An 81 g arrow is fired from a bow whose string exerts an average force of 95 N on the arrow over a distance of 79 cm. What is the speed of the arrow as it leaves the bow?
m/s
1/2 m v^2=95*.79
solve for v.
Work done on arrow = 95N*0.79 m = 75 J
Set that equal to the arrow kinetic anergy ans solve for V
To find the speed of the arrow as it leaves the bow, we can use the concept of work done and kinetic energy.
1. First, let's calculate the work done on the arrow. The work done is equal to the force exerted on the arrow multiplied by the distance over which the force is applied.
Work = Force * Distance
Given: Force = 95 N and Distance = 79 cm = 0.79 m
So, Work = 95 N * 0.79 m = 75.05 J
2. Next, we can calculate the kinetic energy of the arrow. The kinetic energy is equal to half the mass of the arrow multiplied by the square of its velocity.
Kinetic Energy = 0.5 * Mass * Velocity^2
Given: Mass = 81 g = 0.081 kg (since 1 kg = 1000 g)
We need to find the velocity.
3. To relate work done and kinetic energy, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
Work = Change in Kinetic Energy
So, 75.05 J = Kinetic Energy - 0 (Initial Kinetic Energy is 0 since the arrow starts from rest)
Therefore, Kinetic Energy = 75.05 J
4. Now, we can find the velocity of the arrow. Rearranging the formula for Kinetic Energy, we get:
Velocity^2 = (2 * Kinetic Energy) / Mass
Velocity^2 = (2 * 75.05 J) / 0.081 kg
Velocity^2 = 1471.6
Taking the square root of both sides, we find:
Velocity = √1471.6 m/s
Therefore, the speed of the arrow as it leaves the bow is approximately 38.34 m/s.