A 5.00×10^5-kg rocket is accelerating straight up. Its engines produce 1.250×10^7 N of thrust, and air resistance is 4.50×10^6 N. What is the rocket’s acceleration? I just need the formula for finding the acceleration.
The formula for finding the acceleration is:
Acceleration (a) = (Net Force) / Mass
In this case, the net force is the difference between the thrust and air resistance:
Net Force = Thrust - Air Resistance
Therefore, the formula for finding the acceleration is:
Acceleration (a) = (Thrust - Air Resistance) / Mass
Substituting the given values:
Acceleration (a) = (1.250×10^7 N - 4.50×10^6 N) / 5.00×10^5 kg
Now, we can calculate the acceleration.
To find the acceleration of the rocket, you can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. Mathematically, it can be expressed as:
a = F_net / m
Where:
a: acceleration
F_net: net force acting on the object
m: mass of the object
In this case, the rocket's net force can be determined by subtracting the air resistance from the thrust force. Given that the thrust force is 1.250×10^7 N and the air resistance is 4.50×10^6 N, the net force can be calculated as follows:
F_net = F_thrust - F_air_resistance
Plugging in the given values, we have:
F_net = 1.250×10^7 N - 4.50×10^6 N
After evaluating the subtraction, we get:
F_net = 8.00×10^6 N
Now, to find the acceleration, we can substitute the values into Newton's second law equation:
a = F_net / m
Plugging in the values for the net force and the rocket's mass (5.00×10^5 kg):
a = (8.00×10^6 N) / (5.00×10^5 kg)
By dividing the net force by the mass, we can find the rocket's acceleration.
Fth = 1.250*10^7 N. = Force of thrust.
Ra = 4.50*10^6 N. = Air resistance.
m = 5.00*10^5 kg = Mass of the rocket.
a = (Fth-Ra)/m