Answer :
We need to analyze the forces acting on the system and apply the principles of Newton's laws of motion. The coefficient of kinetic friction between m1 and the table is approximately 0.121.
To determine the coefficient of kinetic friction between m1 and the table, we need to analyze the forces acting on the system and apply the principles of Newton's laws of motion.
Mass of m1 (m1) = 14.0 kg
Mass of m2 (m2) = 6.0 kg
Distance fallen by m2 (d) = 1.00 m
Time taken (t) = 1.69 s
Let's consider the forces acting on m2. We have the gravitational force (mg) pulling m2 downward, and the tension force (T) in the string pulling m2 upward. Since m2 is falling, the net force on m2 can be calculated using Newton's second law (F = ma):
Net force on m2 = m2 * g - T
The acceleration of m2 can be calculated using the distance fallen and time taken:
Acceleration (a) = 2 * d / t^2
The tension force in the string is also equal to the force on m1 due to friction. So, the force of friction acting on m1 can be calculated as:
Force of friction (f) = T
Using the equation for kinetic friction, f = μ * N, where μ is the coefficient of kinetic friction and N is the normal force, we need to determine the normal force acting on m1.
The normal force N is equal to the weight of m1, N = m1 * g.
Substituting the known values, we have:
f = μ * m1 * g
To find μ, we need to divide f by the weight of m1:
μ = f / (m1 * g)
Now, let's calculate the force of friction using the acceleration of m2:
f = m2 * a
Substituting the values, we have:
f = 6.0 kg * (2 * 1.00 m) / (1.69 s)^2
Simplifying, we find:
f ≈ 3.550 N
Substituting this value into the equation for μ, we have:
μ = (3.550 N) / (14.0 kg * 9.8 m/s^2)
Calculating the value, we find:
μ ≈ 0.121
Therefore, the coefficient of kinetic friction between m1 and the table is approximately 0.121.
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