A rocket burns 5kg per ejecting it as a gas with a velocity of 1600m/s relative to the rocket. How much force is exerted on the rocket. Also find the velocity exerted when its mass reduces to 1/200 of its initial mass.
To find the force exerted on the rocket, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (Δp) over time (Δt). Mathematically, this can be expressed as:
F = Δp / Δt
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v):
p = m * v
Given that the rocket burns 5kg of fuel per second and the gas is ejected with a velocity of 1600m/s relative to the rocket, we can calculate the rate of change of momentum:
Δp = (mass of gas ejected) * (velocity of gas ejected)
The mass of gas ejected per second is given as 5kg, and the velocity of the gas ejected is given as 1600m/s. Therefore:
Δp = 5kg * 1600m/s
Now, let's calculate the force exerted on the rocket:
F = Δp / Δt
Since we have Δp and Δt is given as 1 second, we can substitute these values into the equation to find the force:
F = (5kg * 1600m/s) / 1s
F = 8000N
Therefore, the force exerted on the rocket is 8000 Newtons.
To find the velocity of the rocket when its mass reduces to 1/200 of its initial mass, we can use the principle of conservation of momentum. The total momentum before and after the mass reduction remains the same.
Let's assume the initial mass of the rocket is M kg, and the final mass is 1/200 of that, which is M/200 kg.
According to conservation of momentum, the momentum before and after the mass reduction can be equated:
(initial momentum) = (final momentum)
(Mass before * Velocity before) = (Mass after * Velocity after)
M * V_initial = (M/200) * V_final
Now, we need to isolate V_final:
V_final = (M * V_initial) / (M/200)
V_final = 200 * V_initial
So, when the mass of the rocket reduces to 1/200 of its initial mass, the velocity of the rocket will be 200 times its initial velocity.