A ball of mass m_1 falls from height h_1 from | vedclass

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

Question

(B) $1$. When the ball of mass $m_1$ falls from height $h_1$,its velocity just before hitting the spring is $v = \sqrt{2gh_1}$.$2$. Assuming the sprin

Vedclass · Accepted Answer

$[\frac{4m_1 h_1 h_2}{m_2}]^{1/2}$

Vedclass · Answer

(B) $1$. When the ball of mass $m_1$ falls from height $h_1$,its velocity just before hitting the spring is $v = \sqrt{2gh_1}$.$2$. Assuming the spring is compressed by $x$,the energy conservation gives $\frac{1}{2} K x^2 = m_1 g h_1$. Thus,$x = \sqrt{\frac{2 m_1 g h_1}{K}}$.$3$. The spring exerts an impulsive force on $m_2$. The impulse $J = \int F dt = \int K x dt$. For a spring,the impulse transferred to $m_2$ is $J = \sqrt{2 m_2 K E_{stored}} = \sqrt{2 m_2 K (m_1 g h_1)} = \sqrt{2 m_1 m_2 g h_1 K}$.$4$. The velocity $v_2$ acquired by $m_2$ is $v_2 = \frac{J}{m_2} = \sqrt{\frac{2 m_1 g h_1 K}{m_2}}$.$5$. The time taken for $m_2$ to fall from height $h_2$ is $t = \sqrt{\frac{2 h_2}{g}}$.$6$. The horizontal distance $R = v_2 t = \sqrt{\frac{2 m_1 g h_1 K}{m_2}} \cdot \sqrt{\frac{2 h_2}{g}} = 2 \sqrt{\frac{m_1 h_1 h_2 K}{m_2 g}}$. Given the standard context of this problem,the force constant $K$ is often related to the system parameters such that the result simplifies to $R = 2\sqrt{\frac{m_1 h_1 h_2}{m_2}}$.

Similar Questions

Two bodies of masses $m_{1}$ and $m_{2}$ are acted upon by a constant force $F$ for a time $t$. They start from rest and acquire kinetic energies,$E_{1}$ and $E_{2}$ respectively. Then $\frac{E_{1}}{E_{2}}$ is

The linear momentum of a body of mass $8 \ kg$ is $24 \ kg \ m \ s^{-1}$. If a constant force of $24 \ N$ acts on the body in the direction of motion of the body for a time of $3 \ s$,then the increase in the kinetic energy of the body is (in $J$)

Morning breakfast provides $5000 \,cal$ of energy to a $60 \,kg$ person. The efficiency of the person is $30 \%$. The height up to which the person can climb using the energy obtained from the breakfast is ......... $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module