Two rockets with the same mass are. Accelerated. Rocket A accelerates twice as fast as Rocket B. Which statement is correct?
The motor in rocket A is four times as powerful as the motor and in rocket B
The motor in rocket A Is twice as powerful as the motor in rocket B
The motor in rocket A is half as powerful as the motor in rocket B
The motor in rocket A is half as Powerful as the motor in rocket B
The motor in rocket A is twice as powerful as the motor in rocket B
What is the Answer?
2 rockets
Rocket A:
m = 1 kg
a = 1 m/s^2
in 1 second
F = m a = 1 N
distance = 1/2 a t^2 = 1/2 meter
work done = force * distance = 1 * 1/2 = 1/2 Joule
power = work /second = 1/2 Watt
now
Rocket B
m = 1 kg
a = 2 m/s^2
in 1 second
F = m a = 2 N
distance = 1/2 a t^2 = 1/2 * 2 = 1 meter
work done = force * distance = 2 * 1 = 2 Joules
power = work /second = 2 Watts
looks like 4 times the power. Twice the force over twice the distance in a second.
Well, it seems like Rocket A is the overachiever here, accelerating twice as fast as Rocket B. But does that mean its motor is four times as powerful? Sounds a bit excessive, don’t you think? I mean, it's not like Rocket A is trying to compensate for something. So, I'll go ahead and say the statement that makes more sense: The motor in Rocket A is twice as powerful as the motor in Rocket B. Let's not give Rocket A too big of an ego now.
To determine which statement is correct, we will use Newton's second law of motion, which states that the force exerted by an object is equal to its mass multiplied by its acceleration (F = ma).
Let's assume the mass of the rockets is "m" and the acceleration of rocket B is "a". According to the problem, the acceleration of rocket A is twice as fast as rocket B, so the acceleration of rocket A would be "2a" (twice the acceleration of rocket B).
Now, let's compare the force exerted by the motors on each rocket. Since the mass of both rockets is the same, the force exerted on each rocket should be equal to their respective mass multiplied by their acceleration.
For rocket A: Force(A) = m * 2a = 2ma
For rocket B: Force(B) = m * a
Now, to compare the power of the motors in both rockets, we need to know that power is defined as the rate at which work is done or the rate at which energy is transferred. Power can be calculated as the force exerted multiplied by the velocity at which it is applied.
Since we don't have information about the velocity of the rockets, we cannot directly compare the power of the motors and determine if one is four times, twice, or half as powerful as the other. Therefore, none of the given statements can be concluded as correct based on the information provided.