Mechanical Engineering Answers

A ball of mass 17.10 kg and diameter 38.13 metre is held fully underwater ( density 1000 kg/m^ 3) Calculate:

a) the upthrust on the ball

b) the density of the ball

c) the percentage of the ball above the surface of the water if it is allowed to float

A storage tank is 4.5 metre wide. It contains a liquid with density 750 kg/m^ 3 to a depth of 7 metre. Calculate the hydrostatic thrust on the side of the tank, and its position from the surface of the liquid.

At a point in an elastic material there are two mutually perpendicular planes, one of which carries a direct tensile stress at 50 N/mm2 and a shear stress of 40 N/mm2, while the other plane is subjected to a direct compressive stress of 35 N/mm2 and a complementary shear stress of 40 N/mm2.

Determine the principal stresses at the point, the position of the planes on which they act and the position of the planes on which there is no normal stress.

Air at a temperature of 100C is compressed at a constant pressure of

1.2MPa from a volume of 2m3 to a volume of 0.4m3. If the initial internal

energy decrease is 4820 KJ, find

a. the work done during the reversible compression

b. the heat transferred

c. the change in enthalpy

shows a 302 stainless steel spring is being applied by a dynamic loading from 150N to

600 N. The spring is peened to induce residual stress on the wire in order to resist fatigue failure. The total number of the coil is shown in Figure Q4 and the spring end is left as squared so that it is able to stand vertically when placed on a flat surface. If the spring index given is 11 and the outer diameter is 66 mm, determine the fatigue factor of safety of this spring. Also, estimate the critical frequency of the spring if the unit weight is given as 76 kN/m².

In Figure below, ω4 = 80 r/min ccw. Determine the number of revolutions per minute of 

link 2 and the velocity of sliding in meters per second at the point of contact. Use a 

velocity scale of 1 mm = 0.0300 m/s.

For the Scotch-yoke mechanism in the Figure below R = 203 mm, θ = 60°, and the crank

speed is 200 r/min. Find the velocity in meters per second and acceleration in meters per

second squared of the slider.

A disk 254 mm in diameter accelerates uniformly from a speed of 1000 r/min to 2000

r/min in 20 s. Find (a) the angular acceleration in radians per second squared and (b) the

revolutions of the disk during the 20-s interval.

An automobile accelerates from a speed of 32.2 km/h to 96.6 km/h in a distance of 89.3

m, which requires 5 s.

(a) If the acceleration is constant, find the acceleration in meters per second squared.

(b) Same as part (a) except the acceleration is not constant. What is the average

acceleration in meters per second squared?

Its shown in physics that the temperature ( ) , u x t at time t at the point x of a long,

insulated rod that lies along the x -axis satisfies the one-dimensional heat equation

2

2

u u

k

t x

 

=

 

, ( k is a constant).

Show that the function ( ) ( ) ( ) 2 u = u x, t = exp −n kt sin nx satisfies the one dimensional

heat equation for any choice of constant n