A 1, kg block moves towards a light spring wi | vedclass

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

Question

(B) Given: Mass $m = 1\, kg$,initial velocity $v_1 = 8\, m/s$,compression $x = 3\, m$.Initial momentum $P_1 = m v_1 = 1 	imes 8 = 8\, kg\cdot m/s$.Fi

Vedclass · Accepted Answer

$16/3\, N/m$

Vedclass · Answer

(B) Given: Mass $m = 1\, kg$,initial velocity $v_1 = 8\, m/s$,compression $x = 3\, m$.Initial momentum $P_1 = m v_1 = 1 	imes 8 = 8\, kg\cdot m/s$.Final momentum $P_2 = P_1 / 2 = 4\, kg\cdot m/s$.Since $P_2 = m v_2$,we have $v_2 = P_2 / m = 4 / 1 = 4\, m/s$.By the law of conservation of energy,the loss in kinetic energy is equal to the potential energy stored in the spring:$\frac{1}{2} m v_1^2 - \frac{1}{2} m v_2^2 = \frac{1}{2} k x^2$$m(v_1^2 - v_2^2) = k x^2$$1 	imes (8^2 - 4^2) = k 	imes 3^2$$1 	imes (64 - 16) = 9k$$48 = 9k$$k = 48 / 9 = 16 / 3\, N/m$.

$A$ $1\, kg$ block moves towards a light spring with a velocity of $8\, m/s$. When the spring is compressed by $3\, m$,its momentum becomes half of the original momentum. The spring constant of the spring is:

Similar Questions

$A$ long spring, when stretched by a distance $x$, has the potential energy $u$. On increasing the stretching to $nx$, the potential energy of the spring will be:

$A$ body of mass $0.15 \ kg$ moving with a velocity of $15 \ ms^{-1}$ comes to rest when it hits a spring that is fixed at the other end. If the force constant of the spring is $1500 \ Nm^{-1}$,then the compression in the spring is: (in $m$)

If a long spring is stretched by $0.02\, m$,its potential energy is $U$. If the spring is stretched by $0.1\, m$,then its potential energy will be

$K$ is the force constant of a spring. The work done in increasing its extension from $l_1$ to $l_2$ will be

An elastic spring of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. Work done during the second stretching is

Vedclass Test Series

Exam Paper Generator

Online Exam Module