Question

a lemon interacts gravitationally with earth. the lemon detaches from its tree and falls.
complete the statements.

• earths gravitational pull on the lemon is the lemons gravitational pull on earth.
• the lemons acceleration as a result of this interaction is earths acceleration as a result of this interaction.

related content
newtons third law

Explanation:

Step1: Apply Newton's third law

Newton's third law states that for every action, there is an equal and opposite reaction. So, Earth's gravitational pull on the lemon is equal to the lemon's gravitational pull on Earth.

Step2: Use Newton's second law \(F = ma\)

The force \(F\) is the same for both the lemon and the Earth (from step 1). Let \(m_{lemon}\) be the mass of the lemon and \(m_{Earth}\) be the mass of the Earth (\(m_{lemon}\ll m_{Earth}\)). For the lemon, \(F = m_{lemon}a_{lemon}\), so \(a_{lemon}=\frac{F}{m_{lemon}}\). For the Earth, \(F = m_{Earth}a_{Earth}\), so \(a_{Earth}=\frac{F}{m_{Earth}}\). Since \(m_{lemon}\ll m_{Earth}\), \(\frac{F}{m_{lemon}}>\frac{F}{m_{Earth}}\), so the lemon's acceleration is greater than Earth's acceleration.

Answer:

Earth's gravitational pull on the lemon is equal to the lemon's gravitational pull on Earth. The lemon's acceleration as a result of this interaction is greater than Earth's acceleration as a result of this interaction.