A 20 kg table initially at rest on a horizontal floor requires a 136 N horizontal force to set it in motion. Once the table is in motion, a 71 N horizontal force keeps it moving at a constant velocity. What is the coefficient of kinetic friction between the table and floor?
Wt = mg = 20 kg * 9.8 N/kg = 196 N. =
Weight of table.
Ft = 196 N. @ 0 Deg. = Force of table.
Fp = 196*sin(0) = 0 = Force parallel to floor.
Fv = 196*cos(0) = 196 N. = Force perpendicular to the floor.
Fn = Fap-Fp-Fk = ma = 0, a = 0.
71-0-Fk = 0,
Fk = 71 N. = Force of kinetic friction.
u*Fv = 71,
196u = 71,
u = 0.362 = Kinetic coefficient of friction.
To find the coefficient of kinetic friction between the table and the floor, we can follow these steps:
Step 1: Calculate the force of static friction.
To calculate the force of static friction, we use the formula:
Fs = μs * N
where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
Since the table is initially at rest on the floor, the force of static friction is equal to the applied force required to set the table in motion, which is 136 N. Thus, Fs = 136 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, the normal force is equal to the weight of the table, which is given as 20 kg. Therefore, N = mg, where m is the mass of the table and g is the acceleration due to gravity (approximately 9.8 m/s²).
N = (20 kg) * (9.8 m/s²) = 196 N.
Step 3: Calculate the coefficient of static friction.
Using the equation Fs = μs * N, we can rearrange it to solve for the coefficient of static friction:
μs = Fs / N.
Substituting the values:
μs = (136 N) / (196 N) = 0.69 (rounded to two decimal places).
Therefore, the coefficient of kinetic friction between the table and floor is approximately 0.69.