Solving for weight and mass in kg in an elevator

In summary, to find the normal force in this scenario, we use the equation Fn=W-ma and substitute the weight W=mg and acceleration a=0.2g. This results in Fn=m(g-0.2g) and when we divide by g, we get the scale reading in kg.
  • #1
Sunwoo Bae
60
4
Homework Statement
A 65 kg woman descends in an elevator that briefly accelerates at 0.20 g downward. She stands on a scale that reads in kg. During this acceleration, what is her weight and what does the scale read?
Relevant Equations
Use Weight= mass*gravitational acceleration and F= ma
Fn= normal force

W=mg
W=(65)(9.8)= 637N

Fn-637= -(65)(0.2*9.8)
Fn= 509.6N

I got the weight of the woman in the elevator, but I have trouble finding what the scale reads in kg. I was given the solution which read:
a = (g-0.2g)= 0.8g
W= 0.8g*509.6N= 52kg.

My questions
1. why do I have to subtract 0.2g from 1g?
2. Why don't they substitute gravitational constant(9.8m/s^2) in "g"?
 
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  • #2
Sunwoo Bae said:
Homework Statement: A 65 kg woman descends in an elevator that briefly accelerates at 0.20kg downward. She stands on a scale that reads in kg. During this acceleration, what is her weight and what does the scale read?
Homework Equations: Use Weight= mass*gravitational acceleration and F= ma

Fn= normal force

W=mg
W=(65)(9.8)= 637N

Fn-637= -(65)(0.2*9.8)
Fn= 509.6N

I got the weight of the woman in the elevator, but I have trouble finding what the scale reads in kg.
You are correct so far. To convert the force to mass you just divide by g and thus you find what the scale reads in Kg.
I was given the solution which read:
a = (g-0.2g)= 0.8g
W= 0.8g*509.6N= 52kg.

My questions
1. why do I have to subtract 0.2g from 1g?
2. Why don't they substitute gravitational constant(9.8m/s^2) in "g"?
1. IF we follow exactly the same route as your solution but replace the numbers in the end we' ll have
$$F_n-mg=-m(0.2g)\Rightarrow F_n=mg-m(0.2g)=m(g-0.2g)$$
So it's a matter of algebra and replace the numbers in the end for why we have to just subtract 0.2g from g and multiply that by the mass m to find the normal force.
2.Because we have to divide the force by g to convert the force ##F_n## to the Kg scale .
 
  • #3
I got it! Thanks a lot!
 

Related to Solving for weight and mass in kg in an elevator

1. How is weight different from mass?

Weight is a measure of the force of gravity acting on an object, while mass is a measure of the amount of matter in an object.

2. How do you solve for weight and mass in kg in an elevator?

To solve for weight and mass in kg in an elevator, you need to know the acceleration due to gravity (9.8 m/s^2) and the elevator's acceleration (if any). Then, you can use the formula F = ma to calculate the force (weight) and the formula m = F/a to calculate the mass.

3. Does weight change in an elevator?

Yes, weight can change in an elevator if the elevator is accelerating or decelerating. This is because the force of gravity acting on the object changes as the elevator's acceleration changes.

4. How does the weight of an object affect the elevator's movement?

The weight of an object affects the elevator's movement by adding to the overall weight of the elevator, which in turn affects the elevator's acceleration. A heavier object will require more force (and therefore more energy) to move the elevator.

5. How does mass affect the elevator's movement?

Mass does not directly affect the elevator's movement, but it is related to weight through the formula w = mg, where w is weight, m is mass, and g is the acceleration due to gravity. So, a heavier mass will result in a higher weight and may require more force to move the elevator.

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