How Do You Calculate Acceleration on an Inclined Plane with Friction?

[HawKMX2004]

Sorry for the double post, but this edit wasnt showing up for me on other post, so i post it here.

I also came across another challenging problem, devising of an equation for Acceleration on an inclined plane.

Q: A toy car is released from rest at the top of a ramp going down to the right. Assuming that friction IS present derive an equation that could determine the acceleration of the car.

SFy - sum of forces in the y direction
SFx - sum of forces in the x direction
Fn - Force Natural
Fgy - Force Gravity in the Y-direction
Fgx - Force Gravity in the X direction
m - Mass
a - Acceleration
U - Coefficient of Friction
Fg - Force of Gracity
Ff - Force of Friction

Here is my work, though I think i went wrong with the sin and cos values

SFy = Fn - Fgy = 0
Fn = Fgy
Fn = cos(Theta)Fg
SFx = Fgx - Ff = ma
SFx = Fgx - FnU = ma
SFx = Fgx = ma + FnU
SFx = sin(Theta)Fg = ma +cos(Theta)Fg
SFx = sin(Theta)Fg / cos(Theta)Fg = ma + U
SFx = tan(Theta) = ma + U
SFx = tan(Theta) - U = ma
SFx = [tan(Theta) - U] / m = a

Once again help would be appreciated..thankz for all help and corrections

 

[UrbanXrisis]

Okay, I'm not going to use those variables because it's too comfusing

First, a=net force/mass
U - Coefficient of Friction
Force of Friction=UmgcosX
Force of the car=mgcosX

Net Force=mgcosX-UmgcosX

a=net force/mass
a=(mgcosX-UmgcosX)/m
a=gcosX-UgcosX

 

[wais]

No need to apologize for the double post, sometimes technology can be frustrating. It's great that you are actively seeking help and corrections for your work.

Your approach to solving this problem using Newton's Second Law is correct. However, there are a few mistakes in your calculations.

Firstly, in your equation for SFy, you have written Fn = cos(Theta)Fg. This should be Fn = sin(Theta)Fg, since the angle Theta is with respect to the x-axis and the force of gravity is acting in the y-direction.

Secondly, in your equation for SFx, you have written SFx = sin(Theta)Fg / cos(Theta)Fg = ma +cos(Theta)Fg. This should be SFx = sin(Theta)Fg - cos(Theta)Fg = ma. The force of friction is acting in the opposite direction of the force of gravity, so it should be subtracted instead of added.

Finally, in your last equation, you have written SFx = [tan(Theta) - U] / m = a. This should be SFx = [tan(Theta) - U]m = a, as the mass should be multiplied to both sides of the equation.

Overall, your approach and understanding of the problem is correct. Just be careful with your calculations and make sure to double check for any mistakes. Keep up the good work!