# Force normal and force along the incline

• MHB
• WMDhamnekar
In summary, the conversation discusses how to compute the force along the incline ($F_{inc}$) and the force normal ($F_n$) for a 10 kg block sitting on an inclined board at a 30 degree angle with the horizontal. The force of gravity ($F_g$) is decomposed into two orthogonal vectors, with $F_{inc}$ and $F_n$ being the legs of a 30-60-90 right triangle. By using trigonometric functions, it is determined that $F_{inc} = 0.5F_g$ and $F_n = 0.87F_g$.
WMDhamnekar
MHB
A 10 kg block sits on a board inclined to an angle of $30^\circ$ with the horizontal.

What are $F_{inc}$ (force along the incline) and the $F_n$ (force normal)?How to compute this?

#### Attachments

• inclined.gif
982 bytes · Views: 81
You are decomposing $${F}_{g}$$ into 2 orthogonal vectors so

$${F}_{g} = {F}_{inc} - {F}_{n}$$

DavidCampen said:
You are decomposing $${F}_{g}$$ into 2 orthogonal vectors so

$${F}_{g} = {F}_{inc} - {F}_{n}$$
Hello,

Here $F_g=-98N$. What is $F_{inc}?$ I think it is $F\langle \cos{60^\circ},\sin{60^\circ}\rangle$ What is $F_{normal}?$

They should be orthogonal to each other means their dot product =0.

The 2 component vectors will be at right angles to one another. One will have an angle of 30 degree to ${F}_{g}$ and the other 60 degrees.

So think of a 30-60-90 right triangle with ${F}_{g}$ the hypotenuse and ${F}_{inc}$ and ${F}_{n}$ the legs.

Last edited:
DavidCampen said:
The 2 component vectors will be at right angles to one another. One will have an angle of 30 degree to $${F}_{g}$$ and the other 60 degrees. So $$asin(30) + bsin(60) = {F}_{g}$$. Which of a and b is $${F}_{inc}$$ and which is $${F}_{n}$$ (and the correct sign) you will have to draw a diagram to figure out.

Hello,

$a\sin{30^\circ}$ is + $F_n$ and $b\sin{60^\circ}$ is $-F_{inc}$. How to compute a and b? Would you explain with a graph?

Yes, excuse me.

$a = {F}_{g}sin(30)$ and $b = {F}_{g}sin(60)$

I edited my post just above to match this.

DavidCampen said:
Yes, excuse me.

$a = {F}_{g}sin(30)$ and $b = {F}_{g}sin(60)$

I edited my post just above to match this.

So, the $F_{normal}=84.957N$ and $F_{inc}=49N$

Dhamnekar Winod said:
So, the $F_{normal}=84.957N$ and $F_{inc}=49N$
Yes.

I drew a diagram. Placing ${F}_{inc}$ on the horizontal axis as one leg of the triangle, ${F}_{n}$ as the vertical leg and ${F}_{g}$ as the hypotenuse I get an angle of 60 deg. between ${F}_{inc}$ and ${F}_{g}$ so the magnitude of ${F}_{inc}$ = ${F}_{g} cos(60) = 0.5 {F}_{g}$ and ${F}_{n} = {F}_{g}sin(60) = 0.87{F}_{g}$.

Last edited:

## 1. What is the force normal and force along the incline?

The force normal is the perpendicular force exerted by a surface on an object that is in contact with it. The force along the incline is the component of the force acting on an object that is parallel to the incline or ramp.

## 2. How are force normal and force along the incline related?

The force normal and force along the incline are related by the angle of the incline. As the angle of the incline increases, the force along the incline also increases, while the force normal decreases.

## 3. What is the role of force normal and force along the incline in determining an object's motion?

The force normal and force along the incline are important in determining an object's motion because they are the two components of the net force acting on the object. The force normal helps to support the weight of the object, while the force along the incline helps to move the object up or down the incline.

## 4. How do you calculate the force normal and force along the incline?

The force normal can be calculated using the formula FN = mg cosθ, where m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of the incline. The force along the incline can be calculated using the formula Fparallel = mg sinθ.

## 5. How does the weight of an object affect the force normal and force along the incline?

The weight of an object affects the force normal and force along the incline because they are both dependent on the mass of the object. A heavier object will have a greater force normal and force along the incline compared to a lighter object, assuming all other variables remain constant.

Replies
7
Views
1K
Replies
20
Views
3K
Replies
9
Views
2K
Replies
13
Views
693
Replies
3
Views
648
Replies
5
Views
2K
Replies
2
Views
1K
Replies
5
Views
2K
Replies
13
Views
1K
Replies
11
Views
2K