A 61-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 815 N. What is the acceleration of the elevator?


m/s2 upward

To find the acceleration of the elevator, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = ma).

In this scenario, the force acting on the man standing on the scale is the difference between his weight and the normal force exerted by the scale.

Weight is calculated as the mass of an object multiplied by the acceleration due to gravity, which is approximately 9.8 m/s^2 on the surface of the Earth.

Weight = mass * acceleration due to gravity
Weight = 61 kg * 9.8 m/s^2
Weight = 598.8 N

Since the man is standing on a scale and the reading on the scale is 815 N, the normal force exerted by the scale is equal to 815 N. Therefore, the net force acting on the man is:

Net force = Force - Normal force
Net force = 598.8 N - 815 N
Net force = -216.2 N

The negative sign indicates that the net force is acting in the opposite direction of the scale's reading. In this case, it means that the elevator is accelerating upward.

Now, we can apply Newton's second law to find the acceleration of the elevator:

Net force = mass * acceleration
-216.2 N = 61 kg * acceleration

Divide both sides of the equation by 61 kg:

acceleration = -216.2 N / 61 kg
acceleration ≈ -3.54 m/s^2

Therefore, the acceleration of the elevator is approximately 3.54 m/s^2 upward.

815- 61*9.8 = 61 a