Describe the procedure for an experiment to determine the mass of an object using an uncalibrated spring…

Question

Describe the procedure for an experiment to determine the mass of an object using an uncalibrated spring balance.

ScanSolve AI Tutor · Accepted Answer

Here is the solution for the experiment "Using an Uncalibrated Spring Balance to Determine the Mass of an Object", using assumed values as requested:

Diagram

\begin{tikzpicture}[scale=1.0]
    % Clamp stand
    \draw[thick] (0,0) -- (0,5);
    \draw[thick] (-1,5) -- (1,5);
    \draw[thick] (0,0) -- (2,0);
    \node at (0.5,5.3) {Clamp};
    \node at (1,0.3) {Stand};

    % Spring
    \draw[thick, decorate, decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}] (0,4.5) -- (0,2.5);
    \node at (0.5,3.5) {Spring};

    % Plastic cup
    \draw (0,2.5) -- (0,2) -- (1,2) -- (1,2.5) -- cycle;
    \draw[thick] (0.5,2.5) -- (0.5,2);
    \node at (0.5,1.7) {Plastic Cup};

    % Metre rule
    \draw[thick] (1.5,0) -- (1.5,5);
    \foreach \y in {0,1,2,3,4,5}
        \draw (1.5,\y) -- (1.6,\y) node[right] {\y};
    \node at (1.8,2.5) {Metre Rule (cm)};

    % Unknown mass (stone) in cup
    \fill[gray!50] (0.5,2.1) circle (0.3);
    \node at (0.5,2.1) {$m_x$};
\end{tikzpicture}

Procedure

Set up the clamp and stand. Securely attach the helical spring to the clamp.
Attach the plastic cup to the free end of the spring using the twine.
Position the metre rule vertically alongside the spring and cup, ensuring the zero mark is at a convenient reference point (e.g., the top of the spring or the bottom of the cup). Record the initial reading ( $L_0$ ) of the bottom of the empty cup.
Carefully place the standard mass ( $m_s = 100 \text{ g}$ ) into the plastic cup.
Allow the spring to settle and record the new reading ( $L_s$ ) of the bottom of the cup.
Remove the standard mass from the cup.
Place the stone of unknown mass ( $m_x$ ) into the plastic cup.
Allow the spring to settle and record the new reading ( $L_x$ ) of the bottom of the cup.
Remove the stone and dismantle the apparatus.

Observations/Results

Standard mass, $m_s = 100 \text{ g}$

Item in Cup	Reading of Bottom of Cup ( $L$ )	Extension ( $x = L - L_0$ )
Empty Cup	$L_0 = 10.0 \text{ cm}$	$0.0 \text{ cm}$
Standard Mass ( $100 \text{ g}$ )	$L_s = 15.0 \text{ cm}$	$x_s = 5.0 \text{ cm}$
Unknown Mass ( $m_x$ )	$L_x = 17.5 \text{ cm}$	$x_x = 7.5 \text{ cm}$

Calculations

Calculate the extension caused by the standard mass.
$x_s = L_s - L_0 = 15.0 \text{ cm} - 10.0 \text{ cm} = 5.0 \text{ cm}$
Calculate the extension caused by the unknown mass.
$x_x = L_x - L_0 = 17.5 \text{ cm} - 10.0 \text{ cm} = 7.5 \text{ cm}$
Determine the unknown mass using the principle of proportionality (Hooke's Law, $F=kx$ , where $F=mg$ ).
Since the extension is directly proportional to the mass, we can write:
$\frac{m_x}{m_s} = \frac{x_x}{x_s}$
Rearrange to solve for $m_x$ :
$m_x = m_s \left(\frac{x_x}{x_s}\right)$
Substitute the observed values:
$m_x = 100 \text{ g} \times \left(\frac{7.5 \text{ cm}}{5.0 \text{ cm}}\right)$ $m_x = 100 \text{ g} \times 1.5$ $m_x = 150 \text{ g}$
Conclusion

The mass of the unknown stone, $m_x$ , was determined to be $\boxed{\text{150 g}}$ .

Precautions
- Ensure the spring is securely clamped and hangs freely without touching the stand or table.
- Read the metre rule at eye level to avoid parallax errors when measuring the positions.
- Allow the spring to come to a complete rest before taking any readings to ensure accurate measurements of extension.
- Ensure the plastic cup is stable and does not swing while taking readings.
- Use a standard mass that is within the elastic limit of the spring to avoid permanent deformation.
- Record all readings carefully and accurately.

Describe the procedure for an experiment to determine the mass of an object using an uncalibrated spring balance.

Answer

Step-by-step solution

Calculate the extension caused by the standard mass.

Calculate the extension caused by the unknown mass.

Determine the unknown mass using the principle of proportionality (Hooke's Law, $F=kx$ , where $F=mg$ ).

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Describe the procedure for an experiment to determine the mass of an object using an uncalibrated spring balance.

Answer

Step-by-step solution

Calculate the extension caused by the standard mass.

Calculate the extension caused by the unknown mass.

Determine the unknown mass using the principle of proportionality (Hooke's Law, F=kxF=kxF=kx, where F=mgF=mgF=mg).

Try one yourself

Still stuck on this one?

More Physics Questions

Determine the unknown mass using the principle of proportionality (Hooke's Law, $F=kx$ , where $F=mg$ ).