A classical mechanics problem by Swapnil Maiti

Classical Mechanics Level 2

An archer pulls back 0.75 m on a bow which has a stiffness of 200 N/m. The arrow weighs 50 g. What is the velocity of the arrow immediately after it crosses the bowstring (traveled 0.75 m)?

20m/s 32.6m/s 47.4m/s 41.9m/s

Swapnil Maiti by Swapnil Maiti , 19, India

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1 solution

Muhammad Erfan
Jul 24, 2015

The Potential Energy of the bow is converted to the Kinetic Energy if the arrow, so:

E P = E K { E }_{ P }={ E }_{ K }

1 2 k x 2 = 1 2 m v 2 \frac { 1 }{ 2 } k{ x }^{ 2 }=\frac { 1 }{ 2 } m{ v }^{ 2 }

v = x k m = ( 0.75 ) ( 200 0.05 ) ≈ 47.4 m s v=x\sqrt { \frac { k }{ m } } =\left( 0.75 \right) \left( \sqrt { \frac { 200 }{ 0.05 } } \right) \approx \quad\boxed{ 47.4\quad\frac{m}{s}}

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