A 84.5-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.93 m/s 2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.57 m/s2?
Weight is Mass (m) x acceleration due to gravity (g). W=mg So,to get back to mass, divde the weight by g.
84.5/9.81= ?kg
Now adjust the value for g for when the elevator is going up or down (add or subtract the elevator velocity)and multiply it by the mass you calculated.
When the elevator is in constant motion (not accelerating) the scale should show 84.5kg.
force =mass(M)* acceleration(A).
To find the apparent weight of a person in different elevator scenarios, we can use the concept of the normal force.
(a) When the elevator is accelerating upward with an acceleration of 1.93 m/s^2:
The apparent weight of a person can be calculated by considering the forces acting on them. In this case, the upward acceleration of the elevator increases the normal force acting on the person.
The formula for calculating the net force on an object is given by:
ΣF = m × a
Where ΣF is the net force acting on the object, m is the mass of the object, and a is the acceleration.
In this situation, the normal force exerted by the scale should balance out the person's weight, taking into account the acceleration. So we have:
ΣF = m × (g + a)
Where g is the acceleration due to gravity (9.8 m/s^2) and a is the acceleration of the elevator (1.93 m/s^2).
Substituting the values:
ΣF = 84.5 kg × (9.8 m/s^2 + 1.93 m/s^2)
= 84.5 kg × 11.73 m/s^2
≈ 990.69 N
Therefore, the apparent weight of the person when the elevator is accelerating upward is approximately 990.69 N.
(b) When the elevator is moving upward at a constant speed:
In this scenario, the elevator is not accelerating. Therefore, the net force on the person will be zero since the gravitational force acting downward is balanced by the normal force acting upward.
So, the apparent weight of the person in this case will be equal to their actual weight, which can be calculated using the formula:
Weight = m × g
Where m is the mass of the person and g is the acceleration due to gravity (9.8 m/s^2).
Weight = 84.5 kg × 9.8 m/s^2
= 827.9 N
Therefore, the apparent weight of the person when the elevator is moving upward at a constant speed is 827.9 N.
(c) When the elevator is accelerating downward with an acceleration of 1.57 m/s^2:
Similar to the first scenario, the acceleration of the elevator will affect the apparent weight of the person. However, in this case, the acceleration is directed downward, which will reduce the normal force acting on the person.
Using the same formula as before:
ΣF = m × (g + a)
But this time, the acceleration will be negative since it is downward:
ΣF = 84.5 kg × (9.8 m/s^2 - 1.57 m/s^2)
= 84.5 kg × 8.23 m/s^2
≈ 694.5 N
Therefore, the apparent weight of the person when the elevator is accelerating downward is approximately 694.5 N.