Block of Sandpaper along the ceiling

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A 5.49 kg block covered in sandpaper is pushed along a ceiling with an 81.6 N force at a 70° angle. The coefficient of kinetic friction is 0.533, leading to a calculation of acceleration that initially results in a negative value, indicating the block would not move. To accurately determine the normal force, the y-component of the applied force must be included, as it affects the frictional force. When the y-component is considered, the calculations yield a positive acceleration, confirming the block can move. Understanding the relationship between applied forces and friction is crucial for solving such problems.
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Homework Statement


A 5.49 kg block covered in sandpaper is pushed along the ceiling of a room under construction. The block is pushed across the ceiling with a force of 81.6 N directed at an angle of 70.0° to the horizontal. If the coefficient of kinetic friction between the paper and the ceiling is 0.533, what acceleration does the block undergo?


Homework Equations


component forces in x-direction = Fextcos70 - Ff

The Attempt at a Solution


ma = Fextcos70 - uFn
= 81.6cos70 - (0.533)(5.49*9.8)
= 27.9 - 28.7

** so i would get a negative number: that doesn't really make sense. Here I say that the normal force is equal in magnitude to the weight. Is this correct? Or do i need to include the y-component of the push when looking for the normal force?
Help would greatly be appreciated!
 
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I'm having trouble with the same problem
 
indietro said:
Here I say that the normal force is equal in magnitude to the weight. Is this correct? Or do i need to include the y-component of the push when looking for the normal force?

you certainly need to do that. suppose you get an hydraulick and push the block against the
ceiling with 10000N. do you think the normal force is still m.g

It is possible to end up with a negative number. That just means that the friction is too large
and the block won't move
 
Thank you! when i also consider the y-component of the push when finding Fn it works out :) and ends up with a positive acceleration
 
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