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
KE = 0.5M*V^2 = 0.5*0.025*80^2 = 80 J.
F*d = F*1 = 80 J.
F = 80 N.
To find the average force acted on the arrow over the given draw distance, we can use the principle of work and energy.
The work done on an object is equal to the force applied on the object multiplied by the displacement of the object in the direction of the force. In this case, the work done by the bow acting on the arrow is equal to the energy in the arrow.
We can calculate the work done using the following formula:
Work = Force × Displacement
The force applied on the arrow can be determined by rearranging the formula as:
Force = Work / Displacement
Given that the work done by the bow is equal to the energy in the arrow, we can substitute the work and displacement values into the equation to find the force:
Force = Energy / Displacement
To calculate the energy in the arrow, we can use the kinetic energy formula:
Energy = (1/2) × mass × velocity^2
Substituting the given values:
Mass = 25 grams = 0.025 kg
Velocity = 80 m/s
Energy = (1/2) × 0.025 kg × (80 m/s)^2
Now we can substitute this energy value and the given displacement of 1 meter into the force equation:
Force = Energy / Displacement
Force = [(1/2) × 0.025 kg × (80 m/s)^2] / 1 m
Calculating this expression will give us the average force acted on the arrow over the given distance.