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 concept of impulse, which is equal to the change in momentum.
First, let's define the given values:
- Mass of expelled gases (m): 1.30 x 10^3 kg/s
- Speed of expelled gases (v): 3.00 x 10^4 m/s
The impulse (J) can be calculated using the equation:
J = m * v
Now let's calculate the impulse:
J = (1.30 x 10^3 kg/s) * (3.00 x 10^4 m/s)
J = 3.90 x 10^7 kg·m/s
The impulse is equal to the change in momentum. Therefore:
J = ∆p
Next, let's calculate the momentum change (∆p) for 1 second. Since the rate of expulsion is given in kg/s, we can multiply the given mass rate by the duration (Δt = 1 s) to find the change in mass:
∆m = (1.30 x 10^3 kg/s) * (1 s)
∆m = 1.30 x 10^3 kg
Now, we can find the momentum change (∆p) using the formula:
∆p = ∆m * v
∆p = (1.30 x 10^3 kg) * (3.00 x 10^4 m/s)
∆p = 3.90 x 10^7 kg·m/s
This momentum change (∆p) is equal to the impulse (J). Therefore, the force exerted on the rocket can be determined by dividing the impulse by the duration (Δt = 1 s), as force is defined as the rate of change of momentum (F = ∆p/Δt):
F = J/Δt
F = (3.90 x 10^7 kg·m/s) / (1 s)
F = 3.90 x 10^7 N
So, the force exerted on the rocket is 3.90 x 10^7 N.