An archer pulls a bowstring back 0.390 m, and the spring constant of the bow is 675 N/m.
a.) Find the amount of work the archer did to draw the bow.
b.) Find the speed an arrow of mass 0.075 kg will have when it is shot from the bow.
Assume no losses from friction.
work in = increase in potential energy = (1/2) k x^2
that becomes kinetic energy of the arrow
= (1/2) m v^2
To find the amount of work the archer did to draw the bow, we can use the formula for work:
Work = (1/2) * k * x^2
where k is the spring constant and x is the displacement of the spring (in this case, the distance the bowstring is pulled back).
a.) To find the amount of work, we can substitute the given values into the formula:
Work = (1/2) * 675 N/m * (0.390 m)^2
Work = 51.62 Joules
To find the speed of an arrow when it is shot from the bow, we can use the principle of conservation of mechanical energy. The work done by the archer in drawing the bow will be equal to the kinetic energy of the arrow.
b.) The work done by the archer is equal to the change in kinetic energy of the arrow:
(1/2) * m * v^2 = 51.62 Joules
where m is the mass of the arrow and v is the speed of the arrow.
Rearranging the equation, we can solve for v:
v^2 = (2 * work) / m
v = √((2 * 51.62 J) / 0.075 kg)
v ≈ 24.04 m/s
Therefore, the speed of the arrow when it is shot from the bow is approximately 24.04 m/s.