Transcript Aim: How can we explain forces on a plane?

Aim: How can we explain
forces at an angle?
Do Now:
Solve for the x and
y components:
x=5N
x
30°
10 N
y
x = 8.7 N
Why do crazy football coaches
say to get low?
 Demo
 http://www.youtube.com/watch?v=eE6x1
rfogIU&feature=related
 If force is at an angle, some component
of the force is in the x direction and
some is in the y
Forces at an Angle
 A 12 kg box is pulled across a table with a force
of 50 N at an angle of 40o above the horizontal.
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Draw a free body diagram
Write a net force equation in the x and y direction
What is the normal force?
If the box moves at a constant velocity, what is the
force of friction?
What is the coefficient of friction?
12 kg
40o
Question 2
 A small child pulls a 25 kg wagon with 30 N of
force over a frictionless surface. The angle
that the handle makes with the ground is 27o
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What is the horizontal component of the force?
What is the vertical component of the force?
Write a net force equation in the x and y direction
What is the acceleration of the wagon
If the wagon starts from rest, how far does the
child go in 4 seconds?
Normal Force
Do you remember where the normal
force is directed?
What if the plane is inclined?
On an incline:
The problem with an incline:
The object moves along
the plane
y
y
x
x
Fg
Everything would need to be
resolved into x and y
components
That’s a lot of sins and cosines
Solution – rotate the x and y
axis
This way, only Fg needs to be resolved
into x and y components - F║ and F┴
FN
How can we solve
for F║ and F┴
FII
Mathematically,
these θ’s are
equal
θ
F
θ
Fg = mg
At rest or moving with a
constant velocity:
FF = ?
FF = F║
FF = Fgsinθ
FF = mgsinθ
FN
FN = ?
FN = F┴
FN = Fgcosθ
FN = mgcosθ
FF
FII
θ
F
θ
Fg
FN
On a frictionless incline:
As θ increases, FII
increases, so Fnet
increases, and the object
accelerates faster
FNet = ma
FF
F║ = ma
FII
Fgsinθ = ma
mgsinθ = ma
θ
F
gsinθ = a
θ
Fg
On a surface with friction…
The force of friction decreases as the
angle increases since:
Remember: cos(90o) = 0 and cos(0o) = 1
The higher the angle, the lower the value of cosine
Ex: A 50 kg object rests on a table that
is inclined 25o from the horizontal. (a)
Determine the components of gravity
acting on the object. (b) What is the
Normal force?
FII = Fgsinθ
FII = mgsinθ
FII = (50 kg)(9.8 m/s2)sin(25o)
FII = 207 N
F = Fgcosθ
F = mgcosθ
F = (50 kg)(9.8 m/s2)cos(25o)
F = 444 N
FN = F┴ = 444 N
What is the force of friction if the object is at rest?
FF = F║
FF = 207 N
Assume the incline is now frictionless
What is the acceleration down the incline?
FNet = ma
F║ = ma
207 N = (50 kg)a
a = 4.14 m/s2
What is the coefficient of static friction?
FF = µFN
207 N = µ(444 N)
µ = 0.47
How far will the object travel in 5 s?
d = vit + ½at2
d = (0 m/s)(5 s) + ½(4.14 m/s2)(5 s)2
d = 51.75 m