Free Body Diagrams: Sine and Cosine Components Explained

The video tutorial explains how to draw a free body diagram and break it into sine and cosine components. It uses the example of a box on an inclined plane to identify forces such as gravity, static friction, and normal force. The tutorial demonstrates how to break these forces into components using trigonometry and verifies the correctness of the breakdown by examining limits.

What is the primary force acting downwards on the box?

• Tension

• Normal force

• Static friction

• Gravitational force (mg)

Which direction does static friction act for a box at rest on an inclined plane?

• Downwards

• Upwards to the right

• Upwards to the left

• Horizontally to the right

What force acts perpendicular to the surface of the incline?

• Gravitational force

• Magnetic force

• Static friction

• Normal force

Which component of the gravitational force acts parallel to the incline?

• mg tangent theta

• mg sine theta

• mg secant theta

• mg cosine theta

Which component of the gravitational force acts perpendicular into the incline?

• mg secant theta

• mg tangent theta

• mg cosine theta

• mg sine theta

What does the sine function in trigonometry relate to in a right triangle?

• Adjacent over opposite

• Adjacent over hypotenuse

• Opposite over adjacent

• Opposite over hypotenuse

What trigonometric identity is used to find the force parallel to the incline?

• Cosine

• Sine

• Tangent

• Cotangent

What happens to the mg cosine theta component as theta approaches zero?

• Equals mg

• Becomes undefined

• Remains constant

• Approaches zero

If the angle theta is at zero degrees, what should the force down the incline ideally be?

• Zero

• mg

• mg sine theta

• mg cosine theta

How is the correctness of the guessed angle's placement verified?

• By measuring the actual angle

• Using a protractor

• Considering the limits as theta approaches zero

• Calculating the resultant force