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 235 m/s and is brought to a halt in a collision that lasts for a time of 6.8 ms. What is the magnitude of the average net force that acts on the box during the collision?
To calculate the magnitude of the average net force acting on the box during the collision, we can use the impulse-momentum principle.
The principle states that the change in momentum of an object is equal to the impulse applied to it:
Impulse = Change in Momentum
The impulse is given by the product of the average net force and the time interval:
Impulse = Average Net Force * Time
The momentum of an object is given by the product of its mass and velocity:
Momentum = Mass * Velocity
In this case, the initial velocity of the box is given as 235 m/s, and it is brought to a halt, so the final velocity is 0 m/s. The mass of the box is given as 41 kg.
Therefore, the change in momentum is:
Change in Momentum = Final Momentum - Initial Momentum
= (0 kg m/s) - (41 kg * 235 m/s)
= -9595 kg m/s
The impulse applied to the box is equal to the change in momentum, so:
Impulse = -9595 kg m/s
Using the equation Impulse = Average Net Force * Time, we can rearrange it to solve for the average net force:
Average Net Force = Impulse / Time
Plugging in the given values:
Average Net Force = (-9595 kg m/s) / (6.8 ms)
≈ -1413.97 N
Therefore, the magnitude of the average net force that acts on the box during the collision is approximately 1413.97 Newtons.