Maximum force so object on top wouldn't start sliding back

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Homework Help Overview

The problem involves two boxes, A and B, where box B is placed on top of box A. The objective is to determine the maximum force that can be applied to box A without causing box B to slide off. The discussion centers around the concepts of friction and acceleration, with specific coefficients of friction provided for the interactions between the boxes and the ground.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the forces of friction acting on both boxes and explore the relationship between maximum acceleration and the force applied to box A. There is a focus on calculating the maximum force before box B begins to slide.

Discussion Status

Some participants have calculated the forces and accelerations involved, with one participant confirming the approach taken by another. There is an ongoing exploration of the calculations related to friction and acceleration, but no explicit consensus has been reached regarding the final answer.

Contextual Notes

Participants are working under the assumption that gravitational acceleration can be approximated as 10 m/s² for their calculations. There is also a focus on ensuring that the frictional forces are correctly applied in the context of the problem.

Arquon
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Homework Statement


Box B is on top of box A. Box A has a mass of 1 kg, B has 0.3 kg. Coefficient of friction between ground and box A is 0.5, between box A and B : 0.75. With what maximum force can I pull box A without box B sliding back ?

m1 = 1 kg
m2 = 0.3 kg
u1 = 0.5
u2 = 0.75

Homework Equations


Ffr = umg
F = ma

The Attempt at a Solution


I got that the force of friction between box A and ground is 6.5 N ( (m1 + m2)u1g )
Between box A and B friction is 2.25 N. ( m2u2g )
So the total force of friction box A receives is 8.75 N. But I can't work out what is the maximum force with which I can pull box A without having box B falling off.
 
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Arquon said:
Between box A and B friction is 2.25 N. ( m2u2g )
That's the key.
Hint: What's the max acceleration that box A can have before it starts to slide?
 
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I got acceleration 7.5 m / s2. Then :
F = Ffr + ma = 6.5 + 9.75 = 16.25 N ( for friction I used friction between box A and ground, and m = 1.3 kg)

Is this correct ?
 
Arquon said:
I got acceleration 7.5 m / s2. Then :
F = Ffr + ma = 6.5 + 9.75 = 16.25 N ( for friction I used friction between box A and ground, and m = 1.3 kg)

Is this correct ?
Looks good to me. (Assuming it's OK for you to use g = 10 m/s^2.)
 
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Yeah, it's ok. Thank you !
 

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