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 need to use the concept of impulse and momentum.
Impulse is defined as the change in momentum of an object. It is given by the equation:
Impulse = Force * time
Momentum is defined as the product of an object's mass and its velocity. It is given by the equation:
Momentum = mass * velocity
Now, let's go step by step to solve the problem:
Step 1: Identify the given quantities
The question provides the following information:
- Rate of gas expulsion: 1.30 x 10^3 kg/s
- Speed of the gas: 3.00 x 10^4 m/s
Step 2: Calculate the mass of the gases expelled in 1 second
Since the rate of gas expulsion is given in kg/s, we can calculate the mass of the gases expelled in 1 second by multiplying the rate by 1 second. Therefore:
Mass expelled in 1 second = (1.30 x 10^3 kg/s) * (1 s) = 1.30 x 10^3 kg
Step 3: Calculate the change in momentum for 1 second
To find the change in momentum, we need to calculate the initial momentum and final momentum. Since the gases are being expelled, the initial momentum is zero because the gases are at rest before they are expelled. The final momentum is given by:
Momentum final = mass * velocity
Momentum final = (1.30 x 10^3 kg) * (3.00 x 10^4 m/s)
Step 4: Calculate the impulse
The impulse is defined as the change in momentum. Therefore:
Impulse = Momentum final - Momentum initial
Impulse = (1.30 x 10^3 kg) * (3.00 x 10^4 m/s) - 0
Impulse = (1.30 x 10^3 kg) * (3.00 x 10^4 m/s)
Step 5: Calculate the force exerted on the rocket
Now that we have the impulse, we can calculate the force exerted on the rocket. The force is related to impulse and time through the equation:
Impulse = Force * time
In this case, the impulse is calculated for 1 second. Therefore, the force can be calculated as:
Force = Impulse / time
Force = (1.30 x 10^3 kg) * (3.00 x 10^4 m/s) / (1 s)
Solving this equation will give you the force exerted on the rocket.
In summary, to solve this problem, follow these steps:
1. Identify the given quantities.
2. Calculate the mass of the gases expelled in 1 second.
3. Calculate the change in momentum for 1 second.
4. Calculate the impulse.
5. Calculate the force exerted on the rocket using the impulse and time relationship.
Plug in the given values into the equations, perform the calculations, and you'll find the answer to the question.