In the absence of external torques, the angular momentum of a system is conserved.
An artificial satellite orbiting the Earth quadruples its kinetic energy.
Assuming no external torques act on the system, the radius of the orbit will ...
a. Decrease by a factor of 4
b. Decrease by a factor of 2
c. Remain the same
d. Increase by a factor of 2
e. Increase by a factor of 4
Would the answer be b..
What I did was figured out the relationship between KE and speed. If KE quadruples, speed would only double. I am not sure about the next step though, I just used the following equation: mvr = nk; this gives me that r and v are inversely related so if v is increasing by 2, r would decrease by 2..
Is this the correct way to go about doing this, or is there another equation that can can used more appropriately for this question..
You have it.
To determine how the radius of the orbit will be affected when the kinetic energy of an artificial satellite quadruples, we need to understand the concept of conservation of angular momentum.
Angular momentum is conserved when no external torques act on a system. In the case of an artificial satellite orbiting the Earth, the only torque acting on the system is the gravitational torque exerted by the Earth's gravity. Assuming no other external torques are involved, the angular momentum of the system will be conserved.
The angular momentum of an object in circular motion is given by the equation:
L = Iω
where L represents the angular momentum, I represents the moment of inertia, and ω represents the angular velocity.
In this scenario, when the kinetic energy of the satellite quadruples, it means that the rotational kinetic energy of the satellite has increased by a factor of 4. Since angular momentum is conserved, and the moment of inertia (I) remains constant, the angular velocity (ω) must decrease to compensate for the increase in kinetic energy.
As the angular velocity decreases, the radius of the orbit will increase. This is because angular velocity is inversely proportional to the radius of the orbit:
ω = v/r
where v represents the linear velocity of the satellite.
Since the linear velocity of the satellite remains constant in this scenario, when the angular velocity decreases, the radius of the orbit increases. Therefore, the correct answer is:
d. Increase by a factor of 2