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Non-uniform motion occurs when an object's velocity changes over time. This happens when there is a resultant (net) force acting on the object. In real-world situations, objects often experience resistive forces that oppose their motion, causing them to speed up, slow down, or eventually move at constant velocity.
Friction is a resistive force that acts between surfaces in contact when they try to slide past each other. It always opposes the direction of motion or potential motion.
There are two types of friction:
When you push a heavy box across the floor:
For a car traveling on a road, the relationship between the driving force and frictional force determines whether the car speeds up, slows down, or maintains constant velocity:
When accelerating:
When traveling at constant velocity:
When decelerating:
Example calculation: A car of mass 800 kg has a forward driving force of 3000 N and accelerates at 2.0 m/s². What is the frictional force?
Step 1: Calculate the resultant force using Newton's Second Law (F = ma): Resultant force = 800 × 2.0 = 1600 N
Step 2: The resultant force is the difference between driving force and frictional force: Resultant force = Driving force − Frictional force 1600 = 3000 − Frictional force Frictional force = 3000 − 1600 = 1400 N
Drag forces are resistive forces that act on objects moving through fluids. A fluid is any substance that can flow - this includes liquids (like water, oil) and gases (like air).
Key characteristics of drag forces:
Air resistance is a specific type of drag force that acts on objects moving through air. When an object moves through air, it collides with air particles. The faster it moves, the more collisions happen per second, so the drag force increases.
Air resistance becomes particularly important at high speeds. This is why:
The fundamental principle: When an object moves faster, the drag force acting on it becomes stronger. When it slows down, the drag force decreases.
A uniform gravitational field means gravity pulls with the same strength everywhere (like near Earth's surface where g ≈ 10 m/s²). When objects fall through air, two main forces act on them:
Let's consider what happens when you drop an object from a height:
At the start of the fall:
As the object speeds up:
Eventually:
This constant velocity is called terminal velocity.
Important note: If there were no air resistance (like on the Moon), the object would keep accelerating at g throughout its entire fall. Air resistance is what causes the acceleration to decrease and eventually become zero.
Terminal velocity is the constant maximum velocity reached by an object moving through a fluid when the drag force equals the driving force (like weight for a falling object). At this point, the resultant force is zero, so there is no acceleration - the object moves at steady speed.
Stage 1 - Initial acceleration:
Stage 2 - Decreasing acceleration:
Stage 3 - Terminal velocity reached:
The graph for an object reaching terminal velocity shows:
The gradient of a velocity-time graph represents acceleration. As the gradient decreases, the acceleration decreases. When the line becomes horizontal, acceleration is zero.
1. Mass/Weight: Heavier objects have greater weight, so they need more air resistance to balance it. Therefore, heavier objects have higher terminal velocities.
2. Surface area: Larger surface area creates more air resistance at any given speed. Therefore, objects with larger surface area (like parachutes) have lower terminal velocities.
3. Shape: Streamlined objects experience less air resistance than irregular shapes, so they have higher terminal velocities.
Consider two skydivers, A and B, where A has greater mass than B.
If they want to meet during the fall, Skydiver B should jump first. Skydiver A (falling faster) can then catch up.
Common misconception about parachutes: When a skydiver opens their parachute, they don't move upward - they decelerate to a new, lower terminal velocity. The parachute increases surface area dramatically, which increases air resistance. The air resistance becomes greater than weight temporarily, causing deceleration, until a new lower terminal velocity is reached.
When air resistance is negligible: If a question states that air resistance is "negligible," this means it is so small that it won't affect the motion. In this case, you can assume there are no drag forces acting on the object.
Upthrust vs. Drag:
For example, a stationary submarine underwater experiences upthrust but no drag. Once it starts moving, it experiences both upthrust and drag.
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