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Question 1

A student sets up an acrylic strip of rectangular cross-section clamped at one end as a horizontal cantilever. A mass mmm is suspended from its free end, resulting in a vertical deflection yyy.

a.

A vertical pointer is attached to the free end of the strip, and its position is read using a vertical millimeter scale clamped behind it.

Explain a procedure, using a method such as a plane mirror or a set-square, to avoid parallax error when judging the reading indicated by the position of the pointer on the scale.

[2]
b.

The theoretical relationship for the deflection yyy is given by:

y=4gmL3Ewt3 y = \frac{4gmL^3}{Ewt^3} y=Ewt34gmL3​

where:

  • LLL is the cantilever length (the distance between the clamped end and the point where the mass is suspended),
  • www is the width of the strip (approximately 2.0 cm2.0\text{ cm}2.0 cm),
  • ttt is the thickness of the strip (approximately 2.0 mm2.0\text{ mm}2.0 mm),
  • EEE is the Young modulus of the acrylic,
  • ggg is the acceleration due to gravity.

A student is asked to determine EEE using this arrangement with the following guidelines:

  • Only one acrylic strip of total length approximately 50 cm50\text{ cm}50 cm is available.
  • The mass mmm must be made using a 100 g100\text{ g}100 g mass hanger and up to four additional 100 g100\text{ g}100 g slotted masses.
  • The experimental procedure must involve only one independent variable.
  • A graphical method must be used to determine EEE.

Explain what the student must do to determine EEE.

[5]

Materials Questions

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