Question

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.

Answer 1

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

Explanation:

Recall that the formula for kinetic energy is given below as

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

where k=kinetic energy (joules), m= mass of object (kg), v= velocity of object m/s)

For cart A

$m_{a}$ = mass of cart A

$v_{a}$ = v = velocity of cart A

$K.E_{a}$ = kinetic energy of cart A

hence, $K.E_{a}$ = $\frac{m_{a}v^{2} }{2}$

For cart B

$m_{b}$ = mass of cart B

$v_{b}$ = 2v = velocity of cart B

$K.E_{b}$ = kinetic energy of cart B

hence, $K.E_{b}$ = $\frac{m_{b}(2v^{2}) }{2}$ = 2$m_{b} v^{2}$

from the question, both cart are identical which implies they have the same mass i.e $m_{a}$ = $m_{b}$ = m which implies that

$K.E_{a}= \frac{mv^{2} }{2}$ and $K.E_{b} =2mv^{2}$

The total kinetic energy K is the sum of cart A and cart B kinetic energy

$K=K.E_{a} + K.E_{b}$

$K=\frac{mv^{2} }{2} + 2mv^{2}$

hence

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