Masses 15 kg and 8 kg are connected by a light string that passes over a friction-less pulley with the 15 kg mass on a table and the 8 kg mass hanging off the edge.
The acceleration of gravity is 9.8 m/s2.
If the 15 kg mass, initially held at rest on the table, is released and moves 1.5 m in 1.5 s, determine the coefficient of kinetic friction
between it and the table.
cry lots
To determine the coefficient of kinetic friction between the 15 kg mass and the table, we need to find the net force acting on the 15 kg mass. We can then use this net force to calculate the coefficient of kinetic friction.
First, let's break down the forces acting on the 15 kg mass:
1. Weight force: This is the force due to gravity acting on the mass hanging off the table. The weight force can be calculated using the formula: weight = mass * acceleration due to gravity. For the 8 kg mass, the weight force would be (8 kg) * (9.8 m/s^2) = 78.4 N.
2. Tension force: The light string connecting the two masses creates tension in the string. Since the string is light and frictionless, the tension force on the 15 kg mass will be equal to the weight force of the 8 kg mass. Therefore, the tension force is also 78.4 N.
3. Friction force: This is the force opposing the motion of the 15 kg mass on the table. The friction force can be calculated using the formula: friction force = coefficient of kinetic friction * normal force. The normal force is equal in magnitude and opposite in direction to the weight force acting on the 15 kg mass.
Now, let's determine the net force acting on the 15 kg mass:
Net force = applied force - friction force - weight force
Since the 15 kg mass is initially held at rest and then released, the applied force is zero. Therefore:
Net force = - friction force - weight force
Since the 15 kg mass moves over a distance of 1.5 m in 1.5 s, we can use the kinematic equation: distance = 0.5 * acceleration * time^2. Rearranging this equation to solve for acceleration, we get:
acceleration = 2 * distance / (time^2)
Substituting the given values, acceleration = 2 * 1.5 m / (1.5 s)^2 = 2 m/s^2.
Now, let's calculate the net force:
Net force = mass * acceleration
Net force = (15 kg) * (2 m/s^2) = 30 N.
Since the applied force is zero, the net force is the sum of the friction force and the weight force:
Net force = - friction force - weight force
30 N = - friction force - 78.4 N
Rearranging the equation, we get:
Friction force = -30 N - (-78.4 N)
Friction force = -30 N + 78.4 N
Friction force = 48.4 N.
Now, let's calculate the normal force:
Normal force = weight force
Normal force = (15 kg) * (9.8 m/s^2) = 147 N.
Finally, we can calculate the coefficient of kinetic friction:
Coefficient of kinetic friction = friction force / normal force
Coefficient of kinetic friction = 48.4 N / 147 N ≈ 0.3298.
Therefore, the coefficient of kinetic friction between the 15 kg mass and the table is approximately 0.3298.