Applying Newton's Laws

Equilibrium and Static Equilibrium

Equilibrium in physics refers to the state in which all the forces acting on an object sum to zero, resulting in no net force. Static equilibrium is a special case where the object is not only in equilibrium but also at rest.

• Equilibrium: Occurs when the vector sum of all forces is zero:

• Static Equilibrium: The object is at rest, so its velocity is zero:

• Example: A book resting on a table is in static equilibrium.

Gravity and Weight

Gravitational Force Near Earth's Surface

Gravity is the force that attracts objects toward the center of the Earth. Near the Earth's surface, this force is approximately constant and is responsible for an object's weight.

• Weight: The force of gravity acting on an object: where is mass and is the acceleration due to gravity ().

• Scales: Measure the normal force, not the true weight.

• Example: A 30 kg boy on an elevator accelerating upward at will have a scale reading of 309.3 N.

Normal Force

Definition and Properties

The normal force is the perpendicular contact force exerted by a surface to support the weight of an object resting on it.

• Normal Force: Opposes gravity and prevents objects from falling through surfaces.

• Notation:

• 3-D Version: Acts perpendicular to the contact surface.

• Example: A block on a table experiences a normal force equal in magnitude and opposite in direction to its weight.

Tension

Force Transmission in Ropes and Strings

Tension is the force transmitted through a rope, string, or cable when it is pulled tight by forces acting from opposite ends.

• Tension: Always acts as a pull, never a push.

• Massless String: Tension is constant throughout.

• Notation:

• Example: Bird feeder supported by cables: , .

Using Newton's Laws

Problem-Solving Strategy

Newton's Second Law () is used to analyze the forces acting on a single object and determine its motion.

1. Pick an object: Focus on one object at a time.

2. Draw a free-body diagram (FBD): Show all forces and angles.

3. Choose a coordinate system: Align axes with the direction of motion or forces.

4. Write Newton's Second Law in each direction:

5. Solve for unknowns or repeat for other objects.

• Example: A 5.0 kg mass on a frictionless surface with a 15 N force at 30° below horizontal: (a) (b) Distance after 2.0 s:

• Inclined Plane Example: 5.8 kg block pulled up a 25° incline by a 32 N force:

Atwood Machine

The Atwood machine is a device used to study the laws of motion with constant acceleration, consisting of two masses connected by a string over a pulley.

• Application: Demonstrates Newton's laws and acceleration due to gravity.

Friction

Kinetic Friction

Kinetic friction acts between surfaces in relative motion and always opposes the direction of motion.

• Kinetic Friction Force: where is the coefficient of kinetic friction and is the normal force.

• Direction: Opposes sliding motion.

• Example: Box sliding down a ramp with .

Static Friction

Static friction prevents motion between two surfaces up to a maximum value.

• Static Friction Force: where is the coefficient of static friction.

• Slippage: If , the object begins to move.

• Coefficients: is usually greater than for the same surfaces.

• Example: Book on a table: , .

Friction Example

Consider a 2.0 kg box on a 1.0 m ramp inclined at 30°. Coefficients: , .

• (a) Will the box slide? Yes

• (b) Acceleration down the ramp:

Friction: Static vs. Kinetic Comparison

Spring/Elastic Force

Hooke's Law

Spring or elastic force always acts to oppose the stretch or compression of a spring. The magnitude is given by Hooke's Law.

• Spring Force: where is the spring constant and is the change in length.

• Spring Constant (): Measures stiffness; larger means a stiffer spring.

• Example: Compressing a spring by 2.8 cm with a force of 12 N gives .

Spring Force Example

Two masses (3 kg and 10 kg) attached to a spring (), compressed by 0.05 m, on a frictionless table.

• Acceleration of 3 kg mass: left

• Acceleration of 10 kg mass: right

Summary Table: Forces in Chapter 5

Additional info: These notes expand on the original slides and handwritten content, providing definitions, formulas, and examples for each force type relevant to Newton's Laws and their applications in classical mechanics.