Answer:
the weight of the person is 57.98kg
Explanation:
According to Newton's second law:
[tex]\sum F=m*a[/tex]
The scale reads the normal force, so if the elevator is going upward:
[tex]N-m.g=m.a[/tex]
[tex]N-m*(9.8)=m.a[/tex]
and if it is going downward:
[tex]N-m.g=m.a[/tex]
[tex]N-m*(9.8)=-m.a[/tex]
so:
[tex]814.7N-m*(9.8)=m.a[/tex]
[tex]321.8N-m*(9.8)=-m.a[/tex]
because the value of the acceleration is equal in magnitude we can substitute one equation into the other.
[tex]814.7N-m*(9.8)=m.(\frac{m*9.8-321.8N}{m})\\\\m=\frac{814.7+321.8}{2*9.8}\\\\m=57.98kg[/tex]
Answer:
Explanation:
Maximum scale reading, R = 814.7 N
Minimum scale reading, R' = 321.8 N
acceleration due to gravity, g = 9.8 m/s²
let a be the acceleration of the elevator.
Case 1: Elevator is moving up :
R - mg = ma
814.7 - mg = ma
814.7 = m (g + a) .... (1)
Case 2: elevator is moving down :
mg - R' = ma
R' = m (g - a)
321 = m (g - a) .... (2)
divide equation (1) by (2)
2.53 (g - a) = g + a
25 - 2.53 a = 9.8 + a
15.2 = 3.53 a
a = 4.31 m/s²
Put in equation (1)
814.7 = m (9.8 + 4.31)
m = 57.8 kg
