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 220 m/s and is brought to a halt in a collision that lasts for a time of 6.5 ms. What is the magnitude of the average net force that acts on the box during the collision?
Round answer to nearest 100,000's place
i.e. 123456789 would therefore be 123500000
To find the magnitude of the average net force acting on the box during the collision, we can use the impulse-momentum equation:
Impulse = change in momentum
Impulse is given by the product of the force and the time it acts on an object:
Impulse = force × time
The change in momentum of the box can be calculated using the formula:
Change in momentum = Mass × (Final velocity - Initial velocity)
Here, the mass of the box is 41 kg, the initial velocity is 220 m/s, and the final velocity is 0 m/s since the box comes to a halt.
Change in momentum = 41 kg × (0 m/s - 220 m/s)
= -9020 kg·m/s
Since the final velocity is 0 m/s, the change in momentum is equal to the initial momentum. Therefore, the impulse acting on the box is:
Impulse = 9020 kg·m/s
Now, we can find the magnitude of the average net force by dividing the impulse by the time:
Average net force = Impulse / Time
Given that the time of collision is 6.5 ms (which is equal to 6.5 × 10^-3 seconds), we can calculate the magnitude of the average net force as follows:
Average net force = 9020 kg·m/s / (6.5 × 10^-3 s)
≈ 1387692307.6923077 N
Rounding the answer to the nearest 100,000's place, we get:
Average net force ≈ 1390000000 N