The mass of a spacecraft is about 480 kg. An engine designed to increase the speed of the spacecraft while in outer space provides 0.09 N thrust at maximum power. By how much does the engine cause the craft's speed to change in 1 week of running at maximum power? Describe any assumptions you made.
a = .09/480
= 9/48000 m/s^2
dv = a dt
= (9/48,000) *7d/w*24h/d*3600s/h
= 113 m/s
we are assuming constant mass. Possibly fuel or even engine components were ejected.
This is just the speed change due to the propulsion. Presumably there are also gravitational forces acting even in space.
To answer this question, we need to make some assumptions:
1. The engine provides a constant thrust of 0.09 N throughout the week.
2. There are no external forces acting upon the spacecraft that could affect its speed.
3. The spacecraft starts from rest.
To find out how much the engine causes the spacecraft's speed to change, we can use Newton's second law of motion:
Force = Mass * Acceleration
Rearranging the equation to solve for acceleration:
Acceleration = Force / Mass
Substituting the given values into the equation:
Acceleration = 0.09 N / 480 kg
Acceleration = 0.0001875 m/s^2
Now, we can use the kinematic equation to calculate the change in speed:
Change in Speed = Acceleration * Time
Substituting the values:
Change in Speed = 0.0001875 m/s^2 * 1 week
Note: Before proceeding, let's convert 1 week into seconds.
1 week = 7 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute
= 604,800 seconds
Change in Speed = 0.0001875 m/s^2 * 604,800 s
Change in Speed ≈ 114 m/s
Therefore, running the engine at maximum power for 1 week would cause the spacecraft's speed to change by approximately 114 m/s.
To determine how much the engine causes the spacecraft's speed to change in 1 week, we need to use Newton's second law of motion, which states that the force (thrust) exerted on an object is equal to the mass of the object multiplied by its acceleration.
1. Calculate the acceleration of the spacecraft:
Using the formula F = ma, where F is the thrust provided by the engine and m is the mass of the spacecraft:
0.09 N = 480 kg * a
a = 0.09 N / 480 kg
a ≈ 0.0001875 m/s²
2. Determine the change in velocity:
The change in velocity can be found by multiplying the acceleration by the time. In this case, the time is 1 week, which is equal to 604,800 seconds (1 week * 7 days * 24 hours * 60 minutes * 60 seconds).
Δv = a * t
Δv = 0.0001875 m/s² * 604,800 s
Δv ≈ 113.4 m/s (rounded to the nearest tenth)
Therefore, running the engine at maximum power for 1 week would cause the spacecraft's speed to change by approximately 113.4 m/s.
Assumptions made:
1. The engine provides a constant thrust throughout the entire duration of 1 week.
2. There are no external forces (such as gravity) acting on the spacecraft, affecting its acceleration.
3. The mass of the spacecraft remains constant during the week.