does anyone know how to show me this physics?

Question

a block that has a mass of 24 kg is initially at rest on an inclined plane. (a) find the component of the weight that is parallel to the plane. (b) find the component of the weight that is perpendicular to the plane. (c) find the maximum force of static friction if the coefficient of static friction is .65. will the block slide down the plane?

Answer 1

You probably suspect that the components of weight are
m*g times either sin or cos of the angle between horizontal and the inclined plane. I'll try to help you understand which to use in which case.

a) Think about this case. What if the inclined plane is really inclined only at 0.0000001 degrees? The parallel force would be about zero, about all the weight would be perpendicular to the plane. Which trig function is zero for an angle of zero? sin.

So for whatever the angle theta is,
Wparallel = m*g*sin(theta)

b) Again, what if it's really not inclined? All the weight is perpendicular. Which trig function gives 1 when the angle is 0? cos.

So for whatever the angle theta is,
Wperpendicular = m*g*cos(theta)

c) The vector Wparallel (answer a) is the force trying to make the mass slide. Using mu to represent the coefficient and N to represent the normal force, the resisting friction is given by
Ff = mu*N
N = Wperpendicular

So, is Ff enough to resist Wparallel?