Mechanical Engineering Answers

A traffic control engineer reports that 75% of the vehicles passing through a checkpoint

are from within the state. What is the probability that fewer than 4 of the next 9 vehicles

are from out of state?

A solid cylinder, 0 ≤ r ≤ b, is initially at zero temperature. For times t > 0, internal energy is generated in the solid at a rate of g(t) per unit volume (W/m3), whereas the boundary surface at r = b dissipates heat by convection into a medium at zero temperature. Obtain an expression for the temperature distribution T(r,t) in the cylinder for times t > 0.

an electric hot plate is maintained at a temperature of 350 degrees Celsius and is used to keep a solution just boiling at 95 degrees Celsius

A vehicle travelling at 70km/hr is accelerating up a hill with a gradient of 1 to 20. If the mass of the car is 1500kg, the frontal area is 1.95m², rolling resistance of 240N and the drag coefficient of the body if 0.035. At this instant, the engine is developing 56.80KW at 4000rev/min and the transmission efficiency is 80%. If the rear axle ratio is 5.2 to 1 and the rolling radius is 35cm. Calculate the acceleration of the vehicle. (Take TR-RG + RR+ RA

The diameter of a brake drum is 30cm the pivot for the brake shoe and the point of application of the force actuating the shoe are 120mm each from the axis of rotation. Assume that the pressure distribution over the brake lining is equal to a single force acting radially and the coefficient of friction is 0.25. Calculate the braking torque exerted by an operating force of 900N on:

i. The leading shoe

ii. The trailing shoe

A motor vehicle of mass 2000 kg travels round a curved path of radius 55 m the coefficient of friction between the tyres and the road surface is 0.75. The track of the vehicle is 1.5m and the centre of gravity is 70cm above ground level. Calculate the maximum speed at which the vehicle can travel round the curve:

i. without skidding outwards ii. without overturning

iii. if the angle of tilt is 300 without overtuming.

a. A shipment of 7 television sets contains 2 defective sets. A hotel makes a random

purchase of 3 of the sets. If x is the number of defective sets purchased by the hotel,

find the probability distribution of X. Express the results graphically as probability

histogram.

b. Find the cumulative distribution function of the random variable X representing the

number of defective in problem a. Then using F(x). Find

P(X=1) and P (0X2)

c. Construct the cumulative distribution function of problem b

Refrigerant-134a at 1.4 Mpa and 90°C is throttled to a pressure of 0.6Mpa. What is the temperature of the refrigerant after throttling.

A nuclear reactor generates 3000MW of heat. The heat is transferred in a heat exchanger of energy transfer efficiency 75% into steam which is expanded in a turbine in order to produce a power output. The steam is condensed in a condenser, releasing 1800MW of heat, and pumped back through the heat exchanger by a feed pump which requires 3% of the power output from the turbine. Determine

A) The net power output from the plant

B) The power output from the turbine

C)The overall thermal efficiency of the plant

A machine component is subjected to fluctuating stress that varies from 40 to 100 N/mm². The corrected endurance limit stress for the machine component is 270 N/mm². The ultimate tensile strength and yield strength of the material are 600 and 450 N/mm² respectively. Find the factor of safety using

(i) Gerber theory

(ii) Soderberg line

(iii) Goodman line

Also, find the factor of safety against static failure.