The machine as shown has 2 rods of length 1, | vedclass

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

Question

(B) Let $l = 1\, m$ be the length of each rod. Let $y$ be the height of the weight from the floor and $x$ be the horizontal distance between the fixed

Vedclass · Accepted Answer

decreasing speed

Vedclass · Answer

(B) Let $l = 1\, m$ be the length of each rod. Let $y$ be the height of the weight from the floor and $x$ be the horizontal distance between the fixed pivot and the roller.From the geometry of the isosceles triangle formed by the two rods,we have the relation: $(x/2)^2 + y^2 = l^2$.Substituting $l = 1$,we get $x^2/4 + y^2 = 1$,which simplifies to $x^2 + 4y^2 = 4$.Differentiating both sides with respect to time $t$:$2x(dx/dt) + 8y(dy/dt) = 0$.Let $v_r = dx/dt$ be the constant speed of the roller and $v_w = dy/dt$ be the speed of the weight.Then $2x v_r + 8y v_w = 0$,which gives $v_w = -(x v_r) / (4y)$.Since the weight is moving up,we consider the magnitude: $v_w = (x v_r) / (4y)$.Substituting $x = \sqrt{4 - 4y^2} = 2\sqrt{1 - y^2}$,we get $v_w = (2\sqrt{1 - y^2} \cdot v_r) / (4y) = v_r \cdot \frac{\sqrt{1 - y^2}}{2y}$.As the roller moves towards the right,the distance $x$ decreases,which means the height $y$ increases.As $y$ increases,the term $\frac{\sqrt{1 - y^2}}{2y}$ decreases.Therefore,the speed of the weight $v_w$ decreases as it moves up.

Similar Questions

In the arrangement shown in the figure,the block of mass $m=2\,kg$ lies on the wedge of mass $M=8\,kg$. Find the initial acceleration of the wedge if the surfaces are smooth and the pulley and strings are massless.

If the acceleration of $A$ is $2 \, m/s^2$ to the left and the acceleration of $B$ is $1 \, m/s^2$ to the left, then the acceleration of $C$ is

The pulleys in the diagram are all smooth and light. The acceleration of $A$ is $a$ upwards and the acceleration of $C$ is $f$ downwards. The acceleration of $B$ is

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

The velocities of block $A$ and block $B$ are shown in the figure. The velocity of block $C$ is ......... $m/s$ (assume that the pulleys are ideal and the string is inextensible).

Vedclass Test Series

Exam Paper Generator

Online Exam Module