Calculating the Mass of the Second Apple: Gravitational Force and Distance Relationship

To find the mass of the second apple, we can use Newton's law of universal gravitation, which states that every point mass attracts every other point mass by a force acting along the line intersecting both points. The formula is: \[ F = G \frac{m_1 m_2}{r^2} \] Where: - \( F \) is the gravitational force between the masses, - \( G \) is the gravitational constant (\(6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\)), - \( m_1 \) and \( m_2 \) are the masses of the two objects, - \( r \) is the distance between the centers of the two masses. Given: - \( F = 2.9 \times 10^{-11} \, \text{N} \) - \( r = 0.25 \, \text{m} \) - \( m_1 = 0.15 \, \text{kg} \) We need to find \( m_2 \). Rearrange the formula to solve for \( m_2 \): \[ m_2 = \frac{F \cdot r^2}{G \cdot m_1} \] Substitute the known values into the equation: \[ m_2 = \frac{2.9 \times 10^{-11} \, \text{N} \times (0.25 \, \text{m})^2}{6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \times 0.15 \, \text{kg}} \] First, calculate the numerator: \[ 2.9 \times 10^{-11} \, \text{N} \times (0.25 \, \text{m})^2 = 2.9 \times 10^{-11} \, \text{N} \times 0.0625 \, \text{m}^2 = 1.8125 \times 10^{-12} \, \text{Nm}^2 \] Next, calculate the denominator: \[ 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \times 0.15 \, \text{kg} = 1.001145 \times 10^{-11} \, \text{Nm}^2/\text{kg} \] Now, divide the numerator by the denominator: \[ m_2 = \frac{1.8125 \times 10^{-12}}{1.001145 \times 10^{-11}} \] \[ m_2 \approx 0.1811 \, \text{kg} \] Therefore, the mass of the second apple is approximately \(0.181 \, \text{kg}\).

To solve for this, you should use the law of universal gravitation: F = G * (m1 * m2) / r^2 where: F is the force between the masses, G is the gravitational constant, m1 is the first mass, m2 is the second mass, r is the distance between the centers of the two masses. The gravitational constant (G) is roughly 6.674 x 10^-11 N(m/kg)^2. You are asked to solve for m2, and so we should rearrange this formula to solve for m2: m2 = F * r^2 / (G * m1) Plugging in the given values: m2 = 2.9 x 10^-11 N * (0.25 m)^2 / (6.674 x 10^-11 N(m/kg)^2 * 0.15 kg) By solving this, we obtain: m2 ≈ 0.16 kg Therefore, the mass of the second apple is approximately 0.16 kg.