3 printers rest on top of each other on a table [FORCES]

[dungas]

Homework Statement

Three printers [X, Y, Z] are placed on top of each other on a table. What force does the middle printer exert on each of the other two printers.

x is on top, y in middle, and z on bottom.

x = 4 kg, y = 3 kg , and z = 2 kg
2. F = ma

The Attempt at a Solution

I can consider the top two printers as one so the weight would be 7 kg.

F = (7kg)(9.8 m/s^2 )
= 68.6 N

That would be the force exerted on z(the bottom printer).

The normal force would be exerted on the top printer so:

F = (5kg)(9.8 m/s^2 )
= 49 N

However this doesn't make sense since, the objects are in equilibrium so they're suppose to be equal...Please help?

 

[mfb]

68.6 N is the force between the middle and the lower printer, and required to support the upper two printers.
You can use the same argument to calculate the force between the upper and the middle printer - you can even save one step, as you don't have to combine objects there.

 

[dungas]

68.6 N is the force between the middle and the lower printer, and required to support the upper two printers.
You can use the same argument to calculate the force between the upper and the middle printer - you can even save one step, as you don't have to combine objects there.

The forces have to balance out so would be just 68.6 between the middle one and the upper one.

Also, since I'm combining objects in my previous calculations. wouldn't it be incorrect because I'm taking into account the forces of two objects when I should be just finding the force exerted by the middle one(y). The thought just came in my mind.

 

[mfb]

The forces have to balance out so would be just 68.6 between the middle one and the upper one.

This would not give balanced forces, as you have nothing to balance the gravitational force of the middle printer then.

Also, since I'm combining objects in my previous calculations. wouldn't it be incorrect because I'm taking into account the forces of two objects when I should be just finding the force exerted by the middle one(y). The thought just came in my mind.

I don't understand what you mean.

Try to solve an easier problem first: Two printers, standing on a table. The upper one has a mass of 4kg, the lower one has a mass of 3kg. What is the force between them? Does this give balanced forces on the upper printer?

 

[Nickie]

I would like to clarify that the weight and force are not the same thing. Weight is a measurement of the force of gravity on an object, while force is a measurement of the interaction between two objects. In this scenario, the weight of each printer is due to the force of gravity pulling down on them.

To answer the question, we need to consider the forces acting on each printer. The top printer (x) is only affected by the force of gravity pulling it downward. The middle printer (y), however, is affected by both the force of gravity pulling it downward and the normal force exerted by the bottom printer (z) pushing it upward.

Using Newton's second law (F=ma), we can calculate the force exerted by the middle printer (y) on the bottom printer (z):

F = ma
F = (3kg)(9.8 m/s^2)
F = 29.4 N

Similarly, we can calculate the force exerted by the middle printer (y) on the top printer (x):

F = ma
F = (3kg)(9.8 m/s^2)
F = 29.4 N

Therefore, the middle printer exerts a force of 29.4 N on both the top and bottom printers. This is because the middle printer is supporting the weight of the top printer and also pushing up against the bottom printer to keep the stack in equilibrium.