Question

a) Define the work W and the power P. What are their units? How much work W do you do when you lift a m =15kg suitcase h=1.5m off the ground? If the lifting is during t=.5s, how much power P are you expanding?

b) Calculate the expression of the pressure p from a fluid column of height h and its density p in the gravitational acceleration g=9.8m/s². Considering the density of water p=1gr/cm³, find the total value of the pressure inside the water in a depth of 10m. (Atmospheric pressure is 1atm=101.3 kPa=101.3*10³ Pa)

c) Write 4 simple mathematical relationships between two quantities A and B. Try to design their graphical representations.

d) Design the thermal scheme of the heat engine. Write the general relationship for its efficiency n.

Answer 1

a) Work = Work is defined (in calculus terms) as the integral of the force over a distance of displacement.
The SI units for work are the joule (J) or newton-meter (N * m), from the function W = F * s where W is work, F is force, and s is the displacement. The joule is also the SI unit of energy.

in simple word to calculate work work = force * displacment in the direction of force

Power :   work done per unit time is called as power.

P = W/t

in given case F = mg ( gravitational force) = 15 *g

s = displacment = -1.5

W = -15*9.81 * 1.5 = 220.725 J

power P = W/t = 220.725 /0.5 = 441.45 W

b) pressure at the bottom will be = P = Patm + $\rho$gH

P = 101300 + 1000 * 9.81* 10

P =199.4 Kpa    answer

c)

(1) A = B  

straight line passing through origin

(2)A = B²

parabola

(3)A² =B

parabola

4) A = e^B

exponential

d)

efficiency = $\eta$ = Woutput / Qinput

high-temperature source T. TH heat in work out engine q, heat out low-temperature sink T, 0°K

( for thermal scheme of the heat engine image attached)