Aim: How can we explain forces at an angle?

Do Now:

Solve for the x and y components: 10 N

x

y

30°

x = 5 N

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. 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?

40o

50 N

12 kg

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 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:

Fg

x

y The object moves along the plane

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

x

y

This way, only Fg needs to be resolved into x and y components - F║ and F┴

FN

Fg = mg

F

FII

θ

θ

How can we solve for F║ and F┴

Mathematically, these θ’s are equal

FN

Fg

F

FII

θ

θ

FF

FN = ?FN = F┴

FN = FgcosθFN = mgcosθ

At rest or moving with a constant velocity:FF = ?FF = F║

FF = Fgsinθ FF = mgsinθ

FN

Fg

F

FII

θ

θ

FF

On a frictionless incline:

FNet = ma

F║ = ma

Fgsinθ = ma

mgsinθ = ma

gsinθ = a

As θ increases, FII increases, so Fnet increases, and the object accelerates faster

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