A 3-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.45. Determine the magnitude of the kinetic frictional force that acts on the box when the elevator is accelerating upward 2.4 m/s2?
frictional force = μ * weight = μ * 3 * (g + 2.4) = 0.45 * 3 * 12.2 ... N
To determine the magnitude of the kinetic frictional force acting on the box when the elevator is accelerating upward, you can follow these steps:
Step 1: Calculate the gravitational force acting on the box.
The gravitational force (weight) acting on the box can be determined using the formula:
Weight = mass * gravitational acceleration
Given that the mass of the box is 3 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 3 kg * 9.8 m/s^2 = 29.4 N
Step 2: Determine the normal force acting on the box.
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 box since the box is resting on a horizontal floor.
Normal force = Weight = 29.4 N
Step 3: Calculate the net force acting on the box.
The net force acting on the box can be determined using Newton's second law of motion:
Net force = mass * acceleration
Given that the mass of the box is 3 kg and the acceleration is 2.4 m/s^2 (upward direction), we can calculate the net force:
Net force = 3 kg * 2.4 m/s^2 = 7.2 N
Step 4: Calculate the kinetic frictional force.
The kinetic frictional force can be determined using the formula:
Frictional force = coefficient of kinetic friction * normal force
Given that the coefficient of kinetic friction is 0.45 and the normal force is 29.4 N, we can calculate the kinetic frictional force:
Frictional force = 0.45 * 29.4 N = 13.23 N
Therefore, the magnitude of the kinetic frictional force acting on the box when the elevator is accelerating upward at 2.4 m/s^2 is approximately 13.23 N.
To determine the magnitude of the kinetic frictional force acting on the box, we need to consider the forces acting on it.
1. Weight of the box:
The weight of the box can be determined using the formula:
Weight = mass x gravity
In this case, the mass of the box is 3 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the box is:
Weight = 3 kg x 9.8 m/s^2 = 29.4 N
2. Normal force:
The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface. In this case, the normal force is equal in magnitude but opposite in direction to the weight of the box. So, the normal force is also 29.4 N.
3. Net force in the vertical direction:
The net force in the vertical direction can be determined using Newton's second law:
Net force = mass x acceleration
In this case, the mass of the box is 3 kg, and the acceleration is provided as 2.4 m/s^2 (upward). Therefore, the net force in the vertical direction is:
Net force = 3 kg x 2.4 m/s^2 = 7.2 N
4. Frictional force:
The frictional force can be calculated using the formula:
Frictional force = coefficient of kinetic friction x normal force
The coefficient of kinetic friction is given as 0.45, and the normal force is 29.4 N. Therefore, the frictional force is:
Frictional force = 0.45 x 29.4 N = 13.23 N
Therefore, the magnitude of the kinetic frictional force that acts on the box when the elevator is accelerating upward with 2.4 m/s^2 is approximately 13.23 N.