To calculate how far the rock should be lifted to increase its gravitational potential energy by 1200 J, we can use the formula for gravitational potential energy (GPE):
\[ \text{GPE} = mgh \]
Where:
- \( \text{GPE} \) is the gravitational potential energy (in joules),
- \( m \) is the mass of the object (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height (in meters) it is lifted.
We also know that the weight (force due to gravity) \( F \) is given by:
\[ F = mg \]
Given that the weight of the rock is 20 N, we can equate the force to \( mg \):
\[ 20 , \text{N} = mg \]
Now, we want to find the height \( h \) that corresponds to an increase in GPE of 1200 J.
Rearranging the formula for GPE to find \( h \):
\[ h = \frac{\text{GPE}}{F} = \frac{1200 , \text{J}}{20 , \text{N}} \]
Now we can calculate \( h \):
\[ h = \frac{1200}{20} = 60 , \text{m} \]
Thus, the rock should be lifted 60 m to increase its gravitational potential energy by 1200 J.
The answer is 60 m.
1 answer