Rather than taking the stairs, Javier gets from the second floor of his house to the first floor by sliding down the banister that is inclined at an angle of 30.0 degrees to the horizontal. If Javier has a mass of 49.1 kg and the coefficient of kinetic friction between Javier and the banister is 0.212, what is the force of kinetic friction impeding Javier's motion down the banister?
F(fr)=μ•N=μ•m•g•cosα
To find the force of kinetic friction impeding Javier's motion down the banister, we can follow these steps:
Step 1: Calculate the gravitational force acting on Javier.
The gravitational force can be found using the formula: gravitational force = mass * gravitational acceleration.
The mass of Javier is given as 49.1 kg, and the gravitational acceleration is approximately 9.8 m/s^2.
So, the gravitational force acting on Javier is: 49.1 kg * 9.8 m/s^2 = 481.18 N.
Step 2: Calculate the normal force.
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, as Javier is sliding down the banister, the normal force is the force exerted by the banister on Javier perpendicular to the incline.
The normal force can be found using the formula: normal force = mass * gravitational acceleration * cos(angle of incline).
In this case, the angle of incline is 30 degrees, so the formula becomes: normal force = 49.1 kg * 9.8 m/s^2 * cos(30).
Evaluating this expression, we find: normal force ≈ 424.79 N.
Step 3: Calculate the force of kinetic friction.
The force of kinetic friction can be found using the formula: force of kinetic friction = coefficient of kinetic friction * normal force.
The coefficient of kinetic friction is given as 0.212, and the normal force is calculated as 424.79 N.
So, the force of kinetic friction impeding Javier's motion down the banister is: 0.212 * 424.79 N ≈ 90.03 N.
Therefore, the force of kinetic friction impeding Javier's motion down the banister is approximately 90.03 N.