How Do You Calculate Tension in Violin Strings?

[hunchback6116]

I wanted to ask for some help, but first a little about me. I am a physician, but my major was mathematics many years ago. Currently, I am reviewing physics "for the fun of it" and I'm using Tipler's text for review. In the newest edition, I am trying to work problem 77 in chapter 6, but I can't seem to get an answer that agrees with the back of the text. The question is as follows:

The four strings pass over the bridge of a violin so that the strings make an angle of 72 degrees with the normal to the plane of the instrument on either side. The total normal force pressing the bridge into the violin is 103N. The length of the strings from bridge to the peg ot which each is attached is 32.6 cm.
(a) Determine the tension in the violin strings, assuming that the tension is the same for each string.
(b) One of the strings is plucked out a distance of 4mm. Make a free-body diagram showing all of the forces acting on the string at that point, and determine the force pulling the string back to its equilibrium position. assume that the tension in the string remaings constant.
(c) Determine the work done on the string in plucking it out that distance.

Answers as given in back of book: (a) 34.4 N; (b) 1.68N; (c) 3.38mJ

My reasoning: 4 total strings; therefore each strings exerts a force of 103N/4=25.75N downward on the bridge. 2Tsin18=25.75, so T=41.7N.

I gave up working the rest since I can't even get this answer to agree. Would someone be kind enough to enlighten this rusty doc and maybe even give me a start on part's b and c?

 

[Andrew Mason]

I wanted to ask for some help, but first a little about me. I am a physician, but my major was mathematics many years ago. Currently, I am reviewing physics "for the fun of it" and I'm using Tipler's text for review. In the newest edition, I am trying to work problem 77 in chapter 6, but I can't seem to get an answer that agrees with the back of the text. The question is as follows:

The four strings pass over the bridge of a violin so that the strings make an angle of 72 degrees with the normal to the plane of the instrument on either side. The total normal force pressing the bridge into the violin is 103N. The length of the strings from bridge to the peg ot which each is attached is 32.6 cm.
(a) Determine the tension in the violin strings, assuming that the tension is the same for each string.
(b) One of the strings is plucked out a distance of 4mm. Make a free-body diagram showing all of the forces acting on the string at that point, and determine the force pulling the string back to its equilibrium position. assume that the tension in the string remaings constant.
(c) Determine the work done on the string in plucking it out that distance.

Answers as given in back of book: (a) 34.4 N; (b) 1.68N; (c) 3.38mJ

My reasoning: 4 total strings; therefore each strings exerts a force of 103N/4=25.75N downward on the bridge. 2Tsin18=25.75, so T=41.7N.

I gave up working the rest since I can't even get this answer to agree. Would someone be kind enough to enlighten this rusty doc and maybe even give me a start on part's b and c?

Your answer is correct if the angle is 18 degrees above horizontal. Text book answers are not always right.

AM