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A bullet is fired from a gun. The force on the bullet is given by F= (600 - 2 x 10^5 t). The force on the bullet becomes zero as soon as it leaves the barrel. What is the impulse imparted to the bullet?
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Impulse imparted to a bullet fired from a gun
- Definition of impulse
- Force on the bullet
- Calculation of impulse
- Calculation of time taken by the bullet to leave the barrel
- Calculation of impulse imparted to the bullet
- Explanation of the result
Impulse is the change in momentum of an object that occurs as a result of a force acting on it for a period of time. It is given by the formula I = FΔt, where I is the impulse, F is the force, and Δt is the time period for which the force acts.
The force on the bullet is given by F= (600 - 2 x 10^5 t), where t is the time elapsed since the firing of the bullet. The force acting on the bullet is decreasing with time and becomes zero as soon as it leaves the barrel of the gun.
As the force acting on the bullet is changing with time, we need to integrate the force over the time period for which it acts to find the impulse imparted to the bullet. The time period for which the force acts is the time taken by the bullet to leave the barrel of the gun. Let us assume that this time period is Δt.
∴ F= (600 - 2 x 10^5 t)
∴ I = ∫F dt = ∫(600 - 2 x 10^5 t) dt (from t=0 to t=Δt)
∴ I = [600t - 10^5 t^2] (from t=0 to t=Δt)
∴ I = [600Δt - 10^5 (Δt^2)]
The force acting on the bullet becomes zero as soon as it leaves the barrel of the gun. Let us assume that the time taken by the bullet to leave the barrel is t_0.
∴ F= (600 - 2 x 10^5 t) = 0 (when t = t_0)
∴ t_0 = 3 x 10^-3 s
Substituting the value of Δt = t_0 in the expression for impulse, we get:
I = [600 x 3 x 10^-3 - 10^5 (3 x 10^-3)^2] = -270 Ns
The negative sign in the value of impulse indicates that the momentum of the bullet is decreasing. The magnitude of the impulse is 270 Ns, which means that the bullet has lost 270 units of momentum as a result of the force acting on it.
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A bullet is fired from a gun. The force on the bullet is given by F= (600 - 2 x 10^5 t). The force on the bullet becomes zero as soon as it leaves the barrel. What is the impulse imparted to the bullet?
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