- #1
dekoi
Andy and Bella move in circular paths about a common point with the same constant angular velocity \omega. Bella's mass is half the mass of Andy. The distance, where Andy is from the centre of the circle, is twice the distance of Bella. Who of the two will experience the greater magnitude of the centripetal force, F_c?
The answer given is that they will experience the SAME force. However, I found otherwise.
Since F_c=m\omega^2R
F_a=m_a\omega^2R_a and F_b=m_b\omega^2R_b
The ratios I obtained were: m_b=\frac{m_a}{2} and R_b=\frac{R_a}{2}.
When I find the ratio, I get:
\frac{F_a}{F_b}=\frac{m_a\omega^2R_a}{m_b\omega^2R_b}=\frac{m_aR_a}{\frac{m_a}{2}\frac{R_a}{2}}
My end result will be the value, 4, which is not 1, which I am looking for in order for the forces to be equal.
Is there a problem with my method, or is the answer given the wrong answer?
The answer given is that they will experience the SAME force. However, I found otherwise.
Since F_c=m\omega^2R
F_a=m_a\omega^2R_a and F_b=m_b\omega^2R_b
The ratios I obtained were: m_b=\frac{m_a}{2} and R_b=\frac{R_a}{2}.
When I find the ratio, I get:
\frac{F_a}{F_b}=\frac{m_a\omega^2R_a}{m_b\omega^2R_b}=\frac{m_aR_a}{\frac{m_a}{2}\frac{R_a}{2}}
My end result will be the value, 4, which is not 1, which I am looking for in order for the forces to be equal.
Is there a problem with my method, or is the answer given the wrong answer?
