Inclined Plane Vector Problem: Understanding the Use of Trigonometric Functions

  • #1
Ineedhelpwithphysics
43
7
Homework Statement
In picture
Relevant Equations
Cos(x), sin(x), angle addition/subtraction.
I'm not really asking for a solution for this problem I just want to clear up a confusion I have.

Why are they multiplying the weight by the sin and cosine of the 30-degree angle?
Isn't weight not affected by anything since it's constant?

Also is the angle of friction 0 because it's a straight line?
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  • #2
Did you post the entire question and solution? It should state that the coordinates chosen are parallel to the ramp (x) and normal to the ramp (y). The use of sin and cos is to find the components of the weight in those directions.
 
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  • #3
haruspex said:
Did you post the entire question and solution? It should state that the coordinates chosen are parallel to the ramp (x) and normal to the ramp (y). The use of sin and cos is to find the components of the weight in those directions.
1697845376188.png

sorry about that
 
  • #4

FAQ: Inclined Plane Vector Problem: Understanding the Use of Trigonometric Functions

What is an inclined plane vector problem?

An inclined plane vector problem involves analyzing the forces acting on an object placed on a slope. These problems typically require understanding how to decompose the gravitational force into components parallel and perpendicular to the inclined surface, using vector and trigonometric principles.

Why are trigonometric functions important in solving inclined plane problems?

Trigonometric functions are crucial because they allow us to break down the gravitational force into components that are parallel and perpendicular to the inclined plane. This decomposition is necessary to analyze the forces accurately and solve for quantities such as acceleration, friction, and normal force.

How do you decompose the gravitational force on an inclined plane using trigonometric functions?

To decompose the gravitational force, you use the angle of the incline (θ). The component of the gravitational force parallel to the incline is given by \(mg \sin(θ)\), and the component perpendicular to the incline is \(mg \cos(θ)\), where \(m\) is the mass of the object and \(g\) is the acceleration due to gravity.

What role does the angle of inclination play in these problems?

The angle of inclination (θ) determines the proportion of the gravitational force that acts parallel and perpendicular to the plane. A steeper angle increases the parallel component (causing the object to slide more easily) and decreases the perpendicular component (reducing the normal force).

Can you provide an example of solving an inclined plane problem using trigonometric functions?

Consider an object of mass \(m\) on an inclined plane with an angle of \(30^\circ\). To find the components of the gravitational force, calculate:- Parallel component: \(mg \sin(30^\circ) = mg \cdot 0.5 = 0.5mg\)- Perpendicular component: \(mg \cos(30^\circ) = mg \cdot \sqrt{3}/2 ≈ 0.866mg\)These components can then be used to analyze the motion of the object and any additional forces, such as friction.

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