# Why is this force the mgCos while the other is mgSin?

• EthanVandals
In summary, the question is asking for the acceleration of a 10kg block on a 60 degree inclined ramp with a coefficient of kinetic friction of 0.3. The gravitational force is split into components of mgcos(theta) and mgsin(theta), with the former being the reactionary force and the latter being the force causing the block to slide down the ramp. The use of trigonometry is necessary to find the vertical components in order to solve for the acceleration. As theta approaches zero, the normal force decreases and ultimately disappears, resulting in a decrease in friction force and an increase in acceleration.
EthanVandals

## Homework Statement

A block is placed on a ramp that is inclined to 60 degrees to the horizon. If the block weighs 10kg and the coefficient of kinetic friction is 0.3, how fast does the block accerlate down the ramp?

Theta=60 degrees
m=10kg
g=10m/s^2
mu=0.3

## The Attempt at a Solution

So far, all I have is the diagram that he gave us in class. I can somewhat tell why we're using the trig functions, but what I'm curious about is why mgsin(theta) is the block sliding down the ramp and mgcos(theta) is the reactionary force of gravity. Why not the other way around?

Draw the vertical lines from the down edge of mg to the opposite sides of plane and see which angle is ##\theta## in the right triangle that is formed. In this triangle, find each vertical side using trigonometry.

This is where theta is to be placed. If you understand why, try to figure it out from there.

You can also ask yourself what happens to the normal force as theta approaches zero? Would Sin or Cos do that?

## 1. Why is one force mgCos while the other is mgSin?

This is because the forces in physics are often broken down into components that are perpendicular to each other. The mgCos force represents the component of the force that acts in the direction of the surface, while the mgSin force represents the component that acts perpendicular to the surface.

## 2. How do we determine which force is mgCos and which is mgSin?

The determination of which force is mgCos and which is mgSin depends on the angle between the force and the surface. If the angle is 0 degrees, the force will be mgCos. If the angle is 90 degrees, the force will be mgSin.

## 3. Can the mgCos force ever be greater than the mgSin force?

No, the mgCos force is always equal to or less than the mgSin force. This is because the mgSin force is the hypotenuse of the triangle formed by the mgCos and mgSin forces, and the hypotenuse is always longer than the other two sides.

## 4. What happens if the surface is angled differently?

If the surface is angled differently, the mgCos and mgSin forces will also be different. The larger the angle, the greater the mgSin force will be in comparison to the mgCos force.

## 5. Why is it important to understand the components of forces?

Understanding the components of forces is important because it allows us to break down complex forces into simpler ones, making it easier to analyze and understand their effects. It also helps in solving problems involving forces, such as calculating the net force acting on an object.

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