In moving a 35kg desk from one side of a room to another, a man finds that a horizontal force of 275N is necessary to set the desk in motion, and a force of 195N is necessary to keep it in motion at a constant speed. What are the coefficients of both static friction and kinetic Friction between the desk and the floor?
Show all your calculations.
M*g = 35 * 9.8 = 343 N. = Wt. of the desk = Normal force(Fn).
A. Fap-Fs = M*a.
275-Fs = 35*0
275-Fs = 0
Fs = 275 N. = Force of static friction.
us = Fs/Fn = 275/343 =[
B. Fap-Fk = M*a.
195-Fk = 35*0
Fk = 195 N. = Force of kinetic friction.
uk = Fk/Fn = 195/343
To find the coefficients of static and kinetic friction between the desk and the floor, we can use the following equations:
1. For static friction (when setting the desk in motion):
Fs = μs * N
2. For kinetic friction (when keeping the desk in motion at a constant speed):
Fk = μk * N
Where:
Fs is the static friction force,
Fk is the kinetic friction force,
μs is the coefficient of static friction,
μk is the coefficient of kinetic friction, and
N is the normal force.
We have two conditions: the force required to set the desk in motion (275N) and the force required to keep it in motion at a constant speed (195N). Let's solve for the coefficients of static and kinetic friction step by step.
Step 1: Finding the normal force (N):
The normal force acting on the desk is equal to its weight, which can be calculated using the formula:
N = m * g
Where:
m is the mass of the desk (35kg) and
g is the acceleration due to gravity (9.8 m/s^2).
N = 35kg * 9.8 m/s^2
N = 343N
Step 2: Finding the coefficient of static friction (μs):
Since the force required to set the desk in motion (275N) is the maximum static friction force, we can equate it to the formula for static friction:
275N = μs * 343N
Simplifying:
μs = 275N / 343N
μs = 0.802
The coefficient of static friction between the desk and the floor is approximately 0.802.
Step 3: Finding the coefficient of kinetic friction (μk):
The force required to keep the desk in motion at a constant speed is equal to the kinetic friction force, so we can equate it to the formula for kinetic friction:
195N = μk * 343N
Simplifying:
μk = 195N / 343N
μk ≈ 0.568
The coefficient of kinetic friction between the desk and the floor is approximately 0.568.
Therefore, the coefficients of static and kinetic friction between the desk and the floor are approximately 0.802 and 0.568, respectively.