A container of mass m is pulled by a constant | vedclass

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

Question

(D) Let the acceleration of the container be $a_c = F/m$. In the frame of the container,the block experiences a pseudo-force $F_p = ma_c = F$ acting t

Vedclass · Accepted Answer

$\frac{\pi F}{2} \sqrt{\frac{1}{km}}$

Vedclass · Answer

(D) Let the acceleration of the container be $a_c = F/m$. In the frame of the container,the block experiences a pseudo-force $F_p = ma_c = F$ acting towards the left.This is equivalent to a spring-mass system starting from its natural length with a constant force $F$ applied to the mass $m$. The effective spring constant is $k$.The angular frequency is $\omega = \sqrt{k/m}$.The time taken to reach maximum compression is half the time period of the oscillation,$t = T/2 = \pi / \omega = \pi \sqrt{m/k}$.During this time,the impulse equation for the system (container + block) in the horizontal direction is $\int F dt = \Delta P = (m+m)v_f - (m+m)v_i$.Since $v_i = 0$,we have $F \cdot t = 2mv_f$.Substituting $t = \pi \sqrt{m/k}$,we get $F \pi \sqrt{m/k} = 2mv_f$.Thus,$v_f = \frac{F \pi}{2} \sqrt{\frac{m}{k}} \cdot \frac{1}{m} = \frac{\pi F}{2} \sqrt{\frac{1}{km}}$.

Similar Questions

$A$ block of mass $m$ is in contact with the cart $C$ as shown in the figure. The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies:

The horizontal acceleration that should be given to a smooth inclined plane of angle $\theta = \sin^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane,relative to the inclined plane is:

$A$ person of $60 \,kg$ mass is in a lift which is coming down such that the man exerts a force of $150 \,N$ on the floor of the lift. Then the acceleration of the lift is $\left(g=10 \,ms^{-2}\right)$ (in $\,ms^{-2}$)

An elevator car whose floor-to-ceiling distance is $2.7\,m$ starts ascending with a constant acceleration of $1.2\,m/s^2$. After $2\,s$ of the start,a bolt falls from the ceiling of the car. The free fall time of the bolt is $(g=9.8\,m/s^2)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module