뒤로L8-10:Newton’s Second Law and Applications: Forces and Free-Body Diagrams
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Section 4.5 Newton’s Second Law
Definition and Mathematical Formulation
Newton’s Second Law describes how the motion of an object changes when a net force acts upon it. The law states that the acceleration a of an object is directly proportional to the net force F acting on it and inversely proportional to its mass m:
Formula:
Direction: The acceleration vector points in the same direction as the net force vector.
Net Force: The net force is the vector sum of all forces acting on the object:
Textbook Form:
Examples and Applications
Example: If a constant force causes an object to accelerate at , doubling the mass (with the same force) halves the acceleration:
Example: If twice the force is applied to an object with four times the mass, the acceleration is:
Section 4.6 Applications of Newton’s Second Law
Conceptual Questions
Comparing Accelerations: Increasing mass with constant force decreases acceleration; increasing force with constant mass increases acceleration.
Example (Wind-blown Basketball): - The drag force acts to the right. - The weight force acts downward. - The net force (vector sum) determines the direction of acceleration, which is in the direction of .
Unit of Force
Definition: The basic unit of force in the SI system is the newton (N).
Formula:
Conversion:
Worked Example: Racing Down the Runway
Scenario: A jet with mass accelerates from rest to over .
Kinematic Equation:
Calculation: Thrust per engine:
Section 4.6 Free-Body Diagrams
Purpose and Construction
Free-body diagrams are essential tools for analyzing forces acting on an object. They visually represent all forces and help in applying Newton’s laws.
Steps to Draw:
Identify all forces acting on the object.
Draw a coordinate system (axes may be tilted for inclined planes).
Represent the object as a dot at the origin.
Draw and label vectors for each force.
Draw and label the net force vector beside the diagram.
Key Principle: The net force vector points in the same direction as the acceleration.
Examples of Free-Body Diagrams
Elevator Moving Upward and Slowing Down: - Tension force (upward) - Weight force (downward) - Net force points downward (since elevator is slowing while moving up)
Ball Tossed Upward: - Only gravity acts downward after release (ignoring air resistance).
Car Parked on a Hill: - Forces include gravity, normal force, and possibly friction.
Skier Towed at Constant Speed: - Forces: tension (parallel to slope), friction (opposes motion), normal force (perpendicular), weight (vertical).
Special Cases and Conceptual Checks
Object Lowered at Constant Speed: - Rope tension equals object’s weight.
Object Lowered at Increasing Speed: - Rope tension is less than object’s weight (net force points downward).
Object Lowered at Decreasing Speed: - Rope tension is greater than object’s weight (net force points upward).
Summary Table: Effects of Force and Mass on Acceleration
Scenario | Force Applied | Mass | Acceleration |
|---|---|---|---|
Original | F | m | |
Twice the Mass | F | 2m | |
Twice the Force, Four Times the Mass | 2F | 4m |
Key Terms
Force (F): A push or pull acting upon an object.
Mass (m): A measure of an object’s inertia; its resistance to acceleration.
Acceleration (a): The rate of change of velocity of an object.
Net Force (): The vector sum of all forces acting on an object.
Newton (N): SI unit of force.
Free-Body Diagram: A graphical representation showing all forces acting on a single object.
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