To find the static friction force on the boy sliding down the banister, calculate the component of gravitational force along the slope, then find the normal force, and use the coefficient of static friction to determine the static friction force.
The question involves calculating the magnitude of static friction force on a boy sliding down a banister that has been coated with a sticky paste. The mass of the boy is 41.2 kg, the coefficient of static friction (μ_s) is 0.72, and the angle of the banister with the horizontal is 52.4°.
First, we calculate the force due to gravity acting down the slope, which is:
F_gravity_slope = m × g × sin(θ)
Here m is the mass of the boy, g is the acceleration due to gravity (9.81 m/s²), and θ is the angle of the slope. Substituting the given values:
F_gravity_slope = 41.2 kg × 9.81 m/s² × sin(52.4°)
Then, we calculate the static friction force using the formula:
F_friction_static = μ_s × F_normal
Since the normal force (F_normal) for an inclined plane is the component of the gravitational force perpendicular to the slope, we get:
F_normal = m × g × cos(θ)
Now we substitute the known values to find F_normal and then use it to calculate F_friction_static.
After the calculations, F_friction_static is the force that would need to be exceeded for the boy to start moving down the banister.