Question

The two masses in the Figure given below, slide on frictionless wires. They are connected by a pivoting rigid rod of length L. Prove that v_2x= - v_1y tan $𝛉$.

Short answer

The result$v_{2x}=-v_{1y}\tan 𝛳$is proven.

Step-by-step solution

Step 1. Write the given information

The angle of inclination is $𝚹$
The masses are attached with a string of length$L$

Step 2. To prove the result v2x=-v1y tan𝛉

Let the distance AB is a and AC is b
According to the Pythagoras theorem,
$a^2+b^2=L^2$
Differentiate the above equation with respect to time
$$\begin{gathered} 2a\frac{da}{dt}+2b\frac{db}{dt}=0 \\ 2a{v}_{2x}+2b{v}_{1y}=0 \\ a{v}_{2x}=-b{v}_{1y} \\ {v}_{2x}=\frac{-b}{a}{v}_{1y} \\ \Rightarrow v_{2x}=-v_{1y}\tan 𝛉 \end{gathered}$$

Thus, the required result is obtained.