A spring is compressed between two toy carts | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) When the spring is released,it exerts an impulse $J = F \cdot t$ on both carts. Since the forces are equal and act for the same time,both carts ac

Vedclass · Accepted Answer

$\frac{s_1}{s_2} = \left( \frac{m_2}{m_1} \right)^2$

Vedclass · Answer

(C) When the spring is released,it exerts an impulse $J = F \cdot t$ on both carts. Since the forces are equal and act for the same time,both carts acquire the same magnitude of momentum $p = m_1 v_1 = m_2 v_2$.The frictional force acting on each cart is $f = \mu m g$.Using the work-energy theorem,the work done by friction equals the change in kinetic energy: $W = \Delta K$.$f \cdot s = \frac{p^2}{2m} \implies \mu m g s = \frac{p^2}{2m}$.Solving for displacement $s$: $s = \frac{p^2}{2 \mu m^2 g}$.Since $p$,$\mu$,and $g$ are the same for both carts,$s \propto \frac{1}{m^2}$.Therefore,the ratio of displacements is $\frac{s_1}{s_2} = \frac{m_2^2}{m_1^2} = \left( \frac{m_2}{m_1} \right)^2$.

Similar Questions

$A$ $10 \,g$ bullet moving at $200 \,m/s$ stops after penetrating $5 \,cm$ of a wooden plank. The average force exerted on the bullet will be .......... $N$.

Two situations are shown in figures $(a)$ and $(b)$. In each case,$m_1 = 3 \ kg$ and $m_2 = 4 \ kg$. If $a_1$ and $a_2$ are the respective accelerations of the blocks in these situations,then the values of $a_1$ and $a_2$ are respectively [ $g = 10 \ ms^{-2}$ ]

What is the value of the contact force $R$ on an object of mass $m$ placed on an inclined plane with angle $\theta$?

$A$ force of $(2.6 \hat{i} + 1.6 \hat{j}) \text{ N}$ acts on a body of mass $2 \text{ kg}$. If the velocity of the body at time $t = 0$ is $(3.6 \hat{i} - 4.8 \hat{j}) \text{ ms}^{-1}$, the time at which the body will just have a velocity along the $x$-axis only is: (in $\text{ s}$)

In the given system,if $M_2 = 2M_1$,the tension in the string is $T$. If the positions of the blocks are interchanged,what will be the new tension in the string?

Vedclass Test Series

Exam Paper Generator

Online Exam Module