Angled Forces: Finding Components, Normal Force, and Acceleration

[Mbenjj0x0xx]

Angled Forces HELP!

QUESTION: A 57.4 kg crate is resting on a plane inclined 30 degrees above the horizontal.
a) Find the compoents of weight forces that are parallel to the plane (Fgx) and perpendicular to the plane (Fgy)

b) Find the normal force

c) Find the acceleration down the plane

d) Find the accleration down the plane if the crate weighed 5620 N

e) does acceleration depend on weight? Does it depend on mass?



2. Homework Equations - How do you set up this problem, or do anything? I'm so lost and I could really use a step by step explanation.



3. An attempt at a solution:

I drew a diagonal line with a box on it. Then I have my Normal force going directly perpendicular to the box, and my Fg going straight down from the box... Then I got lost

 

[LCKurtz]

QUESTION: A 57.4 kg crate is resting on a plane inclined 30 degrees above the horizontal.
a) Find the compoents of weight forces that are parallel to the plane (Fgx) and perpendicular to the plane (Fgy)

b) Find the normal force

c) Find the acceleration down the plane

d) Find the accleration down the plane if the crate weighed 5620 N

e) does acceleration depend on weight? Does it depend on mass?



2. Homework Equations - How do you set up this problem, or do anything? I'm so lost and I could really use a step by step explanation.



3. An attempt at a solution:

I drew a diagonal line with a box on it. Then I have my Normal force going directly perpendicular to the box, and my Fg going straight down from the box... Then I got lost

Start by drawing the 57.4 kg force vector straight down from the incline. From the tip of that vector draw a line perpendicularly back up to the lncline. That forms a little 30-60-90 triangle with your normal force vector as the hypotenuse. The length of the other legs of that triangle give the magnitudes of the normal and parallel forces. You can figure those out because you know the angles.

 

[Architeuthis Dux]

I am happy to help you understand the concept of angled forces and how to solve this problem step by step. Let's break it down into smaller parts and use some equations to help us out.

First, let's define some variables:

m = mass of the crate (57.4 kg)
θ = angle of the inclined plane (30 degrees)
g = acceleration due to gravity (9.8 m/s^2)
Fgx = component of weight force parallel to the plane
Fgy = component of weight force perpendicular to the plane
N = normal force
a = acceleration down the plane

a) To find the components of weight forces, we need to use trigonometry. We can use the sine and cosine functions to find the horizontal and vertical components of the weight force (Fg) respectively.

Fgx = Fg * cosθ
Fgy = Fg * sinθ

Substituting in the values, we get:
Fgx = (57.4 kg)(9.8 m/s^2) * cos30 = 279.9 N
Fgy = (57.4 kg)(9.8 m/s^2) * sin30 = 139.9 N

b) The normal force (N) is the force exerted by the inclined plane on the crate that prevents it from falling through the plane. This force is perpendicular to the plane and equal in magnitude to the weight component perpendicular to the plane (Fgy).

Therefore, N = Fgy = 139.9 N

c) To find the acceleration down the plane, we can use Newton's Second Law of Motion, which states that the net force acting on an object is equal to the mass of the object times its acceleration (ΣF = ma).

Since the only forces acting on the crate are its weight and the normal force, we can write the equation as:
ΣF = Fgx - N = ma

Substituting in the values, we get:
(279.9 N) - (139.9 N) = (57.4 kg)a
a = 2.17 m/s^2

d) If the crate weighed 5620 N, the calculations would be the same except for the weight force (Fg) value, which would now be 5620 N. Substituting this value in the equations, we get:
Fgx = (5620 N) * cos30