Find the normal force on a carton box of mass 10 kg placed on the rigid floor of an elevator, accelerating down by 5m/s25m/s 2 .

To find the normal force on the carton box, we need to consider the forces acting on it.

Step 1: Identify the forces acting on the carton box. In this case, we have the force of gravity (weight) pulling the box downward and the normal force pushing the box upward.

Step 2: Determine the weight of the carton box. The weight is given by the formula W = m * g, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the mass of the box is 10 kg, so the weight is W = 10 kg * 9.8 m/s^2 = 98 N.

Step 3: Determine the net force acting on the box. Since the elevator is accelerating downward, there is an additional force acting on the box in the downward direction. This force is given by the formula F = m * a, where m is the mass of the box and a is the acceleration of the elevator. In this case, the acceleration of the elevator is -5 m/s^2 (negative because it is downward), so the net force is F = 10 kg * (-5 m/s^2) = -50 N.

Step 4: Apply Newton's second law of motion. According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is -50 N and the mass of the box is 10 kg. Therefore, -50 N = 10 kg * a, where a is the acceleration of the box.

Step 5: Solve for the acceleration of the box. Rearranging the equation, we have a = -50 N / 10 kg = -5 m/s^2.

Step 6: Determine the normal force. The normal force is equal in magnitude but opposite in direction to the net force acting on the box. Since the net force is -50 N, the normal force is +50 N.

Therefore, the normal force on the carton box is 50 N.