Question

A 45.0-kg person steps on a scale in an elevator. The scale reads 460 N. What is the magnitude of the acceleration of the elevator?

Answer 1

`10.22m/s^2`

Step-by-step explanation:

We can find the answer using Newton's second law, which is expressed as follows:

`F=ma`

Where
`F` is the force (in Newtons),
`m` is the mass (in kilograms) and
`a` is the acceleration (in
`m/s^2`).

Since we are asked for the acceleration, we clear for
`a` in the last equation:

`a=(F)/(m)`

and we already have the values for the force and the mass:
`F=460N`,
`m=45kg`

so we substitute them in the equation:

`a=(460N)/(45kg) =10.22m/s^2`

The acceleration of the elevator is
`10.22m/s^2`

Answer 2

The magnitude of the acceleration of the elevator is 0.422 m/s²

Step-by-step explanation:

The weight of the person is mass × acceleration of gravity

→ His mass = 45 kg , acceleration of gravity = 9.8 m/s²

→ The weight of the person = 45 × 9.8 = 441 N

The weight acting down ward

The scale reads 460 N

According to Newton's law:

→ ∑ forces in direction of motion = mass × acceleration

→ ∑ forces = 460 - 441 = 19 N

→ mass = 45 kg , acceleration = ?

Substitute the values in the rule above

→ 19 = 45 × acceleration

Divide both sides by 45

→ acceleration = 0.422 m/s²

The magnitude of the acceleration of the elevator is 0.422 m/s²