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 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. In this case, the net force is the difference between the gravitational force and the normal force acting on the man.
Let's break down the problem:
1. Determine the weight of the man:
Weight = mass × acceleration due to gravity
Weight = 61 kg × 9.8 m/s² (acceleration due to gravity)
Weight = 598.8 N
2. Calculate the net force acting on the man:
Net Force = Weight - Normal Force
Since the man is standing on a scale, the normal force is equal to the reading on the scale, which is 815 N.
Net Force = 598.8 N - 815 N
Net Force = -216.2 N (negative sign indicates it is acting in the opposite direction to the positive direction we assumed)
3. Apply Newton's second law:
Net Force = mass × acceleration
-216.2 N = 61 kg × acceleration
acceleration = -216.2 N / 61 kg
acceleration ≈ -3.54 m/s²
The negative sign indicates that the acceleration of the elevator is downward in relation to the man's reference frame. However, since the question asks for the acceleration in relation to the elevator itself, the magnitude of the acceleration is the absolute value, which is approximately 3.54 m/s².
F = ma
you have F and m, so do the math.