Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the height to which a 6 kg weight is lifted given its gravitational potential energy is 70.56 Joules and the acceleration due to gravity is [tex]\( g = 9.8 \, m/s^2 \)[/tex], we can use the formula for gravitational potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height.
We need to solve for [tex]\( h \)[/tex]. Rearranging the formula to solve for height gives:
[tex]\[ h = \frac{PE}{m \cdot g} \][/tex]
Given:
- [tex]\( PE = 70.56 \, J \)[/tex]
- [tex]\( m = 6 \, kg \)[/tex]
- [tex]\( g = 9.8 \, m/s^2 \)[/tex]
Substitute these values into the equation to find the height:
[tex]\[ h = \frac{70.56 \, J}{6 \, kg \cdot 9.8 \, m/s^2} \][/tex]
Calculate [tex]\( 6 \, kg \cdot 9.8 \, m/s^2 \)[/tex]:
[tex]\[ 6 \cdot 9.8 = 58.8 \, kg \cdot m/s^2 \][/tex]
Now, substitute and divide:
[tex]\[ h = \frac{70.56 \, J}{58.8 \, kg \cdot m/s^2} \][/tex]
[tex]\[ h = 1.2 \, m \][/tex]
Therefore, the height is [tex]\( 1.2 \, m \)[/tex].
Thus, the correct answer is:
D. [tex]\( 1.2 \, m \)[/tex]
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height.
We need to solve for [tex]\( h \)[/tex]. Rearranging the formula to solve for height gives:
[tex]\[ h = \frac{PE}{m \cdot g} \][/tex]
Given:
- [tex]\( PE = 70.56 \, J \)[/tex]
- [tex]\( m = 6 \, kg \)[/tex]
- [tex]\( g = 9.8 \, m/s^2 \)[/tex]
Substitute these values into the equation to find the height:
[tex]\[ h = \frac{70.56 \, J}{6 \, kg \cdot 9.8 \, m/s^2} \][/tex]
Calculate [tex]\( 6 \, kg \cdot 9.8 \, m/s^2 \)[/tex]:
[tex]\[ 6 \cdot 9.8 = 58.8 \, kg \cdot m/s^2 \][/tex]
Now, substitute and divide:
[tex]\[ h = \frac{70.56 \, J}{58.8 \, kg \cdot m/s^2} \][/tex]
[tex]\[ h = 1.2 \, m \][/tex]
Therefore, the height is [tex]\( 1.2 \, m \)[/tex].
Thus, the correct answer is:
D. [tex]\( 1.2 \, m \)[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.