Question

1. how does gravity help to demonstrate a cause - and - effect relationship?

1. do objects of different masses fall at different rates? why or why not?

1. what is the rate of acceleration caused by gravity?

1. why doesnt a feather fall at the same rate as an apple?

Explanation:

• Question 2: Gravity is the cause. When an object is released (cause), gravity acts on it, making it fall (effect). For example, when you drop a ball (cause - releasing it in a gravitational field), it accelerates downward (effect - due to gravitational force).
• Question 3: In a vacuum (where there is no air resistance), objects of different masses fall at the same rate. This is because the acceleration due to gravity (\(a = g=\frac{F}{m}\), and \(F = mg\), so \(a = g\) when only gravitational force acts) is independent of mass. However, in the presence of air resistance (a non - gravitational force), objects with larger surface - area - to - mass ratios (like a feather) experience more air resistance relative to their weight and thus may seem to fall slower. But the fundamental acceleration due to gravity for all objects is the same in a vacuum.
• Question 4: On the surface of the Earth, the rate of acceleration caused by gravity is approximately \(g = 9.8\space m/s^{2}\). This value can vary slightly depending on location (e.g., altitude, latitude) due to factors like the Earth's rotation and non - uniform density.
• Question 5: A feather doesn't fall at the same rate as an apple in the presence of air because of air resistance. The feather has a large surface - area - to - mass ratio. The force of air resistance \(F_{air}\) acting on the feather is a significant fraction of its weight (\(W=mg\)). Using Newton's second law \(F_{net}=ma\), where \(F_{net}=mg - F_{air}\). For the feather, \(F_{air}\) is relatively large, so \(a=\frac{mg - F_{air}}{m}=g-\frac{F_{air}}{m}\) is much less than \(g\). For the apple, \(F_{air}\) is a small fraction of its weight, so \(a\approx g\).

Answer:

1. Gravity (cause) makes objects fall (effect).
2. In a vacuum, no (same \(g\) for all). With air resistance, may seem different (due to air resistance).
3. Approximately \(9.8\space m/s^{2}\) on Earth's surface.
4. Air resistance (feather has high surface - area - to - mass ratio).