Physics

Problem

A package of mass

m

is to be raised from rest on the ground to a height

h

such that at the highest point it is moving with speed

v

. Ignore air resistance. a. (i) Derive an expression for the total work that must be done on the package in terms of

m

g

h

and

v

. b. (ii) Using your expression, calculate the work needed when

m = 2\,\text{kg}

h = 4\,\text{m}

v = 3\,\text{m\,s}^{-1}

and

g = 9.8\,\text{m\,s}^{-2}

. c. (iii) For the numerical case in part (ii), determine separately the portions of the total work that go into increasing (a) potential energy and (b) kinetic energy of the package. State the ratio of these two portions.

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