I am reviewing for a test and I don't know how to attempt this question. Could someone please work through this problem and then have the general steps that I need to take to solve the question?
Here is the question:
A rocket expels gases at a rate of 1.30 x 10^3 kg/s with a speed of 3.00 x 10^4 m/s. What is the force exerted on the rocket? Hint: What does Impulse equal to? What is the momentum change for 1 sec?
To solve this question, you can use the concept of impulse and momentum. Here are the general steps you can follow to solve it:
1. Understand the given information:
- The rate at which gases are expelled by the rocket is 1.30 x 10^3 kg/s.
- The speed at which the gases are expelled is 3.00 x 10^4 m/s.
2. Recall the concept of impulse:
- Impulse is the change in momentum of an object and is equal to the force exerted on the object multiplied by the time interval over which the force acts.
- Mathematically, impulse (J) = force (F) x time interval (Δt).
3. Determine the time interval for the momentum change:
- From the given information, you are told to find the force exerted on the rocket for a time interval of 1 second. Therefore, Δt = 1 s.
4. Calculate the momentum change:
- The momentum change (Δp) is equal to the mass of the expelled gas (m) multiplied by its velocity (v).
- Mathematically, Δp = m x v.
5. Determine the mass of the expelled gas:
- From the given information, the rate of gas expulsion is 1.30 x 10^3 kg/s. Therefore, the mass of the expelled gas for a time interval of 1 second is 1.30 x 10^3 kg.
6. Calculate the impulse:
- Multiply the momentum change (step 4) by the time interval (step 3) to get the impulse.
- Mathematically, impulse (J) = Δp x Δt.
7. Determine the force exerted on the rocket:
- The impulse (step 6) is equal to the force (F) multiplied by the time interval (step 3).
- Mathematically, impulse (J) = F x Δt.
- Rearrange the equation to solve for the force:
F = J / Δt.
8. Substitute the values into the equation:
- Plug in the impulse (step 6) and the time interval (step 3) into the equation from step 7 and calculate the force.
By following these steps, you will be able to determine the force exerted on the rocket.