An interstellar ship has a mass of 1.20 X10^6 kg and is initially at rest relative to a star system. a) what constant acceleration is needed to ring the ship up to a speed of .10c (where c is the speed of light, 3.0X10^8 m/s) relative to the star system in 3 days? b) what is that acceleration in g units? c) what force is required for the accelaration? d) If the engines are shut down when .10c is reached (the speed then remains consant) how long does the ship take (start to finish) to journey 5 light months the distance that light travels in 5 months?
I found this question to be quite difficult will you please clearify each part of the question for me? I couldn't figure out what to do.
For (a), compute the velocity change needed in m/s and divide it by three says (converted to seconds). That will be the required acceleration im m/s^2
(b) To convert the acceleration to g's divide by 9.8 m^2/s per g
(c) F = m a
(d) at a speed of 0.1 c, it takes the spacecraft 10 times as long is it would take light to travel the same distance.
Hello, I know this is 3 years late but for people like me who just needed your hints, this basically means that for (a)
take .10(3x10^8)(m/s) and divide it by 3 days/24hrs/3600s and you will get your m/s^2
For (b), take what you got in (a) and divide it by 9.8m/s^2 to get the magnitude.
(c), Multiply (a) by the mass of the ship.
(d) the hint basically answered it..
Sure! Let's break down each part of the question.
a) We are given the mass of the interstellar ship (1.20 × 10^6 kg) and the desired final speed relative to the star system (0.10c, where c is the speed of light, 3.0 × 10^8 m/s). We need to find the constant acceleration required to reach this speed in 3 days.
To solve this, we first need to compute the velocity change needed in m/s. The change in velocity is given by:
Δv = (0.10c - 0) = 0.10c
Next, we convert 3 days to seconds. There are 24 hours in a day and 60 minutes in an hour, so:
3 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute = 259,200 seconds
Finally, we divide the velocity change by the time to get the required acceleration:
acceleration = Δv / t = (0.10c) / 259,200 s
b) Now, we need to convert the acceleration from part (a) to g units. One g is equivalent to 9.8 m/s^2. We divide the acceleration by 9.8 to get the acceleration in g units:
acceleration in g units = acceleration / 9.8 m^2/s per g
c) To find the force required for this acceleration, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration:
Force (F) = mass (m) × acceleration
Given that the mass of the interstellar ship is 1.20 × 10^6 kg (as mentioned in the question) and the acceleration is the one calculated in part (a), we can substitute these values into the equation to find the force.
d) Finally, we need to determine how long it takes for the ship to travel a distance of 5 light months, assuming the engines are shut down when the ship reaches 0.10c. Given that the distance light travels in 5 months (time for light to travel the distance) is equivalent to the distance traveled by the ship, we can conclude that it takes the ship 10 times longer to travel this distance compared to light.
I hope this clarifies each part of the question for you! Let me know if you have any further doubts.