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 71500 kg spacecraft by 64 cm/s, how long should it be fired?
To determine how long 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 exerted by the rocket is 35 N, and the mass of the spacecraft is 71500 kg. We can rearrange the equation to solve for the acceleration: F = ma
35 N = 71500 kg * a
Solving for acceleration:
a = 35 N / 71500 kg
Next, we can use the equation for velocity (v) to calculate the time (t) needed to change the velocity by 64 cm/s. The equation for velocity is:
v = at
Rearranging this equation to solve for time:
t = v / a
Converting the velocity change to meters:
64 cm/s = 0.64 m/s
Plugging in the values:
t = 0.64 m/s / (35 N / 71500 kg)
Simplifying the equation:
t = 0.64 m/s * (71500 kg / 35 N)
t ≈ 13.04 seconds
Therefore, the rocket should be fired for approximately 13.04 seconds to change the velocity of the spacecraft by 64 cm/s.
To find the time for which the rocket should be fired, we can use Newton's second law of motion, which states that the force applied on an object is equal to the rate of change of its momentum.
First, let's convert the change in velocity from centimeters per second to meters per second: 64 cm/s = 0.64 m/s.
The change in momentum (Δp) of the spacecraft can be calculated using the formula:
Δp = mass × Δv
where mass is the mass of the spacecraft and Δv is the change in velocity.
Δp = 71500 kg × 0.64 m/s
Next, we need to determine the time duration (t) for which the rocket should be fired. We can use the formula:
Force = Δp / t
Rearranging the formula, we have:
t = Δp / Force
t = (71500 kg × 0.64 m/s) / 35 N
Now we can calculate the value of t using the given values:
t = (45760 kg·m/s) / 35 N
By taking the ratio of the two quantities, we find:
t ≈ 1307.43 seconds
Therefore, the rocket should be fired for approximately 1307.43 seconds to achieve the desired change in velocity.
Thrust x time, also known as "impulse", must equal the momentum change desired. In your case the momentum change required is
7.15*10^4 kg * 0.64 m/s = 4.58*10^4 kg m/s
Set this equal to 35 Newtons * T and solve for T. It will be in seconds