Question

6. A 73-kg woman stands on a scale in an elevator. The
scale reads 810 N. What is the magnitude and
direction of the elevator's acceleration?

A. 0.23 m/s2 up
B. 1.3 m/s2 up
C. 6.5 m/s2 down
D. 11 m/s2 down

Answer 1

Answer:

b

Explanation:

n = m(g +a)

n= normal force (N)

m=mass (kg)

g=acceleration of gravity

a= acceleration of elevator

rearrange:

a= n/m - g

a= (810 N/73 kg) - 9.8 m/s ^2

a= 1.3 m/s ^2 up

and the acceleration is upwards bc her weight is less than the scale reading

Answer 2

The magnitude and direction of the elevator's acceleration would be $1.296 ms^{-2} \: upward$

Given the Parameters :

• Scale, reading, N = 810 N

• Mass, m = 73 kg
• Acceleration due to gravity, g = 9.8 m/s²

The Normal force can be calculated using the relation :

$N = mg + ma$

$N = m(g + a)$

$g + a = \frac{N}{m}$

$a = \frac{N}{m} - g$

Substituting the Parameters into the equation :

$a = \frac{810}{73} - 9.8$

$a = 11.0959 - 9.8$

$a = 1.296 ms^{-2}$

Scale reading > weight of woman (73 × 9.8)

810 < 715.4 (acceleration will be upward)

Therefore, the acceleration of the elevator would be $a = 1.296 ms^{-2} \: upward$

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