IDNLearn.com provides a collaborative environment for finding accurate answers. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
To find the mass of a ball given its gravitational potential energy, height, and gravitational acceleration, we can use the formula for gravitational potential energy:
[tex]\[ E = m \cdot g \cdot h \][/tex]
where:
- [tex]\( E \)[/tex] is the gravitational potential energy (116.62 J),
- [tex]\( m \)[/tex] is the mass of the ball (what we're trying to find),
- [tex]\( g \)[/tex] is the gravitational acceleration (approximately 9.81 m/s[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height (85 m).
First, we need to rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{E}{g \cdot h} \][/tex]
Now, we can plug in the numerical values provided in the question:
The gravitational potential energy [tex]\( E \)[/tex] is 116.62 J.
The height [tex]\( h \)[/tex] is 85 m.
The gravitational acceleration [tex]\( g \)[/tex] is 9.81 m/s[tex]\(^2\)[/tex].
Substituting these values into the equation, we get:
[tex]\[ m = \frac{116.62 \, \text{J}}{9.81 \, \text{m/s}^2 \cdot 85 \, \text{m}} \][/tex]
Evaluating the denominator:
[tex]\[ 9.81 \, \text{m/s}^2 \cdot 85 \, \text{m} = 833.85 \, \text{J/m} \cdot \text{s}^2 \][/tex]
Now divide the numerator by the denominator:
[tex]\[ m = \frac{116.62 \, \text{J}}{833.85 \, \text{J/m} \cdot \text{s}^2} \][/tex]
This gives us approximately:
[tex]\[ m = 0.1398572884811417 \, \text{kg} \][/tex]
Rounding to two decimal places, the mass of the ball is approximately:
[tex]\[ m \approx 0.14 \, \text{kg} \][/tex]
Therefore, the correct answer is:
- 0.14 kg
[tex]\[ E = m \cdot g \cdot h \][/tex]
where:
- [tex]\( E \)[/tex] is the gravitational potential energy (116.62 J),
- [tex]\( m \)[/tex] is the mass of the ball (what we're trying to find),
- [tex]\( g \)[/tex] is the gravitational acceleration (approximately 9.81 m/s[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height (85 m).
First, we need to rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{E}{g \cdot h} \][/tex]
Now, we can plug in the numerical values provided in the question:
The gravitational potential energy [tex]\( E \)[/tex] is 116.62 J.
The height [tex]\( h \)[/tex] is 85 m.
The gravitational acceleration [tex]\( g \)[/tex] is 9.81 m/s[tex]\(^2\)[/tex].
Substituting these values into the equation, we get:
[tex]\[ m = \frac{116.62 \, \text{J}}{9.81 \, \text{m/s}^2 \cdot 85 \, \text{m}} \][/tex]
Evaluating the denominator:
[tex]\[ 9.81 \, \text{m/s}^2 \cdot 85 \, \text{m} = 833.85 \, \text{J/m} \cdot \text{s}^2 \][/tex]
Now divide the numerator by the denominator:
[tex]\[ m = \frac{116.62 \, \text{J}}{833.85 \, \text{J/m} \cdot \text{s}^2} \][/tex]
This gives us approximately:
[tex]\[ m = 0.1398572884811417 \, \text{kg} \][/tex]
Rounding to two decimal places, the mass of the ball is approximately:
[tex]\[ m \approx 0.14 \, \text{kg} \][/tex]
Therefore, the correct answer is:
- 0.14 kg
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.