# confused ?

why the x component in the picture of the car is ( sin ) and in the second picture “ free body diagram “ the x component is ( cos ) .

is it always the x component  (cos ), is not ? Relevance
• It depends which angle you use. Try the video in the link which explains resolving vectors from basics.

• The angle is with respect to vertical in one diagram and horizontal in the other.

• Pls have a look to the sketch shown below :

The gravitational force parallel to the incline that makes the body sliding down is GF = m*g*sin Θ and  it is the force you have to overcome if you want to move the body up a frictionless incline .

If there is friction , then the friction force FF, parallel to the incline and having the same versus of GF, will be equal to m*g*cos Θ*μ , so the total force F to be applied will be equal to :

F = GF+FF = m*g*sin Θ +  m*g*cos Θ*μ = m*g*(sin Θ + cos Θ*μ )

If the body is kept at rest by the only friction , then it must be :

m*g*sin Θ = m*g*cos Θ*μ

m*g cancels

μ = sin Θ / cos Θ = tan Θ • Remember cos30 = sin60  and sin30 = cos60