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If playing a violin, the tension in a violin string is 2.5 N. When pushed down against the neck of the violin, the string makes an angle of 1.5° with the horizontal. What force must you apply to the string to bring it into contact with the neck? Express your answer using two significant figures.

Part B: If the angle were less than 3.5°, would the required force be greater than, less than, or the same as in Part A?

Answer :

Final answer:

The force you must apply on the violin string is equal to the vertical component of the string's tension. The force needed to bring a violin string into contact with the neck of the violin is calculated using the tension and the angle between the string and violin's neck. When the angle is reduced (less than 3.5°), the force required would be greater due to the smaller denominator in the trigonometric fraction sin(θ).

Explanation:

This question pertains to the concepts of forces, specifically tension and equilibrium as applied in string instruments such as the violin. In this instance, when pushing down on the violin string, the tension in the string counteracts your force. Hence, you create an angle with the horizontal plane. When you apply a second force down on the string, to bring it into contact with the neck of the violin, this force must equal the vertical component of the string's tension. The vertical component can be calculated using trigonometry, specifically sine function; therefore, the string's tension times the angle’s sine must equal the applied force for the string to reach equilibrium again.

Tension in a string equation can be written as T sin θ = mr₁². Here, the you use the first force (2.5 N) and the angle (1.5°) you have to calculate initial tension (T). If the same string is pushed down with a smaller angle (less than 3.5°), the required force would be greater than in the first case. This is because as the angle decreases, the denominator in the trigonometric fraction sin(θ) gets smaller, requiring a larger force to reach the same tension in the string as before.

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