(ignore the other question i posted this is the right one)
A rocket has a pre-ignition mass of 1100kg. On ignition it burns fuel at rate of 20kg s-1 producing a thrust of 10000N. How long after ignition of the fuel, will the rocket lift off?
also explain how is it possible for a rocket to accelerate in space.
(i cant work it outt. i know it involves the rocket thrust equation some how, the newtons 2nd law and suvat's..) thank you
The rocket weight is
M = (1100 - 20 t)*g = 10,780 - 196*t newtons
That equals the thrust when
196*t = 780 N
t = 3.98 seconds
Rockets acclerate during each stage because the thrust stays the same while the mass decreases (until burnout, when the fuel of that stage is gone).
ahh thank you so much!
can you write the actual formulas that you've used because im not sure if i understood it correctly
To determine how long after ignition the rocket will lift off, we need to consider the change in mass of the rocket and apply Newton's second law.
First, let's calculate the change in mass of the rocket over time. We know that the rocket burns fuel at a rate of 20 kg/s, so in time t, the change in mass (Δm) is given by:
Δm = 20 kg/s * t
Next, let's write down Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, the net force is the thrust produced by the rocket, which is 10,000 N. The mass of the rocket is the total mass of the rocket plus the mass of the burned fuel, which can be written as:
m = 1100 kg + Δm
Now, we can substitute the values into the equation:
10,000 N = (1100 kg + 20 kg/s * t) * a
To solve for t, we need to know the acceleration of the rocket.
When a rocket is in space, it can accelerate due to the principle of conservation of momentum. The rocket expels hot gases in one direction, creating a reaction force in the opposite direction (thrust). By Newton's third law, every action has an equal and opposite reaction. As a result, the rocket experiences a net force and accelerates.
So, for the acceleration (a), we can rearrange Newton's second law:
a = F / m
Substituting in the values, we have:
a = 10,000 N / (1100 kg + Δm)
Now, we can substitute this expression for acceleration back into our earlier equation:
10,000 N = (1100 kg + 20 kg/s * t) * (10,000 N) / (1100 kg + Δm)
Simplifying this equation and solving for t will give us the time after ignition when the rocket lifts off.
Please note that to get an accurate solution, we need to use the equation iteratively or numerically as the acceleration changes with time due to the changing mass of the rocket.