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

Electric Charge Field and Potential

Atoms and Radioactivity

Torque and Rotational Motion

Conservation of Energy and Momentum

Scientific Method Physics

Modern Physics

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 $𝛉$ .