# What is the acceleration of a particle sliding down an inclined plane?

• Lavace
In summary, a tile on a roof slides down from rest on a plane inclined at 30 degrees to the horizontal. The coefficient of friction between the tile and the roof is 0.4 and the tile is modeled as a particle of mass 'm' kg. The acceleration of the particle as it slides down the roof is found by dividing the total force down the plane by the mass. By solving for a, the value of 1.5 ms^-2 is obtained.

## Homework Statement

A tile on a roof becomes loose and slides from rest down the roof. The roof is modeled as a plane inclined at 30 degrees to the horizontal. The co-efficent of friction between the tile and the roof is 0.4. The tile is modeled as a particle of mass 'm'kg.

a) Find the acceleration of the particle as it slides down the roof.

## Homework Equations

Fr(Friction Force)=uR
Reaction force from the plane = mgcos(angle)
Fr= 0.4mgcos(angle)
The force of the particle sliding down the plane x = mgsin(angle)
Total force going down the plane is x - Fr=ma

## The Attempt at a Solution

R = mgcos(30)
F = uR
Fr= 0.4mgcos(30).

Total force down the plane as it is sldiing down is:
mgsin(30) - 0.4mgcos(30) = ma

I can't solve this, as there are TWO unknowns, then there's the fact I can't find m. I've tried looking thorugh textbooks but no avail.

This is my first post here =) I am attempting to complete as many practice examination questions throughout March and started early instead.

I believe once I answer a), the rest will be easy as well (a needs to be answered for b and c).

Thanks to all!

Lavace said:
Total force down the plane as it is sldiing down is:
mgsin(30) - 0.4mgcos(30) = ma

I can't solve this, as there are TWO unknowns, then there's the fact I can't find m. I've tried looking thorugh textbooks but no avail.
Hint: Divide by m.

Lavace said:
mgsin(30) - 0.4mgcos(30) = ma

I can't solve this, as there are TWO unknowns, then there's the fact I can't find m. I've tried looking thorugh textbooks but no avail.

Are you sure you need to find m?

Edit: too late, and too similar.

Dear god, I feel embarressed.

I have worked it out, THANK YOU.
mgsin30 - 0.4mgcos(30) = ma

All over m

gsin30 - 0.4gcos(30) = a
1.50 ... = a
1.5ms^-2 = a

Thank you all, I can resume studying now :)

## 1. What is basic statics?

Basic statics is a branch of mechanics that deals with the study of bodies at rest or in uniform motion. It involves analyzing the forces acting on a body and the resulting equilibrium conditions.

## 2. What are the key principles of basic statics?

The key principles of basic statics include the concept of forces, equilibrium, and the interaction between forces and bodies. These principles are essential in understanding the behavior of structures and objects at rest.

## 3. How is basic statics used in real life?

Basic statics is used in various fields such as engineering, architecture, and physics to analyze and design structures such as buildings, bridges, and machines. It is also applied in everyday situations, such as determining the stability of a bookshelf or understanding the forces acting on a ladder.

## 4. What are the main types of forces in basic statics?

The main types of forces in basic statics include tension, compression, shear, and bending. Tension is a pulling force, compression is a pushing force, shear is a sliding force, and bending is a combination of tension and compression.

## 5. How can I solve basic statics problems?

To solve basic statics problems, you need to first identify the forces acting on the body and their direction. Then, you can use the principles of equilibrium to determine the unknown forces. It is important to draw clear and accurate diagrams and use proper unit conversions in your calculations.