Engineering Science - Beams
Example: Support reactions on a simply supported beam
A uniform beam of length 3 m is simply supported at A and B as shown in
the figure. A uniformly distributed vertical load q = 100 N/m acts over the
entire length of the beam. In addition, a concentrated load P = 150 N acts at
a distance d = 1 m from the left end. Find the support reactions.
Engineering Science - Buoyancy
Examples for Buoyancy
 An object immersed in water seems to
weigh less than when it is in air.
 When the object is less dense than the
fluid, it floats.
 Rafts inflated with air float in water.
 A helium-filled balloon floats in air.
Engineering Science - Archimedes’s Principle
“When an object is completely or partially immersed in a fluid, the fluid
exerts an upward force on the object equal to the weight of the fluid that is
displaced by the object.”
Example 01:
A 15.0 kg solid-gold statue is being raised from
a sunk ship, as shown in Figure.
(a) Find the tension in the hoisting cable when
the statue is completely immersed.
(b) Find the tension when the statue is
completely out of the water.
(Density of gold is 19.3 × 103 kg m-3)
Engineering Science - Archimedes’s Principle
Example 02:
A raft is constructed of wood having a density of 6.00 × 102 kg/m3. Its
surface area is 5.70 m2, and its volume is 0.60 m3. When the raft is placed
in fresh water as in Figure, to what depth h is the bottom of the raft
submerged?
Engineering Science - Archimedes’s Principle
Example 03:
A hollow plastic sphere is held below the surface of a freshwater lake by a
cord anchored to the bottom of the lake. The sphere has a volume of
0.650 m3 and the tension in the cord is 900 N.
(a) Calculate the buoyant force exerted by the water on the sphere.
(b) What is the mass of the sphere?
(c) The cord breaks and the sphere rises to the surface. When the sphere
comes to rest, what fraction of its volume will be submerged?