A model rocket has a mass of 0.2 kg, with a motor that can provide a force of 100 N. A second model rocket is being built with the same motor. but it is being designed to accelerate half as much as the first rocket. What kind of change can be made in the design to achieve this objective?
the mass of the second rocket should be 0.1 kg
the mass of the second rocket should be 0.4 kg
the mass of the second rocket should be 0.01 kg
the mass of the second rocket should be 0.2 kg
The correct answer is: the mass of the second rocket should be 0.4 kg.
This can be determined using Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Therefore, if the second rocket is designed to accelerate half as much as the first rocket, the force acting on it should also be half of the force acting on the first rocket.
Since the motor in both rockets provides a force of 100 N, the force acting on the second rocket should also be 100 N. We can rearrange Newton's second law to solve for mass:
Force (F) = mass (m) * acceleration (a)
100 N = m * a
Given that the acceleration of the second rocket is half of the first rocket's acceleration, we can substitute a/2 for the acceleration:
100 N = m * (a/2)
200 N = m * a
m = 200 N / a
Since the mass of the first rocket is 0.2 kg, we can substitute this value for m in the equation:
0.2 kg = 200 N / a
Solving for a:
a = 200 N / 0.2 kg
a = 1000 m/s^2
Substituting this value of a into the equation to find the mass of the second rocket:
m = 200 N / 1000 m/s^2
m = 0.2 kg
Therefore, the mass of the second rocket should also be 0.2 kg.