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, we can use the principles of impulse and momentum. First, let's discuss the general steps you can follow to solve this kind of problem:
1. Identify and write down the given information: In this case, we are given the rate at which gases are expelled (1.30 x 10^3 kg/s) and the speed at which the gases are expelled (3.00 x 10^4 m/s).
2. Analyze what the question is asking for: The question asks for the force exerted on the rocket.
3. Determine the principles and equations needed: In this case, we need to use the principle of impulse, which states that the impulse experienced by an object is equal to the change in momentum it undergoes. The equation for impulse is Impulse = Change in momentum.
Now let's apply these steps to solve the given question:
Step 1: The given information is as follows:
- Rate of expulsion of gases: 1.30 x 10^3 kg/s
- Speed of the expelled gases: 3.00 x 10^4 m/s
Step 2: The question asks for the force exerted on the rocket.
Step 3: We need to use the principle of impulse, which states that Impulse = Change in momentum.
To calculate the force exerted on the rocket, we first need to calculate the change in momentum. The momentum change can be calculated by multiplying the mass of the expelled gases by the change in velocity. In this case, since the gases are expelled at a constant speed, the change in velocity is simply the speed of the gases.
Step 4: Calculate the change in momentum:
Change in momentum = (Rate of expulsion of gases) x (Change in velocity)
= (1.30 x 10^3 kg/s) x (3.00 x 10^4 m/s)
Step 5: Calculate the force exerted on the rocket using the principle of impulse:
Impulse = Change in momentum
Force x Time = Change in momentum
Since the question asks for the force exerted on the rocket, which is the force per second, we can simplify the equation as follows:
Force = Change in momentum / Time
Force = (1.30 x 10^3 kg/s) x (3.00 x 10^4 m/s) / 1s
Now, you can substitute the given values into the equation and calculate the force exerted on the rocket.