What is the Elevator's Acceleration Direction When the Scale Reads Higher?

[Quincy]

Homework Statement

An object weighs 65 kg. When it is in an elevator on a bathroom scale, the scale reads 82 kg. What is the acceleration of the elevator and what is its direction?

Homework Equations

F_G = mg

The Attempt at a Solution

(82 kg)(9.8) = 803.6 N
803.6 N = (65 kg)(a)
a = 12.36

12.36 - 9.8 = 2.6 m/s² upwards

 

[LowlyPion]

Homework Statement

An object weighs 65 kg. When it is in an elevator on a bathroom scale, the scale reads 82 kg. What is the acceleration of the elevator and what is its direction?

Homework Equations

F_G = mg

The Attempt at a Solution

(82 kg)(9.8) = 803.6 N
803.6 N = (65 kg)(a)
a = 12.36

12.36 - 9.8 = 2.6 m/s² upwards

Is this a question?

Or a victory lap?

Looks ok to me.

 

[Quincy]

Also, what would the free body diagram look like? Would there be a normal force upwards, and the gravitational force & the force from elevator pointing downwards?

 

[heth]

Also, what would the free body diagram look like? Would there be a normal force upwards, and the gravitational force & the force from elevator pointing downwards?

What are the scales that the object is sitting on actually measuring?

 

[Quincy]

What are the scales that the object is sitting on actually measuring?

They are measuring mass. I was also surprised by this since one would think they'd be measuring weight/Newtons... Anyways, is the free body diagram correct?

 

[heth]

They are measuring mass. I was also surprised by this since one would think they'd be measuring weight/Newtons... Anyways, is the free body diagram correct?

You could place the scales against a vertical wall and push on them horizontally. The scales would give a reading in kg. But would that have anything to do with mass? The mass of a push?! :-)

If you figure out how the scales actually work and what they are measuring, then you'll be able to figure out if the free body diagram is correct.

 

[LowlyPion]

Also, what would the free body diagram look like? Would there be a normal force upwards, and the gravitational force & the force from elevator pointing downwards?

There is the N force up and the m*(g + a) down.

The Scale is measuring force, but as nothing in life is ever so simple it's marked in units of mass weight, which is the way I think most people interact with mass.

 

[Quincy]

There is the N force up and the m*(g + a) down.

The Scale is measuring force, but as nothing in life is ever so simple it's marked in units of mass weight, which is the way I think most people interact with mass.

The normal force is upwards, the gravitational force is downwards, and (m)(a) is downwards? By (m)(a), do you mean the force of the elevator? Or is there no force from the elevator?

 

[LowlyPion]

The normal force is upwards, the gravitational force is downwards, and (m)(a) is downwards? By (m)(a), do you mean the force of the elevator? Or is there no force from the elevator?

The acceleration within the frame of reference of the elevator (the scene of the problem) is (g + a).
So m*(g + a) is the force it is exerting on the scale and the spring in the scale back upward.

If you want to draw force diagrams for the elevator then you need to know what its mass is as well as the mass of the objects in the elevator.