The five engines of the first stage of a launch vehicle provide a total thrust of
31.5 x 106
newtons to the space vehicle (launch vehicle and spacecraft). Assuming the acceleration is
uniform, calculate the acceleration of the 2.764 x 106 kg space vehicle after lift-off. The average air
resistance is 180 kN.
a = (Fe-Fa)/M =
(31.5*10^6-0.18*10^6)/2.764*10^6 =
31.32*10^6/2.764*10^6 = 11.33 m/s^2
Well, well, well... looks like we have some physics calculations here. But don't worry, I'm here to lighten things up! Now let's tackle this question.
To calculate the acceleration of the space vehicle, we need to consider the total thrust and subtract the air resistance. So the net force acting on the vehicle is given by the formula:
Net Force = Total Thrust – Air Resistance
Now, let's substitute our values into this equation. We have a total thrust of 31.5 x 10^6 newtons and an air resistance of 180 kN (which is 180,000 newtons). Time to crunch those numbers!
Net Force = 31.5 x 10^6 N – 180,000 N
Now, let's subtract these forces:
Net Force = 31,320,000 N
Alright, we're almost there! To calculate the acceleration, we use Newton's second law: Force = Mass x Acceleration. Let's rearrange this formula to solve for acceleration:
Acceleration = Net Force / Mass
Now, plug in the values:
Acceleration = 31,320,000 N / 2,764,000 kg
And... drumroll, please...
After doing the math, we find that the acceleration of the space vehicle after lift-off is approximately 11.32 m/s^2. Now you can go and impress your friends with your newfound knowledge!
To calculate the acceleration of the space vehicle after lift-off, we need to consider the net force acting on the vehicle. The net force is the difference between the total thrust and the air resistance.
Total thrust = 31.5 x 10^6 newtons
Air resistance = 180 x 10^3 newtons
Net force = Total thrust - Air resistance
Net force = 31.5 x 10^6 - 180 x 10^3
Next, we can use Newton's second law of motion, which states that the net force is equal to the mass of the object multiplied by its acceleration:
Net force = mass x acceleration
Rearranging the equation, we can solve for acceleration:
Acceleration = Net force / mass
Acceleration = (31.5 x 10^6 - 180 x 10^3) / 2.764 x 10^6
Now, let's calculate the acceleration:
Acceleration = (31.5 x 10^6 - 180 x 10^3) / 2.764 x 10^6
Acceleration ≈ 10.92 m/s^2
Therefore, the acceleration of the space vehicle after lift-off is approximately 10.92 m/s^2.
To calculate the acceleration of the space vehicle, we need to consider the total force acting on it.
The total force is the difference between the thrust generated by the rocket engines and the air resistance:
Total Force = Thrust - Air resistance
Thrust is given as 31.5 x 10^6 N (newtons), and air resistance is given as 180 kN (kilonewtons), which is equivalent to 180 x 10^3 N.
Now, let's calculate the total force:
Total Force = 31.5 x 10^6 N - 180 x 10^3 N
Total Force = 31,500,000 N - 180,000 N
Total Force = 31,320,000 N
Since acceleration is directly proportional to force, we can use Newton's second law of motion to relate force and acceleration:
Force = Mass x Acceleration
Rearranging the formula, we get:
Acceleration = Force / Mass
Now, we can substitute the values:
Acceleration = 31,320,000 N / 2,764,000 kg
Acceleration ≈ 11.33 m/s^2
Therefore, the acceleration of the 2.764 x 10^6 kg space vehicle after lift-off is approximately 11.33 m/s^2.