Airplane flight recorders must be able to survive catastrophic crashes. Therefore, they are typically encased in crash-resistant steel or titanium boxes that are subjected to rigorous testing. One of the tests is an impact shock test, in which the box must survive being thrown at high speeds against a barrier. A 41-kg box is thrown at a speed of 185 m/s and is brought to a halt in a collision that lasts for a time of 5.9 ms. What is the magnitude of the average net force that acts on the box during the collision?
m•v=F•Δt
F=m•v/ Δt =41•185/5.9•10^-3 = 1.29•10^6 N
To calculate the magnitude of the average net force acting on the box during the collision, we can use the impulse-momentum principle.
The impulse-momentum principle states that the change in momentum of an object is equal to the impulse applied to it. The impulse can be calculated as the product of the net force and the time of collision.
Impulse (J) = Net Force (F) × Time (t)
We can calculate the impulse by first determining the change in momentum of the box.
Momentum (p) = mass (m) × velocity (v)
Initial momentum (p1) = m × v
Final momentum (p2) = 0 (because the box is brought to a halt)
Change in momentum (Δp) = p2 - p1 = 0 - (m × v)
Since the change in momentum is equal to the impulse, we can write:
J = Δp = 0 - (m × v)
Now, we can solve for the net force (F):
J = F × t
F = J / t
F = (0 - (m × v)) / t
Plugging in the given values:
m = 41 kg (mass of the box)
v = 185 m/s (speed of the box)
t = 5.9 × 10^(-3) s (collision time)
F = (0 - (41 kg × 185 m/s)) / (5.9 × 10^(-3) s)
Calculating this expression will give you the magnitude of the average net force that acts on the box during the collision.