Question

Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the drawstring back 56 cm from its rest position and holds it in position with a force of 158 N. If the mass of the arrow is 58 g and the "spring" is massless, what is the speed (in m/s) of the arrow immediately after it leaves the bow?

Answer 1

Answer:

 v=39.05 m/s

Explanation:

Given that

x= 56 cm

F= 158 N

m= 58 g = 0.058 kg

Lets take spring constant = k

At the initial position,before releasing the arrow

F= k x

By putting the values

F= k x

158= 0.56 k

k=282.14 N/m

Now from energy conservation

Lets take final speed of the arrow after releasing

$\dfrac{1}{2}kx^2=\dfrac{1}{2}mv^2$

k x²=mv²

282.14 x 0.56² = 0.058 v²

v=39.05 m/s