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The heart of man pumps 4litres of blood per minute at a pressure of 130mm of mercuryIf density of mercury is 13.6g/cm3.Find the power of heart 0.02w 0.2w 3.2w 1.2w

The heart of man pumps 4litres of blood per minute at a pressure of 130mm of mercuryIf density of mercury is 13.6g/cm3.Find the power of heart


0.02w


0.2w


3.2w


1.2w

Grade:10

6 Answers

Shivam Bhagat
22 Points
10 years ago
power=work /time=f*d/t=f*v(v=velocity) Assume the area to be 1 mm2. Power=hdg*v h=height d=density g=acc. Due to gavity v=velocity(here = rate of flow of blood) ANS is 1.15= 1.2W(TAKE CARE OF THE UNITS)
Ayush Pateria
20 Points
10 years ago

WORK DONE W IS GIVEN BY
W = F X D
F = PA (PRESSURE X AREA)
OR W = P A.D = P (AD) = P V
OR WORK DONE = PRESSURE X VOLUME
HERE PRESSURE P = 130mm OF Hg = 105 * 130/760
OR P = 13 x 105 / 76 Pa
VOLUME V = 4L = 4000 cm3 = 4x10-3 m3
HENCE W = PV = (13 x 105 / 76 ) x 4x10-3
OR Wok done  = 68.42 JOULES
NOW THE PUMPING OF 4 L OF BLOOD IS DONE IN 1min = 60s
THUS POWER = WORK DONE/TIME
OR POWER = 68.42/60 = 1.1403 WATTS

Vikas TU
14149 Points
10 years ago
P =work /time
f*d/t=f*v(v=velocity)
Assume the area to be 1 mm2.
Power=hdg*v h=height d=density g=acc.
Due to gavity v=velocity(here = rate of flow of blood)
ANS is 1.15= 1.2W
infernape
11 Points
4 years ago
V = volume = 4 L 
h = pressure = 130 mm of mercury 
p = density = 13.6 gm/cm^3 
t = time = 1 minute 

The Volume of blood 
V = 4 litres 
V = 4 x 10^3 cm^3 
V = 4 x 10^-3 m^3 

Work done is given by the formula --> Force x Distance 
Note that Force = Pressure x Area, & Volume = Area x Distance 

Therefore: 
Work = Force x Distance 
Work = Pressure x Area x Distance 
Work = Pressure x Volume 
Work = (h)(p)(g)(V) 

Power is Work "over" time = hpgV / t 

We already know: 
v = volume = 4 L => 4x10^-3 m^3 
h = pressure = 130 mm of mercury => 0.13 m 
p = density = 13.6 gm/cm^3 = 13.6x10^3 
t = 1 minute => 60 seconds 

The extra variable is: 
g = gravity = 9.8 m/s^2 

Plug these numbers into the Power equation: 
Power = hpgV/t 
Power = [(0.13)(13.6x10^3)(9.8)(4x10^-3)]/(60) 
Power = 69.3056 / 60 
Power = 1.155093 

Therefore the power of the heart is approximately 1.155 W
Mahendra Chapagain
26 Points
4 years ago
actually:power formula is WORK DONE/TIME
now,
1.work done =force*displacement
                   =pressure*area*displacement   (because:pressure=force/area)
                   =height*density*gravity*area*displacement  (in context of liquid pressure p=hdg)
                  =HDGV finally (because area*displacement taken as volume)
2.time taken
at last formula of power=HDGV/T
solving
(0.13*13.6*1000*9.8*4/1000)60
ans:1.155 i.e.1.2 watt
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

P = work /time f*d/t
= f*v (v=velocity)
Assume the area to be 1 mm2.
Power = hdg*v
h = height
d = density
g = acc.
Due to gavity v = velocity(here = rate of flow of blood)
ANS is 1.15= 1.2W

Thanks and Regards

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