Movers are looking to lower a cabinet out of an open window to a mattress on the ground below. One end of a rope is tied to a 130. kg dresser, looped through a pulley, and the other end of the rope is tied to a cabinet. If the coefficient of kinetic friction between the dresser and floor is 0.670 and the tension on the rope is 1.25×103 N, what is the mass of the cabinet?
64.4 kg
185 kg
97.3 kg
63.8 kg
To find the mass of the cabinet, we need to use the principles of Newton's second law and the concept of friction.
Step 1: Identify the forces acting on the dresser.
There are two main forces acting on the dresser: the tension force from the rope pulling it downward and the force of kinetic friction opposing its motion on the floor.
Step 2: Calculate the gravitational force on the dresser.
The gravitational force (F_gravity) on the dresser can be calculated using the formula: F_gravity = m_gravity * g, where m_gravity is the mass of the dresser and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, F_gravity = 130 kg * 9.8 m/s^2.
Step 3: Calculate the force of kinetic friction.
The force of kinetic friction (F_friction) can be calculated using the formula: F_friction = coefficient of kinetic friction * normal force, where the normal force is equal to the gravitational force (since the dresser is not accelerating vertically). In this case, F_friction = 0.670 * F_gravity.
Step 4: Calculate the net force on the dresser.
The net force (F_net) acting on the dresser is the difference between the tension force and the force of kinetic friction. In this case, F_net = Tension force - F_friction.
Step 5: Apply Newton's second law and solve for the mass of the cabinet.
According to Newton's second law, the net force is equal to the mass multiplied by the acceleration (F_net = mass * acceleration). Here, since the dresser is not accelerating vertically, the net force is zero (F_net = 0). So, 0 = mass * 0, which means the mass of the cabinet does not affect the net force.
Step 6: Determine the mass of the cabinet.
Since the mass of the cabinet does not affect the net force, we cannot determine it solely based on the given information. Therefore, none of the given options (64.4 kg, 185 kg, 97.3 kg, 63.8 kg) can be considered the correct answer.