A bullet of mass 20 grams is fired into a wall with velocity of 400 ms 1. If the bullet penetrates the wall to a depth of 1cm, find the resistive force of the wall.
momentum = m v = .020*400 = 8 kg m/s
stops in 1 cm = .01 meter
average speed during stop = 200m/s
so time to stop t = .01/200 = 5*10^-5 seconds
Average force = change of momentum/time
= (8/5)10^5 = 160,000 Newtons
Is this the only way?
Nope,
say F = ma
a = 400/t
so t = 400/a
d = Vi t -(1/2)a t^2
d = 400 t - (1/2)(400/t)t^2
d = 400 t - 200 t = 200 t
t = d/200 = .01/200 = 5*10^-5 s again
a = 400/t = 8*10^6
F = m a = .02*8*10^6 = 160,000 N
again :)
Ty :)
To find the resistive force of the wall, we can use the principle of impulse-momentum. The impulse experienced by the bullet as it penetrates into the wall is equal to the change in momentum.
The equation for impulse is given by:
Impulse = Change in momentum
The momentum of an object is calculated using the formula:
Momentum = mass × velocity
Given that the mass of the bullet is 20 grams (0.02 kg) and the initial velocity of the bullet is 400 m/s, we can calculate the initial momentum of the bullet:
Initial momentum = 0.02 kg × 400 m/s = 8 kg⋅m/s
The change in momentum is equal to the final momentum minus the initial momentum.
The final velocity of the bullet after penetrating the wall is assumed to be zero since it comes to rest. Therefore, the final momentum is zero.
Change in momentum = Final momentum - Initial momentum
= 0 - 8 kg⋅m/s
= -8 kg⋅m/s
The negative sign indicates that the direction of the impulse is opposite to the initial momentum.
Now, we can express the impulse in terms of the resistive force and the time during which it acts according to the equation:
Impulse = Force × Time
Since both the impulse and resistive force act in the same direction, we can rewrite the equation as:
Force = Impulse / Time
The time taken for the bullet to penetrate the wall can be derived from the velocity and depth of penetration.
The formula for time taken to penetrate a distance is given by:
Time = Distance / Velocity
Given that the bullet penetrates the wall to a depth of 1 cm (0.01 m), we can calculate the time taken:
Time = 0.01 m / 400 m/s = 0.000025 s
Now, substituting the values into the equation for force:
Force = -8 kg⋅m/s / 0.000025 s
Calculating the result:
Force = -8 kg⋅m/s ÷ 0.000025 s = -320,000 N
Therefore, the resistive force of the wall is 320,000 Newtons.