To determine the height at which a 6 kg weight must be lifted to give it a gravitational potential energy of 70.56 Joules, we can use the formula for gravitational potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the gravitational potential energy (70.56 J),
- [tex]\( m \)[/tex] is the mass (6 kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²),
- [tex]\( h \)[/tex] is the height in meters.
We need to solve for [tex]\( h \)[/tex]. Rearranging the formula to solve for height, we get:
[tex]\[ h = \frac{PE}{m \cdot g} \][/tex]
Substituting the given values into this equation:
[tex]\[ h = \frac{70.56}{6 \cdot 9.8} \][/tex]
First, calculate the denominator:
[tex]\[ 6 \cdot 9.8 = 58.8 \][/tex]
Now, divide the potential energy by this product:
[tex]\[ h = \frac{70.56}{58.8} \][/tex]
Perform the division:
[tex]\[ h = 1.2 \, \text{m} \][/tex]
Therefore, the height at which the 6 kg weight must be lifted to have a gravitational potential energy of 70.56 Joules is [tex]\( \mathbf{1.2} \, \text{m} \)[/tex].
Among the given choices, the correct answer is:
B. [tex]\( 1.2 \, \text{m} \)[/tex]
