of gravity of the rod is at G which is 75 mm from B. The engine

speed is 200 r.p.m.

Fig. 5

For the position shown, in which OB is turned 45° from OA, Find 1. the velocity of G and the

angular velocity of AB, and 2. the acceleration of G and angular acceleration of AB.

• Define coriolis component of acceleration along with its direction. Also derive expression for

it.

The mechanism, as shown in Fig. 3, has the dimensions of various links as follows: AB = DE

= 150 mm; BC = CD = 450 mm; EF = 375 mm. The crank AB makes an angle of 45° with the

horizontal and rotates about A in the clockwise direction at a uniform speed of 120 r.p.m. The

lever DC oscillates about the fixed-point D, which is connected to AB by the coupler BC. The

block F moves in the horizontal guides, being driven by the link EF. Determine: 1. velocity of

the block F, 2. angular velocity of DC, and 3. rubbing speed at the pin C which is 50 mm in

diameter.

The owner of a video store has contacted you to develop a system to keep track of videos and rentals. He feels that with the growing number of customers, such a system will greatly help in managing accounts and providing better customer service.

List the process model that you think will be most appropriate for the above situations. Also list your reasons for choosing the process mode.

p^2+q^2=z (quasilinear or non linear equation)

Air is used as a working substance in a given internal combustion engine, which is

supplied with heat at a constant volume. Based on the data, calculate the following:

1)Pressure and temperature of the ending of isentropic expansion.

2)Pressure rise rate

3)Thermal efficiency of the cycle

4)The work of the cycle

5.The average pressure of the cycle

Givens:

k=1.4

r=10

T 1 =285 K

T 3 =2274 K

p 1 =1.013 bar

v 1 =0.5 m 3 /kg

A deep groove ball bearing has dynamic capacity of 2020 N and is to operate on the

following work cycle.

Radial load of 5800 N at 200 rpm for 25% of the time

Radial load of 8900 N at 500 rpm for 20% of the time

Radial load of 3500 N at 400 rpm for remaining time

Assuming the lads are steady and the inner race rotates, find the expected average

life of the bearing in hours.