Final answer:
To find the elevator's acceleration, calculate the difference between the scale reading (normal force) and the man's weight, then divide by his mass. The acceleration of the elevator is approximately 1.147 m/s² upwards.
Step-by-step explanation:
The question asks for the acceleration of the elevator given the scale reading and the mass of the man. First, we should note that when the elevator is at constant velocity or at rest, the scale reading equals the man's weight, which is the product of his mass and the acceleration due to gravity (9.8 m/s²). However, when the elevator is accelerating, the scale reading will differ from the weight.
Here's how you calculate it:
First, find the man's weight by multiplying his mass by the acceleration due to gravity:
Weight (W) = mass (m) × gravity (g) = 76 kg × 9.8 m/s² = 744.8 N.
The scale reads 832 N, which is the normal force (Fn), and since this is greater than his weight, there is an upward acceleration (a).
To find the acceleration, use Newton's second law: Net force (Fnet) = mass (m) × acceleration (a). Here the net force is the difference between the normal force and weight: Fnet = Fn - W.
Therefore, 832 N - 744.8 N = 87.2 N is the net force.
Now calculate the acceleration: a = Fnet / m = 87.2 N / 76 kg = 1.147 m/s².
The acceleration of the elevator is approximately 1.147 m/s² upwards.