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A [tex]\(6 \, \text{kg}\)[/tex] weight is lifted off the ground to a height that gives it [tex]\(70.56 \, \text{J}\)[/tex] of gravitational potential energy. What is its height? Acceleration due to gravity is [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex].

A. [tex]\(3.2 \, \text{m}\)[/tex]
B. [tex]\(1.2 \, \text{m}\)[/tex]
C. [tex]\(0.09 \, \text{m}\)[/tex]
D. [tex]\(11.8 \, \text{m}\)[/tex]



Answer :

GinnyAnswer
To determine the height at which a 6 kg weight is lifted to give it a gravitational potential energy of 70.56 joules, we can use the formula for gravitational potential energy:

[tex]\[ \text{Potential Energy} (PE) = \text{mass} (m) \times \text{gravitational acceleration} (g) \times \text{height} (h) \][/tex]

Given the values:
- Mass ([tex]\( m \)[/tex]) = 6 kg
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.8 m/s²
- Potential energy ([tex]\( PE \)[/tex]) = 70.56 J

We need to solve for the height ([tex]\( h \)[/tex]). Rearrange the formula to solve for [tex]\( h \)[/tex]:

[tex]\[ h = \frac{\text{Potential Energy}}{\text{mass} \times \text{gravitational acceleration}} \][/tex]

Substitute the given values into the formula:

[tex]\[ h = \frac{70.56 \, \text{J}}{6 \, \text{kg} \times 9.8 \, \text{m/s}^2} \][/tex]

Simplify:

[tex]\[ h = \frac{70.56}{58.8} \][/tex]

[tex]\[ h = 1.2 \, \text{m} \][/tex]

Therefore, the height at which the 6 kg weight is lifted to give it 70.56 joules of gravitational potential energy is:

[tex]\[ \boxed{1.2 \, \text{m}} \][/tex]

So the correct answer is:
B. 1.2 m

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