For the given figure,find the speed of block | vedclass

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

Question

(A) Let $h$ be the vertical distance from the pulley to the horizontal path of the ring,and $x$ be the horizontal distance of the ring from the vertic

Vedclass · Accepted Answer

$2\sqrt{3} \, m/s$

Vedclass · Answer

(A) Let $h$ be the vertical distance from the pulley to the horizontal path of the ring,and $x$ be the horizontal distance of the ring from the vertical line passing through the pulley.The length of the string segment from the ring to the pulley is $L = \sqrt{x^2 + h^2}$.The total length of the string is constant,so the speed of block $A$ is equal to the rate at which the length of the string segment $L$ decreases.$v_A = -\frac{dL}{dt} = -\frac{d}{dt}(\sqrt{x^2 + h^2}) = -\frac{1}{2\sqrt{x^2 + h^2}} \cdot 2x \cdot \frac{dx}{dt} = -\frac{x}{L} \cdot v_{ring}$.From the geometry,$\sin 	heta = \frac{x}{L}$.Therefore,$v_A = v_{ring} \cdot \sin 	heta$.Given $v_{ring} = 4 \, m/s$ and $	heta = 60^\circ$,we have:$v_A = 4 \cdot \sin(60^\circ) = 4 \cdot \frac{\sqrt{3}}{2} = 2\sqrt{3} \, m/s$.

For the given figure,find the speed of block $A$ when $\theta = 60^\circ$. The ring moves horizontally with a constant speed of $4 \, m/s$.

Similar Questions

If $m_1 = 4m_2$,what is the acceleration of $m_2$? The acceleration of $m_1$ is $a$.

Calculate the acceleration of the block $B$ in the figure,assuming the surfaces and the pulleys $P_1$ and $P_2$ are all smooth and the pulleys and string are massless.

$A$ thin uniform rod of length $L$ is resting against a wall and the floor as shown in the figure. Its lower end $A$ is pulled towards the left with a constant velocity $v$. Then the downward velocity $v^{\prime}$ of the other end $B$ when the rod makes an angle $\theta$ with the floor is

At a given instant,block $A$ is moving with a velocity of $5\,m/s$ upwards. What is the velocity of block $B$ at that time?

What is the acceleration of block $B$ for the given system?

Vedclass Test Series

Exam Paper Generator

Online Exam Module