In Example 6.7, let \(m_{1}=3 m_{2}\).

(a) Where on axis A is the center of mass of the two-cart system?

(b) Where on axis A would you need to place a third cart of inertia \(m_{3}=m_{1}\) so that the center of mass of the three-cart system is at the position of cart 2 ?

Data from Example 6.7

The positions of two identical carts at rest on a low-friction track are measured relative to two axes oriented in the same direction along the track. On axis A, cart 1 is at \(x_{\mathrm{A} 1}\) and cart 2 is at \(x_{\mathrm{A} 2}\). On axis \(\mathrm{B}\), cart 1 is at the origin and cart 2 is at \(x_{\mathrm{B} 2}\).

Determine the position of the center of mass of the two-cart system relative to each axis.

If instead of identical carts you have \(m_{1}=2 m_{2}\), what is the position of the center of mass on each axis?