What is the difference in PE between a 1.70 kg mass at a height of 8.50 m and a 2.40 g mass at a height of \( 10,000 \mathrm{~m} \) ? [?] J

To find the difference in potential energy (PE) between the two masses, we can use the formula for gravitational potential energy: \[ PE = mgh \] where: - \( m \) is the mass in kilograms, - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)), - \( h \) is the height in meters. ### Step 1: Calculate the potential energy of the 1.70 kg mass at 8.50 m \[ m_1 = 1.70 \, \text{kg} \] \[ h_1 = 8.50 \, \text{m} \] \[ PE_1 = m_1 g h_1 = 1.70 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 8.50 \, \text{m} \] Calculating \( PE_1 \): \[ PE_1 = 1.70 \times 9.81 \times 8.50 \] \[ PE_1 \approx 1.70 \times 83.485 = 141.93 \, \text{J} \] ### Step 2: Calculate the potential energy of the 2.40 g mass at 10,000 m First, convert the mass from grams to kilograms: \[ m_2 = 2.40 \, \text{g} = 0.00240 \, \text{kg} \] \[ h_2 = 10,000 \, \text{m} \] \[ PE_2 = m_2 g h_2 = 0.00240 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 10,000 \, \text{m} \] Calculating \( PE_2 \): \[ PE_2 = 0.00240 \times 9.81 \times 10,000 \] \[ PE_2 \approx 0.00240 \times 98100 = 235.44 \, \text{J} \] ### Step 3: Calculate the difference in potential energy Now, we find the difference in potential energy: \[ \Delta PE = PE_2 - PE_1 \] \[ \Delta PE = 235.44 \, \text{J} - 141.93 \, \text{J} \] \[ \Delta PE \approx 93.51 \, \text{J} \] ### Final Answer The difference in potential energy between the two masses is approximately: \[ \Delta PE \approx 93.51 \, \text{J} \]