Let's fill in the blanks in the provided table and sentences:
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Number \\
of \\
washers
\end{tabular} &
\begin{tabular}{c}
Mass of \\
washers \\
[tex]$m_w(g)$[/tex]
\end{tabular} &
\begin{tabular}{c}
Mass of \\
washers \\
[tex]$m _w(kg)$[/tex]
\end{tabular} &
\begin{tabular}{c}
Acceleration \\
due to gravity \\
[tex]$a _{ g }\left( m / s ^2\right)$[/tex]
\end{tabular} &
\begin{tabular}{c}
Force of \\
gravity on the \\
washers \\
[tex]$F _g\left(kg \cdot m / s ^2\right)$[/tex]
\end{tabular} &
\begin{tabular}{c}
Applied force \\
of washers \\
on the car \\
[tex]$F _{w c}(N)$[/tex]
\end{tabular} \\
\hline
1 & 4.9 & 0.0049 & 10 & 0.049 & 0.049 \\
\hline
3 & 14.7 & 0.0147 & 10 & 0.147 & 0.147 \\
\hline
\end{tabular}
### Step-by-Step Solution
1. Acceleration Due to Gravity ( [tex]\(a_g\)[/tex] ):
- The acceleration due to gravity for any object is [tex]\(10 \, m/s^2\)[/tex].
2. Conversion of Mass from Grams to Kilograms:
- The mass of 3 washers is given as [tex]\(14.7 \, g\)[/tex].
- To convert this to kilograms:
[tex]\[
mass \, (kg) = \frac{mass \, (g)}{1000}
\][/tex]
[tex]\[
mass \, of \, 3 \, washers \, (kg) = \frac{14.7 \, g}{1000} = 0.0147 \, kg
\][/tex]
3. Calculating the Force:
- The force of gravity [tex]\(F_g\)[/tex] acting on the washers is calculated using the formula [tex]\(F = ma\)[/tex], where [tex]\(m\)[/tex] is mass and [tex]\(a\)[/tex] is acceleration due to gravity.
- For 3 washers:
[tex]\[
F_g = mass \times acceleration \, due \, to \, gravity
\][/tex]
[tex]\[
F_g = 0.0147 \, kg \times 10 \, m/s^2 = 0.147 \, N
\][/tex]
- This is the force applied by the washers due to gravity on the car, denoted as [tex]\(F_{wc}\)[/tex].
### Filling in the Blanks
- The acceleration due to gravity for any object, including 1 washer on the string, is always assumed to be [tex]\(10\)[/tex] [tex]\(m/s^2\)[/tex].
- The mass of 3 washers, when converted to kg, is [tex]\(0.0147\)[/tex] kg.
- The applied force of 3 washers will increase the applied force on the car to [tex]\(0.147\)[/tex] N.
These values are filled into the table and sentences based on the given assumptions and calculations.
