The space shuttle has a mass of 2,000,000 kg. At liftoff, the engines generate a force of 32,000,000 N. What is the velocity of the shuttle after 10 minutes if the acceleration rate were 13 m/s/s? What is the acceleration of the shuttle?
The trust force is countering gravity, and the excess is accelerating.
EngineForce= mass(g + a)
solve for a.
Then,
vfinal=acceleration*time.
change time to seconds.
Well, if the space shuttle is generating that much force, it better be a pretty strong engine! But let's see what we can calculate here.
To find the acceleration of the shuttle, we can use the formula: EngineForce = mass * (gravity + acceleration)
Given that the mass of the shuttle is 2,000,000 kg and the engine force is 32,000,000 N, we can rearrange the equation to solve for acceleration:
Acceleration = (EngineForce / mass) - gravity
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Step 1: Calculate the acceleration of the shuttle
Given:
Mass of the space shuttle (m) = 2,000,000 kg
Force generated by the engines (F) = 32,000,000 N
Using Newton's second law of motion (F = ma), we can rearrange the formula to find the acceleration (a):
a = F / m
a = 32,000,000 N / 2,000,000 kg
a = 16 m/s²
The acceleration of the shuttle is 16 m/s².
Step 2: Calculate the velocity of the shuttle after 10 minutes
Given:
Time (t) = 10 minutes = 10 * 60 seconds = 600 seconds
Acceleration (a) = 16 m/s²
Using the formula for velocity (v):
v = a * t
v = 16 m/s² * 600 s
v = 9600 m/s
The velocity of the shuttle after 10 minutes is 9600 m/s.
To find the acceleration of the shuttle, you can use the formula:
EngineForce = mass * (gravity + acceleration)
In this case, the mass of the space shuttle is given as 2,000,000 kg, and the engine force is given as 32,000,000 N. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Substituting these values into the formula, we get:
32,000,000 = 2,000,000 * (9.8 + acceleration)
Now, we can solve for acceleration:
32,000,000 = 2,000,000 * 9.8 + 2,000,000 * acceleration
32,000,000 = 19,600,000 + 2,000,000 * acceleration
2,400,000 = 2,000,000 * acceleration
acceleration = 2,400,000 / 2,000,000
acceleration = 1.2 m/s^2
Therefore, the acceleration of the shuttle is 1.2 m/s^2.
Next, to find the velocity of the shuttle after 10 minutes, we can simply use the following formula:
vf = acceleration * time
In order to use this formula, we need to convert the time from minutes to seconds. Since there are 60 seconds in a minute, we can multiply 10 minutes by 60 to get 600 seconds.
Substituting the values into the formula, we get:
vf = 1.2 * 600
vf = 720 m/s
Therefore, the velocity of the shuttle after 10 minutes would be 720 m/s.