A block with mass of 15kg rests on a ramp with 40degrees incline. If the static coefficient of friction?

Question

between the ramp and the block is 0.25, will the block stay where it is placed or will it start to slide down the ramp? (back up with calculations)

Answer 1

Force = Mass x Acceleration

Downhill Force
Fd = 15 g sin 40°
Fd = 9.64 g

Uphill Force (friction)
Ff = 15 g cos 40° x 0.25
Ff = 2.87 g

Will slide (Fd > Ff)

Answer 2

1. convert mass to weight w=mg w=15*9.8 w= 147 N
2. analyze forces on ramp
w cos 40=weight component perpendicular to ramp = 147cos40 =112.61 N
w sin 40 = weight component parallel to ramp = 147sin40 = 94.49 N
3. SCF = 0.25 = friction force / perpendicular component
0.25 = friction / 112.61 so friction on ramp = 28.15 N
4. mass will slide down ramp as soon as 28.15 N is overcome by 94.49 N of force.

Answer 3

The block will slide.

The force of gravity (Fg) acting on the ramp is the product of the mass of the block and the acceleration of gravity. This yields Fg=ma. This force acts straight down.

This force can be broken into its component forces, one of which acts into the ramp, and the other acts in the direction of the downhill incline. Consider these three forces creating a right triangle, with the center of the block at the apex. The angle of the apex of this triangle is the same as the angle of the incline (per similar triangles, angles of intersection, etc.).

The force acting into the ramp is found by using the cosine function. The cosine of 40 degrees is equal to the force acting into the ramp divided by the force of gravity. cos(40) = Fn/Fg. In this case Fn becomes the normal force, which we need to determine Ffr (the force of friction). When we rearrange the equation, Fn = Fg*cos(40) = 98.1 Newtons.

The force acting in the direction of the downward incline (Finc) is the same formula, using the sine of 40 degrees. sin(40) = Finc/Fg. Finc = Fg*sin(40) = 109.6 Newtons.

Now, we compare the force of friction (Ffr) to the force acting along the incline. Ffr = cfr*Fn = the coefficient of static friction times the normal force. This gives us .25*98.1 = 24.5. This is much less than Finc, which is 109.6, so the block slides.

Answer 4

It will slide, because I have coated the ramp with butter.