Question

A person stands on a scale inside an elevator at rest. The scale reads 700 N.

a) What is the persons mass?

b) The elevator accelerates upward momentarily at the rate of 1.5 m/s squared. What does the scale read then?

c) The elevator than moves with a steady (uniform) speed of 4 m/s. What does the scale read?

Answer 1

a) The person's mass is 71.43 kg. b) When the elevator accelerates upward at 1.5 m/s², the scale would read 107.15 N. c) When the elevator moves with a steady speed of 4 m/s, the scale would read 700 N.

Step-by-step explanation:

To answer these questions, we can use Newton's second law of motion which states that the force acting on an object is equal to its mass multiplied by its acceleration.

a) To determine the person's mass, we can use the formula F = ma, where F is the force (700 N) and a is the acceleration due to gravity (9.8 m/s^2). Rearranging the formula, we have m = F/a. So, the person's mass would be 700 N/9.8 m/s^2 = 71.43 kg.

b) When the elevator accelerates upward at a rate of 1.5 m/s², we can use the formula F = ma again. The force exerted on the person in the elevator would be F = (71.43 kg)(1.5 m/s²) = 107.15 N. Therefore, the scale would read 107.15 N.

c) When the elevator moves with a steady (uniform) speed of 4 m/s, the acceleration is zero because there is no change in velocity. Hence, the force exerted on the person would be equal to their weight, which is 71.43 kg x 9.8 m/s² = 700 N. Therefore, the scale would read 700 N.

Answer 2

a) The mass of the person, m = 71.43 kg

b) The scale reading when elevator has an acceleration, W = 807.15 N

c) The scale reading when elevator has constant speed, W = 700 N

Step-by-step explanation:

Given data,

The weight of the person inside the elevator, W = 700 N

The upward acceleration of elevator, a = 1.5 m/s²

The uniform speed of the elevator, v = 4 m/s

a) The mass of the person,

m = W /g

= 700 N / 9.8 m/s²

= 71.43 kg

b) The weight of the person,

W = mg + ma

= 700 N + 71.43 kg x 1.5 m/s²

= 807.15 N

c) When the speed is constant,

W = mg

= 700 N

The scale reading when the velocity is constant, W = 700 N