Objects with masses m1 = 11.0 kg and m2 = 6.0 kg are connected by a light string that passes over a friction-less pulley as in the figure below. If, when the system starts from rest, m2 falls 1.00 m in 1.48 s, determine the coefficient of kinetic friction between m1 and the table.
6 g - T = 17 a
T - mu(11 g) = 11 a
what is a?
d = (1/2) a t^2
1 = (1/2)a(1.48)^2
a = .913 m/s^2
6 g - T = 15.5 so T = 6 g - 15.5
so
6 g - 15.5 - 11 g mu = 10.0
let g = 9.8 and solve for mu
To determine the coefficient of kinetic friction between m1 and the table, we need to follow these steps:
Step 1: Analyze the forces acting on the system.
In this case, there are two forces acting on m2: the force of gravity pulling it downwards (m2 * g) and the tension in the string pulling it upwards. We can also assume that there is a kinetic frictional force acting on m1.
Step 2: Write the equations of motion for each object.
Using Newton's second law (F = ma), we can write the equation of motion for m2: m2 * a = m2 * g - T, where a is the acceleration of m2 and T is the tension in the string.
Step 3: Relate the acceleration of m2 to the motion of m1.
Since m1 and m2 are connected by a string passing over a pulley, their accelerations are related. The acceleration of m2 is equal to the acceleration of m1, which we can denote as a.
Step 4: Express the tension in terms of m1 and m2.
The tension in the string can be expressed as T = m1 * g - m1 * a.
Step 5: Use the given information to calculate the acceleration.
The problem states that m2 falls 1.00 m in 1.48 s. We can use the kinematic equation s = ut + 0.5 * a * t^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time to solve for a.
Given: s = 1.00 m, t = 1.48 s, u = 0 (starting from rest)
Using the equation: 1.00 = 0.5 * a * (1.48^2)
Solving for a, we find a = 1.00 / (0.5 * 1.48^2).
Step 6: Substitute the values into the tension equation and calculate the coefficient of kinetic friction.
Substituting the values into the tension equation, we get:
T = m1 * g - m1 * a
Solving for T and substituting the given values:
T = (11.0 kg * 9.8 m/s^2) - (11.0 kg * 1.00 / (0.5 * 1.48^2))
Calculate T using this equation.
Finally, we can find the coefficient of kinetic friction between m1 and the table using the equation:
frictional force = coefficient of kinetic friction * normal force.
Since the normal force is equal to the weight of m1 (m1 * g), we can calculate the coefficient of kinetic friction by rearranging the equation:
coefficient of kinetic friction = frictional force / (m1 * g).
Calculate the frictional force by multiplying the coefficient of kinetic friction by (m1 * g), and then divide it by (m1 * g) to obtain the coefficient of kinetic friction.