Scale Hanging From Ceiling of Elevator Question

[hueyosie]

Homework Statement

An object is hung from a spring scale attached to the ceiling of an elevator. The scale reads 65 N when the elevator is standing still. What is the reading of the scale when the elevator is moving upward with a speed of 7.6 m/s and decelerating at 2.4 m/s^2?

Homework Equations

F=ma

The Attempt at a Solution

I know that I should use the F=ma equation but according to the solutions guide, I should use F=ma=Wa/g to get (65 N)(-2.4 m/s^2)/(9.81 m/s^2) = -16 N
then do -16N-(-65N) = 49N. I am not understanding where the Wa/g part came from or why I should subtract -65N from -16N. Any help would be much appreciated! I'm having a lot of trouble with my physics class :(

 

[tal444]

Wa/g is where your are dividing the weight of the scale by acceleration of gravity to get the mass of the scale, then you multiply by the acceleration of the elevator to get the force acting on the scale. As for the second part, think about it. When you are deccelerating in an elevator going up, do you feel heavier or lighter? Does the decceleration "take away" or "add to" your weight?

 

[hueyosie]

Wa/g is where your are dividing the weight of the scale by acceleration of gravity to get the mass of the scale, then you multiply by the acceleration of the elevator to get the force acting on the scale. As for the second part, think about it. When you are deccelerating in an elevator going up, do you feel heavier or lighter? Does the decceleration "take away" or "add to" your weight?

Oh, I definitely understand it now! Thank you sooo much for explaining it to me! :)

 

[tal444]

Np ;)

 

[asteriatic]

Hello,

Thank you for reaching out for help with your physics class. I can understand how it can be confusing to see the Wa/g term in the solution and why the -65N is being subtracted from the -16N. Let me try to explain it in a simpler way.

First, let's look at the forces acting on the object in the elevator. When the elevator is standing still, the only force acting on the object is its weight, which is equal to 65 N. This is because the object is not accelerating, so the net force on it must be zero. This is represented by the equation F = ma, where F is the net force, m is the mass of the object, and a is its acceleration.

Now, when the elevator starts moving upward with a speed of 7.6 m/s, the object also starts moving with the same speed. This means that the object is now accelerating, and the net force on it is no longer zero. In fact, the net force on the object is equal to its weight (65 N) plus the force that the elevator is exerting on it to accelerate it upward. This is where the Wa/g term comes in.

The Wa/g term represents the force that the elevator is exerting on the object to accelerate it upward. This force is equal to the weight of the object (W) multiplied by the acceleration of the elevator (a) divided by the acceleration due to gravity (g). This is because the weight of an object is given by the formula W = mg, where m is the mass of the object and g is the acceleration due to gravity. So, when we substitute mg for W in the Wa/g term, we get F = ma = mg(a/g) = Wa/g.

Now, since the elevator is decelerating at 2.4 m/s^2, the acceleration of the elevator is negative (-2.4 m/s^2). This means that the force that the elevator is exerting on the object is also negative (-16 N). This force is in the opposite direction to the weight of the object, which is why it is subtracted from the weight (-65 N). This gives us a net force of -16 N - (-65 N) = 49 N, which is the reading on the scale.

I hope this explanation helps to clarify things for you. Remember, when in doubt, always go back to the basic principles and equations and try