To calculate the work done in lifting the roller coaster train to a height of 100 meters, we can use the work-energy principle which states that the work done against gravity is equal to the increase in potential energy.
The formula for gravitational potential energy (PE) is:
\[ PE = mgh \]
where:
- \(m\) is the mass (in kg),
- \(g\) is the acceleration due to gravity (in m/s²), and
- \(h\) is the height (in m).
Given:
- \(m = 5000 , \text{kg}\),
- \(g = 10 , \text{m/s}^2\),
- \(h = 100 , \text{m}\).
Now, substituting in the values:
\[ PE = 5000 , \text{kg} \times 10 , \text{m/s}^2 \times 100 , \text{m} \]
\[ PE = 5000 \times 10 \times 100 \]
\[ PE = 5000000 , \text{J} \]
Thus, the work done to lift the train up to the top of the hill is 5,000,000 J (or 5 MJ).