The energy of a moving particle can be calculated by the following equation E =

Question

The energy of a moving particle can be calculated by the following equation E = mgh + 1/2 mv^2 where m is mass, g is acceleration due to gravity, h is height above an elevation datum and v is the velocity of the particle. Given the values of m = 55.2 grams and g = 1.390 times 10^6 inches/min^2 and h = 150 feet and v = 3.2 meters/second a. Show that the given relation is dimensionally consistent using base dimensions. b. Explain why foot*pound-force (ft*lb_t) is a valid unit for energy. c. Convert the value for mass, m, such that the value for potential energy could be reported in English units of Foot-Pounds. Report your converted value to the appropriate number of significant figures d. Convert the value for gravitational acceleration. such that the value for potential energy could be reported in English units of Foot-Pounds. Report your converted value to the appropriate number of significant figures. e. Convert the value for velocity, v, such that the value for potential energy could be reported in English units of Foot-Pounds. Report your converted value to the appropriate number of significant figures. f. What is the kinetic energy of the particle in English units of Foot-Pounds? Report your final value in scientific notation with 3 significant figures of precision.

Explanation / Answer

a] Energy has unit of Joule

In RHS, mgh has unit of Nm = Joule and also 0.5mv^2 has unit kgm^2/s^2 = Nm = Joule.

So it is dimensionally consistent.

b] foot*pound-force has dimension of Force*distance which is dimension of work or energy.

c] m = 55.2gram = 0.1217 pounds

d] g = 9.8 m/s^2 = 32.2 ft/s^2

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