Forces and AnglesPhysics 11

More bad jokes…

Review: Free-body diagrams:

Free-body diagrams are used to show the relative magnitude and direction of all forces acting on an object. What if some of the

forces were not in the x or y plane???????

Forces at angles:

We will break the forces with angles into their x and y components using trigonometry!

Review: Fnet

Remember we are only worried about Fnet in the direction of the motion So sometimes we really only need either

the x or y component of the force at an angle.

Example 1:

You need to move a 25.5 kg wooden crate across a wooden floor (µ=0.20). You pull with a rope attached at a 15º to the horizontal with a force of 276N.

a. Calculate the Fapp(X) and Fapp(Y).

b. What is the acceleration of the crate?

a.

Fapp(x)= 276 N * cos 15

= (276)(0.9659) = 267 N

Fapp(y)= 276 N * sin 15

= (276)(0.2588) = 71.4 N

=15º

b. FBD Only need to consider x axis forces as that is the plane of

the motion. Ff = µFN

= (0.20)[(25.5)(9.81) = 50.0 N Fnet= Fapp(x) + Ff

= 267N – 50N = 217 N

Fnet= ma217= (25.5)a

8.5 m/s2 = a

Is it easier to push or pull a sled?

Pulling a Sled

A child of 35kg is sitting on a sled that has a coefficient of kinetic friction of 0.10 with the snow. If the parent who is pulling the sled pulls up with an angle of 25°, with what are the component forces? Draw FBD

FBD

Fg

Ff

FN

Fa

Break Applied Force into Components

Fay

Fax

Fa

aay

aay

aay

aax

aax

aax

FF

FF

FF

FF

FF

FF

)423(.

)25sin(

sin

)906(.

)25cos(

cos

Example: Pushing a Sled

A child of 35kg is on a sled that has a µk =0.10 with the snow. If the parent who is pushing the sled pushes down with an angle of 25°, with what are the component forces. Draw FBD.

FBD

Fg

Ff

FN

Fa

Break Applied Force into Components

Fay

Fax

Fa

aay

aay

aay

aax

aax

aax

FF

FF

FF

FF

FF

FF

)423.(

)25sin(

sin

)906(.

)25cos(

cos

Practice:

Force Components: Vectors WS Do 5d and 6c together

Page 171 #11, 12 (assume no Ff) Page 208 # 24, 25