Question

Rather than taking the stairs, Martin gets from the second floor of his house tothe first floor by sliding down the banister that is inclined at an angle of 30.0°to the horizontal. a) If Martin has a mass of 45 kg and the coefficient of slidingfriction between Martin and the banister is 0.20, what is the force of frictionimpeding Martin's motion down the banister? b) If the banister is madesteeper (inclined at a larger angle), will this have any effect on the force of friction? If so, what?

Answer 1

The gravitational force of Martin can be broken down into two components:

The normal force (perpendicular to the banister), and the tangential force (parallel to the banister).

Only the normal force is taken into account for frictional force.

Ff = frictional force

FN = normal force

c = coefficient of sliding friction

Fg = mg = gravitational force = 45 kg * 9.81 m/s^2 = 441.45 N

FN = Fg*cos(theta) = 441.45cos(30) = 382.31 N

Ff = c*FN = 0.2*382.31 = 76.46 N

^answer for part a

If the banister is made steeper, the angle theta increases.

When the angle theta increases, cos(theta) decreases.

When cos(theta) decreases, FN will also decrease.

When FN decreases, Ff also decreases.

Therefore, when the angle is made steeper, the frictional force decreases.

^answer for part b