Chapter 2: Q. 75 (page 63)

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

Expert verified

The result $v_{2 x} = - v_{1 y} \tan 𝛳$ 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
$2 a \frac{d a}{d t} + 2 b \frac{d b}{d t} = 0 2 a v_{2 x} + 2 b v_{1 y} = 0 a v_{2 x} = - b v_{1 y} v_{2 x} = \frac{- b}{a} v_{1 y} \Rightarrow v_{2 x} = - v_{1 y} \tan 𝛉$

Thus, the required result is obtained.

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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

Step by step solution

Step 1. Write the given information

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

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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 v2x= - v1y tan 𝛉.

Short Answer

Step by step solution

Step 1. Write the given information

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

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Study anywhere. Anytime. Across all devices.

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 $𝛉$ .