Small rockets are used to make tiny adjustments in the speeds of satellites. One such rocket has a thrust of 35 N. If it is fired to change the velocity of a 72300 kg spacecraft by 64 cm/s, how long should it be fired?
Calculate the desired momentum change.
72300 kg * 0.64 m/s = ?
That equals the impulse needed.
Divide the impulse by the force to get the time needed.
To find the duration for which the rocket should be fired, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the force is the thrust of the rocket, and the mass is the mass of the spacecraft. The acceleration can be calculated using the change in velocity and the firing duration.
First, let's convert the change in velocity into m/s:
64 cm/s = 0.64 m/s
Next, calculate the acceleration using the formula:
F = m * a
a = F / m
Substituting the given values:
a = 35 N / 72300 kg
Now, we can find the duration by rearranging the formula for acceleration:
a = Δv / Δt
Substituting the values:
0.64 m/s = (35 N / 72300 kg) * Δt
To isolate Δt, we can divide both sides by (35 N / 72300 kg):
0.64 m/s / (35 N / 72300 kg) = Δt
Now, we can calculate the firing duration:
Δt = 0.64 m/s / (35 N / 72300 kg)
Using this formula, we can determine the duration for which the rocket should be fired.