Question

Part A: What force does the apple exert on Earth? Express your answer with the appropriate units. Enter a positive value if the force is upward and a negative value if the force is downward.

Part B: Compare the magnitudes of the accelerations of the apple and Earth due to these forces.
Given that the mass of the apple is approximately 140 g and the mass of Earth is about 6×10^24 kg, determine the magnitude of the accelerations of both the apple and Earth due to these forces.

Answer 1

The apple exerts a force equal to its weight (1.372 N) upward on Earth. The acceleration of the apple is 9.8 m/s², and the acceleration of Earth is negligible due to its massive size.

Step-by-step explanation:

According to Newton's third law of motion, if the apple exerts a force on Earth, then Earth exerts an equal and opposite force on the apple. Since the apple is pulled toward Earth, it exerts an equal force upward on Earth. The magnitude of this force is the weight of the apple, which can be calculated using Newton's second law, F = ma, where m is the mass of the apple and a is the acceleration due to gravity (g = 9.8 m/s²). Since the apple's mass is given as 140 grams (0.14 kg), the force it exerts on Earth is F = 0.14 kg × 9.8 m/s², which equals 1.372 N, and is directed upward.

Comparing the accelerations of the apple and Earth due to these forces, the acceleration of the apple is straightforward - it is the acceleration due to gravity of 9.8 m/s². However, the acceleration of Earth due to this same force is negligible because Earth's mass is extremely large. Using F = ma, if we solve for acceleration (a = F/m), for Earth it would be 1.372 N / 6×10²⁴ kg, which is an insignificantly small number, effectively zero for practical purposes.