Carts A and B are identical and are moving toward each other on a track. The speed of cart A is v, while the speed of cart B is

Question

DedPeter

12 days ago

13

Carts A and B are identical and are moving toward each other on a track. The speed of cart A is v, while the speed of cart B is

2v. In the Earth reference frame, the system of the two carts has kinetic energy K.

Physics

1 answer:

serg [3.4K] · Answer 1 · 2026-03-28T20:59:54+03:00

k= $\frac{5mv^{2} }{2}$

To find kinetic energy, we use the following formula:

k = $\frac{mv^{2} }{2}$

where k represents kinetic energy (measured in joules), m is the object's mass (in kg), and v signifies the object's velocity (in m/s). For cart A, we denote the mass as

and the velocity as

translating to the kinetic energy of cart A. Hence, $K.E_{a}$ = $\frac{m_{a}v^{2} }{2}$

For cart B, we define the mass as

and the velocity as 2v leading to the kinetic energy of cart B. Thus, $K.E_{b}$ = $\frac{m_{b}(2v^{2}) }{2}$ = 2 $m_{b} v^{2}$

Considering that both carts are the same, it follows they possess identical mass, i.e., $m_{a}$ = $m_{b}$ = m. Therefore, the total kinetic energy K comprises the sum of the kinetic energies of cart A and cart B.