Answer :
To complete the table with the given data, we'll use the formula for gravitational potential energy (GPE), which is:
[tex]\[ \text{GPE} = \text{mass} \times g \times \text{height} \][/tex]
where [tex]\( g = 9.81 \, \text{N/kg} \)[/tex] is the gravitational acceleration on Earth.
Let's fill in the missing values:
1. Row 2: We need to find the mass when the height is missing and GPE is 117.72 J.
- Given GPE = 117.72 J, height = 6 m, and [tex]\( g = 9.81 \, \text{N/kg} \)[/tex], we find the mass as:
[tex]\[ \text{mass} = \frac{\text{GPE}}{g \times \text{height}} \][/tex]
[tex]\[ \text{mass} = \frac{117.72}{9.81 \times 6} = 6.0 \, \text{kg} \][/tex]
2. Row 4: Calculate the GPE using the given mass and height.
- Given mass = 5000 kg, height = 0.6 m, and [tex]\( g = 9.81 \, \text{N/kg} \)[/tex]:
[tex]\[ \text{GPE} = 5000 \times 9.81 \times 0.6 = 29430.0 \, \text{J} \][/tex]
3. Row 5: Determine the mass when GPE is given as 98100 J and height is 10 m.
- Given GPE = 98100 J, height = 10 m, and [tex]\( g = 9.81 \, \text{N/kg} \)[/tex]:
[tex]\[ \text{mass} = \frac{\text{GPE}}{g \times \text{height}} = \frac{98100}{9.81 \times 10} = 999.9999999999999 \, \text{kg} \][/tex]
Here's the completed table with the calculated values:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Mass (kg)} & \text{Height (m)} & \text{GPE (J)} \\
\hline
5 & 2 & 98.1 \\
\hline
6.0 & 6 & 117.72 \\
\hline
20 & 5 & 392.4 \\
\hline
5000 & 0.6 & 29430.0 \\
\hline
999.9 & 10 & 98100 \\
\hline
67 & 44 & 19.62 \\
\hline
\end{array}
\][/tex]
[tex]\[ \text{GPE} = \text{mass} \times g \times \text{height} \][/tex]
where [tex]\( g = 9.81 \, \text{N/kg} \)[/tex] is the gravitational acceleration on Earth.
Let's fill in the missing values:
1. Row 2: We need to find the mass when the height is missing and GPE is 117.72 J.
- Given GPE = 117.72 J, height = 6 m, and [tex]\( g = 9.81 \, \text{N/kg} \)[/tex], we find the mass as:
[tex]\[ \text{mass} = \frac{\text{GPE}}{g \times \text{height}} \][/tex]
[tex]\[ \text{mass} = \frac{117.72}{9.81 \times 6} = 6.0 \, \text{kg} \][/tex]
2. Row 4: Calculate the GPE using the given mass and height.
- Given mass = 5000 kg, height = 0.6 m, and [tex]\( g = 9.81 \, \text{N/kg} \)[/tex]:
[tex]\[ \text{GPE} = 5000 \times 9.81 \times 0.6 = 29430.0 \, \text{J} \][/tex]
3. Row 5: Determine the mass when GPE is given as 98100 J and height is 10 m.
- Given GPE = 98100 J, height = 10 m, and [tex]\( g = 9.81 \, \text{N/kg} \)[/tex]:
[tex]\[ \text{mass} = \frac{\text{GPE}}{g \times \text{height}} = \frac{98100}{9.81 \times 10} = 999.9999999999999 \, \text{kg} \][/tex]
Here's the completed table with the calculated values:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Mass (kg)} & \text{Height (m)} & \text{GPE (J)} \\
\hline
5 & 2 & 98.1 \\
\hline
6.0 & 6 & 117.72 \\
\hline
20 & 5 & 392.4 \\
\hline
5000 & 0.6 & 29430.0 \\
\hline
999.9 & 10 & 98100 \\
\hline
67 & 44 & 19.62 \\
\hline
\end{array}
\][/tex]
