Determining the Acceleration (Inclined Plane Problem)

  • Thread starter yandereni
  • Start date
  • #1
13
1

Homework Statement


A crate lies on a plane tilted at an angle θ = 22.0° to the horizontal, with μkin = 0.12.
a.) determine the acceleration of the crate as it slides down the plane
b.) if the carton starts from rest 9.30m up the plane from its base, what will be the carton's speed when it reaches the bottom?

this is the most confusing so far....

Homework Equations


ΣFhorizontal = Ffrict+Fgrav(sin22) = ma
ΣFvertical = Fnorm + Fgrav(cos22) = ma
Vfinal2= VInitial2 + 2a(displacement)
ples.jpg

The Attempt at a Solution


ΣFhorizontal = (0.12)(Fnorm)+Fgrav(sin22) = ma
= 0.12Fn + 0.375Fg=ma
= 0.12(0.279Fg + ma) = ma
= 0.111Fg + 0.12ma = ma
= 0.111Fg = 0.88ma
=Fg = 7.928ma
ΣFvertical = Fnorm + Fgrav(cos22) = ma
= Fn - 0.927Fg = ma
=Fn=0.927Fg+ma
= Fn= 0.927(7.928ma)
=Fn = 7.349ma

since I didnt really know what to do next..
7.928ma/7.349ma= 1.079
so i assumed that was the acceleration

then...

Vfinal2 = (0m/s)2 + (2)(1.079m/s2)(9.3m)
Vfinal2=(20.07m/s)
(Vfinal2)1/2=(20.07m/s)1/2
Vfinal=4.480m/s


Thanks in Advance!
 
  • Like
Likes DAVID H HAINDONGO

Answers and Replies

  • #2
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
16,139
8,169
Your approach to part b) is correct, but the value for the acceleration is wrong.

To be honest, I couldn't really understand what you were doing in part a).

The first step is to find the normal force acting on the block. If we call this ##F_n##, can you work out what ##F_n## is?
 
  • #3
NascentOxygen
Staff Emeritus
Science Advisor
9,244
1,072
You have written subscript "horizontal" where you should call it "down the slope". Similarly, you wrote "vertical" where you should have "normal to the slope".

Don't forget that friction acts opposite to the direction of motion. So with the block sliding down the slope here, friction will be acting up the slope.
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,516
6,424
ΣFvertical = Fnorm + Fgrav(cos22) = ma
As NascentOxygen posted, you mean Fnormal, not Fvertical, but what is a in that equation? Yes, I know it's an acceleration, but what acceleration exactly?
 

Related Threads on Determining the Acceleration (Inclined Plane Problem)

Replies
5
Views
3K
Replies
1
Views
6K
  • Last Post
Replies
12
Views
2K
Replies
1
Views
5K
Replies
2
Views
4K
  • Last Post
Replies
9
Views
2K
Replies
13
Views
3K
  • Last Post
Replies
10
Views
6K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
8
Views
7K
Top