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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedStudy GuidesUnit 2: Force & Translational DynamicsTensionTension in Ideal & Non-Ideal Strings

Tension in Ideal & Non-Ideal Strings (College Board AP® Physics 1: Algebra-Based)

Study Guide

Ann Howell

Written by: Ann Howell

Reviewed by: Caroline Carroll

Tension in ideal strings

  • An ideal string has negligible mass and does not stretch when under tension

    • An ideal string is described as inextensible

  • An ideal string can also refer to an ideal

    • cable

    • chain

    • wire

    • rope

  • The tension in an ideal string is the same at all points within the string

  • An ideal string does not exist in reality, but they are used in model systems to simplify calculations

An ideal string under tension

Repulsive forces between electrons in neighbouring atoms of an inextensible string, equal whether string is under tension or not.
A light inextensible string under and not under tension both have equal repulsive forces between electrons.

Worked Example

A person of mass 55 space kg has fallen off a slack line stretched under tension between the peaks of two mountains. The person is suspended by a light inextensible string at the mid point of the slack line, equidistant from each peak. The weight of the person has caused the slack line to sink at an angle of 4.0 degree to the horizontal. The person and the slack line are stationary.

A person is hanging from the middle of a slack line. Tension forces TL and TR are shown at 4-degree angles. Cartesian plane axes are labeled.

Which of the following gives the magnitude of the tension in the slack line?

A      550 space straight N

B      393 space straight N

C      3928 space straight N

D      7857 space straight N

The correct answer is C

Answer:

Step 1: Analyze the scenario

  • The slack line is assumed to be an ideal string

    • So tension is uniform along it

    • and its mass is negligible

  • The slack line is not completely horizontal because of the person's weight

    • This means the slack line has both vertical and horizontal components of tension

  • The system is stationary, so the tension in the left side T with rightwards arrow on top subscript Lmust equal the tension in the right side T with rightwards arrow on top subscript R

    • So, T with rightwards arrow on top subscript L space equals space T with rightwards arrow on top subscript R space equals space T with rightwards arrow on top

Step 2: Determine the vertical component of the tension in the slack line

  • Draw a diagram and label the sides of the tension triangle in relation to the angle to the horizontal 4.0 degree

SOHCAHTOA mnemonic with a right angled triangle illustration showing components: opposite, adjacent, hypotenuse. The mnemonic letters are handwritten and color-coded.

  • Determine the correct trigonometric function to calculate the vertical component of tension T with rightwards arrow on top subscript y

opposite space equals space sin open parentheses theta close parentheses space times space hypotenuse

opposite space equals space sin open parentheses 4.0 close parentheses space times space T with rightwards arrow on top

T with rightwards arrow on top subscript y space equals space 0.07 T with rightwards arrow on top

Step 3: Resolve the system of forces acting on the slack liner vertically

F with rightwards arrow on top subscript g space equals space 0.07 T with rightwards arrow on top subscript L space plus space 0.07 T with rightwards arrow on top subscript Rg g g

stack F subscript g with rightwards arrow on top space equals space 0.14 T with rightwards arrow on top

Step 4: Calculate the magnitude of the tension in the slack line

F with rightwards arrow on top subscript g space equals space m g with rightwards arrow on top space equals space 0.14 T with rightwards arrow on top

open parentheses 55 space cross times space 10 close parentheses space equals space 0.14 T with rightwards arrow on top

T with rightwards arrow on top space equals space fraction numerator 550 over denominator 0.14 end fraction

T with rightwards arrow on top space equals space 3928 space straight N

  • Therefore, option C is correct

Tension in non-ideal strings

  • In a string with nonnegligible mass, tension may not be the same at all points within the string

    • So a non-ideal string has an extension that may not be the same at all points

  • A non-ideal string can also refer to a non-ideal

    • cable

    • chain

    • wire

    • rope

  • In reality all strings are non-ideal

    • There is more extension in some points than in others

A non-ideal string under tension

Comparing non-ideal string under tension and non-tension, showing repulsive and attractive electric forces, notes on dipoles, and electron distribution in atoms.
A non-ideal string extends by different amounts at different points

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    Author
    Reviewer
    Ann Howell

    Author: Ann Howell

    Expertise: Physics Content Creator

    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students, no matter their schooling or background.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.