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?
I believe I have parts of the problem but am not sure. Please help.
Sure! I can help you with this problem. Let's break it down step by step.
Step 1: Understand the problem
The problem is asking for the force exerted on the rocket when it expels gases at a certain rate and speed. To solve this, we need to use the concept of impulse and momentum change.
Step 2: Recall the formula for impulse
Impulse is defined as the change in momentum of an object. It can be calculated using the formula:
Impulse = Force x Time
Step 3: Calculate the momentum change
To find the momentum change for 1 second, we need to multiply the rate of gas expulsion by the speed of the gases:
Momentum change = Rate x Speed
Step 4: Use the formula for impulse to find the force
Since we now know the momentum change, we can plug it into the impulse formula to find the force:
Impulse = Force x Time
We are given the time of 1 second, and we know the momentum change, so we can rearrange the formula to solve for the force:
Force = Impulse / Time
Now, let's put it all together and solve the problem.
Given:
Rate of gas expulsion = 1.30 x 10^3 kg/s
Speed of gases = 3.00 x 10^4 m/s
Time = 1 second
Step 5: Calculate the momentum change
Momentum change = (Rate of gas expulsion) x (Speed of gases)
Momentum change = (1.30 x 10^3 kg/s) x (3.00 x 10^4 m/s)
Momentum change = 3.9 x 10^7 kg·m/s
Step 6: Calculate the force
Force = Momentum change / Time
Force = (3.9 x 10^7 kg·m/s) / (1 second)
Force = 3.9 x 10^7 N
So, the force exerted on the rocket is 3.9 x 10^7 Newtons.
In summary, to solve this problem, you need to calculate the momentum change by multiplying the rate of gas expulsion by the speed of the gases. Then, you can use the formula for impulse to find the force by dividing the momentum change by the time.