A missile of mass 4kg is fired through a stack of asbestos sheets 1.8m thick.If the missile approaches the asbestos with a velocity of 540m/s and emerges with a velocity of 270m/s,determine the average resistance R of the sheets.
I am quite uncertain what resistance means. However, the average force of resistance can be calculated.
ForceResistance*distance=KEentering-KEleaving
forceResistance*1.8=1/2 *4(540^2-270^2)
solve for the average force of resistance.
To determine the average resistance R of the asbestos sheets, we can use the principle of impulse and momentum.
The impulse-momentum principle states that the change in momentum experienced by an object is equal to the impulse acting on it. In this case, the impulse is equal to the average resistance provided by the asbestos sheets.
The change in momentum, ∆p, can be calculated using the equation:
∆p = m * ∆v
Where:
m is the mass of the missile (4 kg)
∆v is the change in velocity (final velocity - initial velocity)
Therefore:
∆p = 4 kg * (270 m/s - 540 m/s)
= -1080 kg·m/s (negative sign indicates a decrease in momentum)
Since impulse is equal to the change in momentum, we can write:
Impulse = R * ∆t
Where:
R is the average resistance (what we need to find)
∆t is the time taken for the missile to pass through the asbestos sheets
To calculate ∆t, we need to know the distance traveled by the missile through the asbestos sheets. In this case, the thickness of the asbestos sheets is given as 1.8 m.
Therefore:
∆t = ∆x / v
Where:
∆x is the distance traveled (1.8 m)
v is the velocity of the missile (540 m/s)
∆t = 1.8 m / 540 m/s
= 0.0033 s
Now we can substitute the values back into the impulse equation:
Impulse = R * ∆t
-1080 kg·m/s = R * 0.0033 s
To find R, we can rearrange the equation:
R = -1080 kg·m/s / 0.0033 s
= -327,273 N (negative sign indicates resistance in the opposite direction)
Therefore, the average resistance R of the asbestos sheets is approximately 327,273 N.