Two bodies X and Y have masses and and speeds and

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power

Problem

Two bodies X and Y have masses

m_X

and

m_Y

and speeds

v_X

and

v_Y

, respectively. (i) Derive an expression for the ratio of their kinetic energies

\dfrac{K_X}{K_Y}

in terms of the ratios

\dfrac{m_X}{m_Y}

and

\dfrac{v_X}{v_Y}

. (ii) Using your expression, find

\dfrac{K_X}{K_Y}

when

m_X : m_Y = 1 : 3

and

v_X : v_Y = 3 : 1

. (iii) Show that if the speed of a body is tripled while its mass is halved, its kinetic energy becomes

\dfrac{9}{2}

times the original value. (iv) Explain how the derived results support the conclusion that increasing speed is generally a more effective way to raise kinetic energy than increasing mass.

Related theory

Kinetic Energy
Work and Energy
Work Energy and Power

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