A 8.0×10−2 arrow hits the target at 25 and penetrates 3.8 before stopping. What average force did the target exert on the arrow?
0.9
To find the average force exerted by the target on the arrow, we can use Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration.
However, in this case, we don't have the mass of the arrow or the acceleration directly. Instead, we can use the concept of impulse.
Impulse is defined as the change in momentum of an object and can be calculated by multiplying the force applied to an object by the time over which the force is applied. Mathematically, impulse (J) is given by the equation:
J = F * Δt
Where:
J = Impulse
F = Force
Δt = Change in time
Since we know the initial velocity (v_i), the final velocity (v_f), and the displacement (Δx) of the arrow, we can calculate the change in momentum using the equation:
Δp = m * Δv
Where:
Δp = Change in momentum
m = Mass of the arrow
Δv = Change in velocity
We can also express change in velocity using the equation:
Δv = v_f - v_i
Now, combining these equations, we can write:
J = Δp = m * (v_f - v_i)
Since impulse is equal to the average force multiplied by the change in time, we can write:
F * Δt = m * (v_f - v_i)
The mass of the arrow cancels out, so we are left with:
F = (m * (v_f - v_i)) / Δt
To calculate the average force, we need to know the time over which the force was applied (Δt). Unfortunately, that information is not provided in the question.