Question

Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50 cm and holds it in position with a force of 150 N. If the mass of the arrow is 50 g and the "spring" is massless, what is the speed of the arrow immediately after it leaves the bow?

a) 30 m/s
b) 15 m/s
c) 20 m/s
d) 25 m/s

Answer 1

To determine the speed of the arrow immediately after it leaves the bow, we can use the principles of conservation of energy. The potential energy stored in the bow is converted into kinetic energy of the arrow when it is released. However, without knowing the force constant of the bow, we cannot calculate the speed of the arrow.

Step-by-step explanation:

To determine the speed of the arrow immediately after it leaves the bow, we can use the principles of conservation of energy. The potential energy stored in the bow is converted into kinetic energy of the arrow when it is released. The formula for kinetic energy is given by KE = 0.5 * mass * velocity^2.

First, we need to find the potential energy stored in the bow. The potential energy is given by PE = 0.5 * k * x^2, where k is the force constant of the bow and x is the displacement of the bow from its equilibrium position.

The displacement of the bow is given as 50 cm, which is equal to 0.5 m. The force constant k is not given, so we are unable to calculate the potential energy stored in the bow. Without this information, we cannot determine the speed of the arrow.