General Physics 1: Free-falling Objects

When objects are in free fall, they move solely under gravity's influence. This fascinating phenomenon affects everything from raindrops to rockets returning to Earth.

This section introduces the core principles that govern how objects behave when falling freely, helping you understand why a hammer and feather would fall at the same rate on the moon!

Freely Falling Objects: Basic Concept

Free fall occurs whenever objects move under gravity's influence alone. Scientists often demonstrate this concept with specialized equipment showing how objects of different masses fall at identical rates.

In a vacuum chamber demonstration, a feather and a stone fall at exactly the same speed because air resistance is removed. This striking visual proves that gravity accelerates all objects equally regardless of their mass.

💡 Without air resistance, a feather would hit the ground at the same time as a bowling ball if dropped from the same height!

Understanding Free Fall

A freely falling object is any object moving under gravity's influence alone. This includes objects thrown upward, downward, or released from rest - all are considered freely falling once released.

Every object in free fall experiences the same downward acceleration due to gravity $approximately 9.8 m/s²$, regardless of its initial motion or mass. This acceleration is constant throughout the fall.

The equal falling rate of different objects can be demonstrated using tubes - one filled with air where objects fall at different rates, and an evacuated (vacuum) tube where they fall at identical rates.

Free Fall: Objects Dropped from Rest

When an object is dropped from rest, its initial velocity is zero $v₁ = 0$. As it falls, it accelerates downward at a constant rate of 9.8 m/s².

We typically use the y-axis (instead of x) for vertical motion problems. The acceleration due to gravity is represented as aᵧ = g = -9.80 m/s² (negative because downward motion is typically assigned a negative value).

🔍 The negative sign for gravity's acceleration doesn't mean it's slowing down - it just indicates direction relative to our coordinate system!

Free Fall: Objects Thrown Downward

When you throw an object downward, it starts with a non-zero initial velocity (vᵢ ≠ 0). Since we typically consider upward as positive, the initial velocity of a downward-thrown object is negative.

The acceleration remains the same as with dropped objects: aᵧ = g = -9.80 m/s². This constant acceleration causes the object to continuously increase speed as it falls.

The key difference from objects dropped from rest is that downward-thrown objects have a head start in velocity, making them reach the ground faster and with greater final speed.

Free Fall: Objects Thrown Upward

When throwing an object upward, it has a positive initial velocity (vᵢ > 0), but gravity immediately begins slowing it down. The object reaches its maximum height when velocity becomes zero $vₘₐₓ ₕₑᵢgₕₜ = 0$.

Gravity's acceleration $aᵧ = g = -9.80 m/s²$ acts downward throughout the entire motion, even while the object is moving upward. After reaching maximum height, the object begins falling back down.

🚀 Try thinking about this like tossing a ball - it slows down on the way up, stops momentarily at the top, then speeds up on the way down, all because gravity pulls consistently!

For symmetrical motion, the time going up equals the time coming down $t𝑢𝑝 = t𝑑𝑜𝑤𝑛$ and the final velocity will have the same magnitude as the initial velocity but in the opposite direction $vᵢ = -vf$.

Free Fall: Detailed Example

Let's follow an object thrown upward with an initial velocity of 20.0 m/s. At the starting point A, the velocity is positive (upward) while acceleration remains -9.8 m/s² throughout.

At point B $t = 2.04s$, the object reaches its maximum height of 20.4m where its velocity becomes zero momentarily. Gravity continues pulling it downward.

By point C $t = 4.08s$, the object returns to its original height with velocity -20.0 m/s, equal in magnitude but opposite to its initial velocity. The journey continues downward to point E, where it reaches -50.0m with velocity -37.1 m/s.

This example illustrates how position and velocity change continuously throughout free fall, even while acceleration remains constant at -9.8 m/s².

Sample Free Fall Problems

These problems demonstrate how to apply free fall equations in different scenarios. When solving them, remember that acceleration due to gravity is constant at -9.8 m/s².

For dropped objects (like the euro coin from Pisa), use initial velocity of zero and find position and velocity at different time intervals using y = ½gt² and v = gt.

For objects thrown downward $like the stone with initial velocity 1.68 m/s$, you'll need to find height or final velocity using kinematic equations that account for non-zero initial velocity.

🧮 When solving these problems, break them into parts! For example, when a ball is thrown from a building, separate the upward motion, maximum height point, and downward motion.

Exercise Problems

These practice problems cover all types of free fall scenarios: objects thrown downward, upward, and determining various parameters like time, velocity, and height.

When solving the arrow problem (shooting vertically upward), note that the total time of 12 seconds represents both upward and downward motion combined. The key insight is that for objects returning to the same height, the final and initial speeds are equal in magnitude.

For multi-part problems like the cliff example, solve each segment separately: first calculate time to maximum height, then determine that height relative to a reference point, and finally calculate total travel time and final velocity.