equlibrum. Analyze Because the block is on an avetinea surtace, the normal force

Question

equlibrum. Analyze Because the block is on an avetinea surtace, the normal force perpendicutar to the surface does not balance the downward force of geavity. The normal force and the force of gravity sroduce a net force that tends to stide the block down the incine. Static fection acts atong the drection the surface to balance thes combined force of gravity and the normal force. But as the angie of inclination increases, the combined force tending to slide the ouock increases, requiring a ttronger force of static friction, until the force of static friction reaches its largest possible value given by At that point, any further increase in the angle of inclination results in unbatanced forces that accelerate the block we need to find the largest possible angle of inetination 0 for which the forces can still baiance. We choose ther direction to be parallel to the inclined surface and they perpendicular to it. Because the block is in equilibrium, the force components must balance separately aiong the r direction and along the direction. The force of gravity in thexdirection (mg) sin(0) must be balanced by the force of static friction Equation (1) F. mg sino f, o Similarly, along the y direction, the n force from the surface must balance the corresponding component of force from gravity Equation (2) E F, a m mg cos(0) o solving Equation (2) for ng ntcos(0))-1 and substituting into Equation aves Equation (3) mgsun(0) sin(0) ntan(0) cos(6) when the block is on the verge of sipping, fp 0 and the force of static friction has reached its maximum value mas An and 0. into Equation (3) gives Equation (4) pa, tan(0) For the measured critical angle of He 24 we find from Equation (4) that

Explanation / Answer

As per the equation (4) provided in the image,

muX= tan ( critical angle)

Mu X = tan (24)

mus= 0.445

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