Download We seek an equation with power on the left hand side

1. A solid uranium cylinder weighs 91.53 N in air and 86.63 N when
submerged in water.
a. The volume of the cylinder is ----------mt^3
b. The density of uranium is---------kg/mt^3
Solution: We have the following formula for measuring relative density,
where, W is the weight of uranium in air and F is that when
submerged in water.
G = 91.53/(91.53-86.63)
= 91.53 / 4.9
= 18.6796
So we have the relative density of uranium.
Usually we will see the relative density of matter with respect to density of
water. We know that the density of water is 1000 kg/m3. Then
density of uranium = 18.6796*1000
= 18,679.6 kg/m3
Given solid uranium cylinder weighs 91.53 N in air. Then
the mass of uranium cylinder = 91.53 / g
where ‘g’ is the acceleration due to gravity. Therefore,
the mass of uranium cylinder = 91.53 / 9.8
= 9.34 kg
2. On each heartbeat, about 70 cm^3 of blood is forced from a human heart
at an average pressure of approx 105 mm Hg.
a. If the heart beats 70 times per minute, the average power output of the
heart is ---------- watts
We have an equation with units of Watts on both sides, which expresses the
average power output of the heart as the product of the output pressure and
the stroke volume, divided by the stroke duration:
Power = P V / t.
Watt is equivalent in SI units to a kilogram - meter squared per second
cubed
We have to make all the given units in to SI units.
Given,
The stroke volume = 70 cm^3
= 70/1000000
= 0.00007 m^3
Heart beats 70 times in 1 minute. i.e. 70 times in 60 seconds. i.e. 7/6 times in
1 second.
So stroke duration = 6/7
= 0.8571
Output pressure = 105 mm of Hg which is already in SI units.
Then,
Power = P V / t
= (105*0.00007)/0.8571
= 0.008575 Watt