What is the difference in PE between a 3.20 kg mass at a height of 4.30 m and a 6.50 g mass at a height of \( 1,000 \mathrm{~m} \) ? [?] 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 3.20 kg mass at 4.30 m \[ PE_1 = m_1 g h_1 = (3.20 \, \text{kg}) \times (9.81 \, \text{m/s}^2) \times (4.30 \, \text{m}) \] Calculating this: \[ PE_1 = 3.20 \times 9.81 \times 4.30 \] \[ PE_1 \approx 3.20 \times 9.81 \times 4.30 \approx 135.76 \, \text{J} \] ### Step 2: Calculate the potential energy of the 6.50 g mass at 1,000 m First, convert the mass from grams to kilograms: \[ m_2 = 6.50 \, \text{g} = 0.00650 \, \text{kg} \] Now calculate the potential energy: \[ PE_2 = m_2 g h_2 = (0.00650 \, \text{kg}) \times (9.81 \, \text{m/s}^2) \times (1000 \, \text{m}) \] Calculating this: \[ PE_2 = 0.00650 \times 9.81 \times 1000 \] \[ PE_2 \approx 0.00650 \times 9810 \approx 63.865 \, \text{J} \] ### Step 3: Find the difference in potential energy Now, we can find the difference in potential energy: \[ \Delta PE = PE_1 - PE_2 \] \[ \Delta PE = 135.76 \, \text{J} - 63.865 \, \text{J} \approx 71.895 \, \text{J} \] ### Final Answer The difference in potential energy between the two masses is approximately: \[ \Delta PE \approx 71.90 \, \text{J} \]