A rocket weighs 2.0 X 107 N. Its engines exert a force of 2.5 X 107 N at liftoff.
What is the rocket's acceleration when it lifts off?
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To calculate the acceleration of the rocket when it lifts off, we 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.
The net force acting on the rocket is the difference between the force exerted by its engines and its weight. We can calculate this as follows:
Net force = Force exerted by engines - Weight
Given:
Force exerted by engines = 2.5 X 10^7 N
Weight = 2.0 X 10^7 N
Substituting the values into the equation, we have:
Net force = 2.5 X 10^7 N - 2.0 X 10^7 N
Net force = 0.5 X 10^7 N
The mass of the rocket is not given in the question. Without the mass, we cannot determine the acceleration. The acceleration of an object depends on both the net force acting on it and its mass. So, we need the mass of the rocket to find its acceleration.
To find the rocket's acceleration when it lifts off, use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
1. First, identify the given information:
- The weight of the rocket (W) = 2.0 X 10^7 N
- The force exerted by the engines (F) = 2.5 X 10^7 N
2. The weight of the rocket is equal to the force of gravity acting on it, which is the product of the mass of the rocket (m) and the acceleration due to gravity (g). Therefore, we can write:
W = m * g
3. Rearrange the equation to solve for mass:
m = W / g
Since the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute this value into the equation:
m = W / 9.8
Plug in the known value for the weight of the rocket to find its mass.
4. Substitute the mass of the rocket and the force exerted by the engines into Newton's second law of motion:
F = m * a
Rearranging the equation to solve for acceleration:
a = F / m
Plug in the known values for the force exerted by the engines and the mass of the rocket to find its acceleration.
Now, let's calculate the rocket's acceleration when it lifts off:
m = (2.0 X 10^7 N) / 9.8 m/s^2
m ≈ 2.04 X 10^6 kg
a = (2.5 X 10^7 N) / (2.04 X 10^6 kg)
a ≈ 12.25 m/s^2
Therefore, the rocket's acceleration when it lifts off is approximately 12.25 m/s^2.