Question

Two carts of masses 20 kg and 300 kg on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails are same. If the 200 kg cart travels a distance of 36 m and stops, then the distance travelled by the cart weighing 300 kg will be

Answer 1

Let mass of cart be $m_1=200kg$ and $m_2=300kg$

Let $s_1$ and $s_2$ be displacement of mass of mass $m_1$ and $m_2$

Let$\mu$ be coefficient of friction between cart and rail.

According to work energy principle, the change in kinetic energy of object is equal to net work done on the object.

For $m_1$

$F_1.s_1=\frac{1}{2}{m}_1{v}_1^2$

For $m_2$

$F_2.s_2=\frac{1}{2}{m}_2{v}_2^2$

Substituting for F

$\mu m_{1}g{s}_1=\frac{1}{2}{m}_1{v}_1^2$

$\mu m_{2}g{s}_2=\frac{1}{2}{m}_2{v}_2^2$

$\mu g{s}_1=\frac{1}{2}{v}_1^2......\left(1\right)$

$\mu g{s}_2=\frac{1}{2}{v}_2^2......\left(2\right)$

Again from conservation of momentum

$m_1{v}_1+m_2{v}_2=0$

$\frac{v_1}{v_2}=\frac{m_2}{m_1}$

From (1) and (2)

$\frac{s_1}{s_2}=\frac{v_1^2}{v_2^2}$

From (3)

$\frac{s_1}{s_2}=\frac{m_2^2}{m_1^2}$

$\frac{36}{s_2}=\frac{9}{4}$

$s_2=\frac{36\times 4}{9}$

$s_2=16m$