Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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

A. [tex]\( 0.09 \, m \)[/tex]

B. [tex]\( 1.2 \, m \)[/tex]

C. [tex]\( 11.8 \, m \)[/tex]

D. [tex]\( 3.2 \, m \)[/tex]


Sagot :

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]