If a crane worker lifts a crate with a mass of 120 kg from the ground to a shipping container that is 30 meters off the ground, by how much has the worker increased the gravitational potential energy of the crate? (Recall that g \( =9.8 \mathrm{~m} / \mathrm{s}^{2} \) )

To calculate the increase in gravitational potential energy (GPE) of the crate, we can use the formula: \[ \text{GPE} = m \cdot g \cdot h \] where: - \( m \) is the mass of the crate (in kilograms), - \( g \) is the acceleration due to gravity (in meters per second squared), - \( h \) is the height (in meters) to which the crate is lifted. Given: - \( m = 120 \, \text{kg} \) - \( g = 9.8 \, \text{m/s}^2 \) - \( h = 30 \, \text{m} \) Now, substituting the values into the formula: \[ \text{GPE} = 120 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 30 \, \text{m} \] Calculating this step-by-step: 1. Calculate \( 120 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \): \[ 120 \cdot 9.8 = 1176 \, \text{N} \] 2. Now multiply by the height \( 30 \, \text{m} \): \[ 1176 \, \text{N} \cdot 30 \, \text{m} = 35280 \, \text{J} \] Thus, the increase in gravitational potential energy of the crate is: \[ \text{GPE} = 35280 \, \text{J} \] So, the worker has increased the gravitational potential energy of the crate by **35,280 joules**.