A 25 gram arrow fired from a bow has a speed of 80m/s. The energy in the arrow came from work done by the bow that acted over a 1m "draw" distance. What average force acted on the arrow over this distance?
Convert the velocity (80m/s) to accleration using Vf^2= Vi^2 + 2ad. After you find your accleration substitue that accleration value into Fnet = ma.
or, the easier way...
energybullelt=workinput
1/2 mass*80^2=avgforce*1meter
solve for avgforce
To find the average force acting on the arrow over a distance, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Given:
Mass of the arrow (m) = 25 grams = 0.025 kg
Speed of the arrow (v) = 80 m/s
Distance over which the force was applied (d) = 1 m
First, let's calculate the kinetic energy of the arrow:
Kinetic Energy (KE) = (1/2) * m * v^2
Substituting the given values:
KE = (1/2) * 0.025 kg * (80 m/s)^2
KE = 80 Joules
Since the energy in the arrow came from the work done by the bow, the work done on the arrow is equal to the kinetic energy gained:
Work (W) = KE = 80 Joules
The work done can be calculated by the formula:
Work = Force * Distance
Rearranging the formula:
Force = Work / Distance
Substituting the given values:
Force = 80 Joules / 1 meter
Force = 80 Newtons
Therefore, the average force acting on the arrow over a distance of 1 meter is 80 Newtons.