A Paschal is a unit of pressure in SI units. Pressure is a force divided by an a

Question

A Paschal is a unit of pressure in SI units. Pressure is a force divided by an area N/m^2. If the pressure on a tank is 3.00 times 10^6 Pa, what is the pressure in: a. kiloNewtons per square centimeter? b. pounds per square foot? c. pounds per square inch? Einstein's equation for energy is E=mc^2, where m is mass in kilograms and c is the velocity of light in meters per second. a. The unit for energy in SI units is a Joule, which is a N-m. Through unit conversions, demonstrate that the Einstein's energy equation results in the unit of a Joule b. The unit for energy in US units is a ft-lb. Through unit conversions, demonstrate that the Einstein's energy equation results in the unit of a ft-lb. A Porsche's engine exerts 229 ft-lb (foot-pounds) of torque at 4600 rpm (revolutions per minute). What is the value of torque in N middot m? What is the product of 4.5 times 10^-3 Mg * 200 ms? Show answer in correct units with correct prefix. Water has a density of 1.94 slug/ft^3 in US units. Convert this to SI units min kg/m^3.

Explanation / Answer

1)

a)

P = 3*10^6 Pa = 3*10^6 N/m2

= 3*10^3 kN/m2

= 3*10^3 kN/(100cm)^2

= 0.3 kN/cm2

b)

P = 0.3 *10^3*0.2248 pound/cm2

= 0.3*10^3*0.2248/(0.0328)^2 pound/ft

= 6.269*10^4 psf

c)

P =  6.269*10^4/12^2 psi

= 435.3 psi

2)

a)

unit of Energy = N.m

unit of N = kg.m/s2

So, unit of Energy = (kg.m/s2)*m = kg.m2/s2 = Joule

Now, energy of mass,m = kg

unit of c = speed of light = m/s

So, unit of E = mc^2 = kg*(m/s)^2 = kg.m2/s2 = units of Joule

c)

Unit of E = mc^2 = kg*(ft/s)^2 = kg.ft^2/s2 = (kg*ft/s2)*ft

Now, kg.ft/s2 has unit of ln

So, E = mc2 has units of ft-lb

3)

Torque = 229 ft-lb

1ft = 0.3048 m

1 lb = 4.448 N

So, torque = 229*0.3048*4.448 = 310.47 N.m

4)

4.5*10^-3Mg * 200 ms = 4.5*10^-3*10^6*200*10^-3 g.s

= 900 g.s

5)

1.94 slug/ft^3

1 slug = 14.594 kg

1 ft = 0.3048 m

So, density = 1,94*14.594/0.3048^3 = 999.84 kg/m3

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