What is the procedure to determine the density of a wire using a metre rule, micrometer screw gauge, and…

Question

What is the procedure to determine the density of a wire using a metre rule, micrometer screw gauge, and electronic balance?

ScanSolve AI Tutor · Accepted Answer

Here is the solution for the experiment "Determining the Density of a Wire", using assumed values as requested:

Diagram

\begin{tikzpicture}[scale=1.0]
    % Wire
    \draw[thick, gray] (0,0) -- (4,0);
    \node at (2,0.3) {Wire};

    % Metre Rule
    \draw[thick] (0,-0.5) -- (4,-0.5);
    \foreach \x in {0,1,2,3,4}
        \draw (\x,-0.5) -- (\x,-0.6) node[below] {\x};
    \node at (2,-1) {Metre Rule (cm)};
    \draw[<->] (0,0.5) -- (4,0.5) node[above, midway] {$L$};

    % Micrometer Screw Gauge (simplified)
    \draw[thick] (5,0) rectangle (6,1);
    \draw[thick] (6,0.5) -- (7,0.5);
    \draw[thick] (7,0) rectangle (8,1);
    \draw[thick, gray] (6.5,0.5) circle (0.1); % Wire inside
    \node at (6.5,1.3) {Micrometer};
    \node at (6.5,0.2) {Screw Gauge};
    \draw[<->] (6.4,0.7) -- (6.6,0.7) node[above] {$d$};

    % Electronic Balance (simplified)
    \draw[thick] (9,0) rectangle (10,1);
    \draw[thick] (9.5,1) -- (9.5,1.5);
    \draw[thick] (9.2,1.5) rectangle (9.8,1.8);
    \node at (9.5,0.5) {Balance};
    \node at (9.5,1.65) {$m$};
\end{tikzpicture}

Procedure

Measure the mass ( $m$ ) of the given piece of wire using an electronic balance. Record the reading.
Place the wire on a flat surface and use a metre rule to measure its total length ( $L$ ). Take multiple readings along the wire if it's not perfectly straight, and calculate the average.
Use a micrometer screw gauge to measure the diameter ( $d$ ) of the wire. Take at least three readings at different points along the wire and at different orientations (e.g., rotating the wire) to account for any non-uniformity. Calculate the average diameter.
Calculate the radius ( $r$ ) of the wire using the average diameter ( $r = \frac{d}{2}$ ).
Calculate the volume ( $V$ ) of the wire using the formula for the volume of a cylinder, $V = \pi r^2 L$ .
Calculate the density ( $\rho$ ) of the wire using the formula $\rho = \frac{m}{V}$ .

Observations/Results

Assumed mass of the wire, $m = 15.7 \text{ g}$
Assumed length of the wire, $L = 50.0 \text{ cm}$

Reading	Diameter ( $d$ )
1	$0.81 \text{ mm}$
2	$0.79 \text{ mm}$
3	$0.80 \text{ mm}$
Average	$0.80 \text{ mm}$

Average diameter, $d = 0.80 \text{ mm}$

Calculations/Conclusion

Convert all measurements to consistent units (e.g., SI units
kg, m).
$m = 15.7 \text{ g} = 0.0157 \text{ kg}$ $L = 50.0 \text{ cm} = 0.500 \text{ m}$ $d = 0.80 \text{ mm} = 0.00080 \text{ m}$
Calculate the radius ( $r$ ) of the wire.
$r = \frac{d}{2} = \frac{0.00080 \text{ m}}{2} = 0.00040 \text{ m}$
Calculate the volume ( $V$ ) of the wire.
$V = \pi r^2 L$ $V = \pi (0.00040 \text{ m})^2 (0.500 \text{ m})$ $V = \pi (1.6 \times 10^{-7} \text{ m}^2) (0.500 \text{ m})$ $V = 2.513 \times 10^{-7} \text{ m}^3$
Calculate the density ( $\rho$ ) of the wire.
$\rho = \frac{m}{V}$ $\rho = \frac{0.0157 \text{ kg}}{2.513 \times 10^{-7} \text{ m}^3}$ $\rho = 62475.13 \text{ kg/m}^3$
Rounding to a reasonable number of significant figures (e.g., 3 sig figs based on mass and length):
$\rho \approx 6.25 \times 10^4 \text{ kg/m}^3$
The density of the wire was determined to be \boxed{\text{6.25 \times 10^4 kg/m^3}}.

Precautions
- Ensure the electronic balance is zeroed before measuring the mass of the wire.
- Take multiple readings for the length of the wire and calculate the average to minimize random errors.
- When using the micrometer screw gauge, ensure it is properly calibrated (check for zero error) and apply gentle pressure to avoid deforming the wire.
- Take multiple readings for the diameter at different points along the wire and at different orientations to account for any irregularities in the wire's thickness.
- Read all instruments at eye level to avoid parallax errors.
- Ensure the wire is straight when measuring its length.

What is the procedure to determine the density of a wire using a metre rule, micrometer screw gauge, and electronic balance?

Step-by-step solution

Convert all measurements to consistent units (e.g., SI units

Calculate the radius ( $r$ ) of the wire.

Calculate the volume ( $V$ ) of the wire.

Calculate the density ( $\rho$ ) of the wire.

Still stuck on this one?

More Physics Questions

What is the procedure to determine the density of a wire using a metre rule, micrometer screw gauge, and electronic balance?

Step-by-step solution

Convert all measurements to consistent units (e.g., SI units

Calculate the radius (rrr) of the wire.

Calculate the volume (VVV) of the wire.

Calculate the density (ρ\rhoρ) of the wire.

Still stuck on this one?

More Physics Questions

Calculate the radius ( $r$ ) of the wire.

Calculate the volume ( $V$ ) of the wire.

Calculate the density ( $\rho$ ) of the wire.