Exam Instructions and Calculator Settings

General Guidelines

This section outlines the rules and expectations for the exam, emphasizing academic honesty and proper problem-solving techniques.

• Show all work: Full solutions, including equations and reasoning, are required for credit.

• Units: All answers must include correct units.

• Calculator mode: Ensure trigonometric functions are set correctly, e.g., , .

• Ask for clarification: If a question is unclear, seek help during the exam.

Forces and Free-Body Diagrams

Analyzing Forces on Objects

Understanding how to draw and analyze free-body diagrams is essential for solving problems involving forces.

• Free-body diagram: A graphical representation showing all forces acting on an object.

• Types of forces: Tension, gravity (weight), normal force, friction, applied force.

• Newton's Second Law:

• Components of forces: Forces can be resolved into x and y components using trigonometry.

Example: For a ball of mass 0.4 kg moving in a horizontal plane at 0.7 m/s, the tension in the string provides the centripetal force required for circular motion.

• Centripetal force:

• Tension components: ,

Work, Energy, and Power

Work Done by Forces

Work is the transfer of energy via a force acting over a distance. The work done by different forces can be calculated using their respective formulas.

• Work by a constant force:

• Gravitational work:

• Work-energy theorem:

Example: Calculating the work done by the gravitational force on a block sliding down an incline.

Power

Power is the rate at which work is done or energy is transferred.

• Definition:

• Application: Engine power required to accelerate a car.

Friction and Inclined Planes

Static and Kinetic Friction

Frictional forces oppose the motion of objects and are classified as static (preventing motion) or kinetic (opposing ongoing motion).

• Static friction:

• Kinetic friction:

• Normal force: The perpendicular contact force exerted by a surface.

Example: Calculating the frictional force and normal force for a block on an inclined plane.

Spring Force and Hooke's Law

Elastic Potential Energy

Springs store energy when compressed or stretched, described by Hooke's Law and elastic potential energy.

• Hooke's Law:

• Elastic potential energy:

• Work done by spring:

Example: A block attached to a spring is pulled and released; calculate its speed using energy conservation.

Impulse and Momentum

Collisions and Conservation of Momentum

Momentum is conserved in isolated systems. Impulse is the change in momentum resulting from a force applied over time.

• Momentum:

• Impulse:

• Conservation of momentum:

Example: A ball collides with the ground and bounces back; calculate the impulse and final velocity.

Summary Table: Forces on an Inclined Plane

This table summarizes the main forces acting on a block on an inclined plane and their formulas.

Additional info:

• Some diagrams and equations were inferred from context and standard physics curriculum.

• All equations are provided in LaTeX format for clarity.

• Examples and applications are based on typical introductory physics problems.