
Physics Tutoring Session #12 Work, Energy and Power on Mon. 7th March, 2016 @ 5:00pm  6:00pm,
Physics
Chima Sunday (Tutor)
07032016 15:34:00 +0000Work W is said to be done, when a force F move a body to a distance s, in the direction of the applied force F. (When F and s are parallel we have a maximum workdone)
Therefor W = F × s.
S.I unit is in joule.
Definition of a joule: a joule is define as the workdone when a force of 1Newton moves a body through a distance of 1metre in the direction of the applied force.
But when the applied force F is at an angle say θ We resolve the force to its horizontal component
Therefor W = Fscosθ
Example(1)
A force of 150N is attached to a mass of 200kg at an angle of 30 to drag it though a horizontal distance of 10m. How much work is done by the force.
A. 1200J
B. 1300J
C. 2000J
D. 1299J
E. 1290J
(Post utme, futo 2013/2014)
solution
From the formular,
W = Fscosθ
F = 150N
S = 10m
θ = 30^{o}
W = 150 × 10 × cos30 = 1299J.
Option D.
If we pull a body of mass m up in an incline plane of angle θ and of height h metre, Then the work done would be that of against the weight plus friction. i.e work done is that against friction plus the one against gravity. But we need to resolve the weight to its horizontal component to obtain Wsinθ. recall that frictional for F = μR.
where coefficient of static friction, and R the normal Recation.
there total workdone W in moving the body a distance of s is given as
W = (Wsinθ + μR)s.
Energy
this is define as the ability to do work. Its a scalar quantity and has same unit with work. We group Energy into Renewable(inexhaustible) and NonRenewable(exaustible)
Energy appears in may forms e.g are sound energy, wind energy, electrical energy, mechanical energy, nuclear enegy, heat energy,solar energy, chemical energy etc.
The principle of conservation of energy state thus that energy can neither be created nor destroyed but can be transformed from one form to another.
Mechanical Energy is made up of
i)Kinetic Energy: which is the energy possesed by a body due to its motion. It si given by
K.E = (1/2)mv^{2}
ii)Potential Energy
This is the energy posses by a body by the virtue of its position h. It is given as
P.E = mg × h
Conservation law on Mechanical Energy
This is illustrated when a body is dropped from a height say h, its P.E is maximum at height h and K.E = 0, when it falls at a distance say x metres, it losses P.E, But the loss in P.E is converted to K.E. given the total energy T = P.E + K.E
i.e T = mgh_{1} + (1/2)mv^{2}
T = mgx + (1/2)mv^{2}
Example(2)
A 5kg mass is dropped from a height of 30m above the ground. Determine the velocity of the mass when it is 18m above the ground. (g = 10ms^{2})
Solution
total energy T = F(mg) × dist = 5 *10 * 30 = 1500J
recall that T = mgh_{1} + (1/2)mv^{2}
m = 5kg, g = 10.
therefor T = 5*10*18 + 5*v^{2}
by subject formular v^{2} = (T  mgh_{1} )1/m = 2(1500  5*10*18)1/5 = 240
v = 15.5m/s.
Alternatively we can still get the same resultknowing that the lost in P.E = gain in K.E
So loss in P.E = mg(h  h_{1}), h = 30m and h_{1} = 18
So loss in P.E = gain in K.E
mg(h  h_{1}) = (1/2)mv^{2}
by subject formular
v^{2} = 2g(h  h_{1}) = 2 * 10 * (30  18) = 240
therefor v = 15.5m/s
POWER
This is define as the rate of doing work
Power p = work/time
it is measured in watts (W)
It can also be express as P = (F * s)/t = F * s/t = F*v, were v is velocity.
Example(3)
If a pump ejects 30kg of water in 60s through a vertical height of 3m. Calculate the minimum power of the pump. (g = 10m/s^{2})
Solution
Work done = P.E = mgh = 30*10*2 = 600J
Power P = WORKDONE/TIME = 600/60 = 10W.
Please do go through the script above and document your questions accordingly, and also prepare for a similar questions culled from JAMB and from other exams. See You in Class at 5:00PM
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