Question

A 600 N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is 900 kg. As the elevator starts moving, the scale reads 420 N. Part A Find the acceleration of the elevator (magnitude and direction). Express your answer with the appropriate units.

Answer 1

The acceleration of the elevator is 1 m/s² in the downward direction.

Step-by-step explanation:

To find the acceleration of the elevator, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this case, the net force is the difference between the reading on the scale and the weight of the student. The weight of the student is given by the formula W = mg, where m is the mass of the student and g is the acceleration due to gravity.

Given that the reading on the scale is 420 N and the weight of the student is 600 N, we can set up an equation: 420 N = (900 kg)(a) - 600 N. Solving for a, we find that the acceleration of the elevator is 1 m/s².

The direction of the acceleration can be determined by considering the forces acting on the student. Since the scale reading is less than the weight of the student, there must be a net downward force.

Therefore, the acceleration of the elevator is in the downward direction.