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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? The acceleration due to gravity is [tex]$g = 9.8 \, \text{m/s}^2$[/tex].

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



Answer :

GinnyAnswer
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]

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