For a translating block with slipping find the maximum force F

  • #1
annamal
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Homework Statement
For a translating block with slipping find the maximum force F to cause no tipping
Relevant Equations
Ig*alpha = sum of moments
For this translating block problem, below is the solution. I was wondering why if I took the moment about the center of gravity G, the answer for F would no longer be the same because ##I_G \alpha = -\mu_k N (h/2) + N (b/2) - F*d = 0## because ##\alpha = 0##
$$F = \frac{-\mu_k mg (h/2) + mg(b/2)}{d}$$
What am I doing wrong by taking the moment about G though?
Screenshot 2024-03-19 at 9.15.09 PM.png
 
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  • #2
annamal said:
## -\mu_k N (h/2) + N (b/2) - F*d = 0##
Is ##d## the correct distance for the last term on the left-hand side?
 
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  • #3
TSny said:
Is ##d## the correct distance for the last term on the left-hand side?
Resolved, that was my mistake. The distance is d - h/2.
 
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FAQ: For a translating block with slipping find the maximum force F

What is the basic setup for a problem involving a translating block with slipping?

The basic setup involves a block placed on a surface, where a force F is applied to it. The block translates (moves) across the surface while experiencing friction, which may cause it to slip. The problem typically requires determining the maximum force F that can be applied before the block starts to slip.

What role does friction play in determining the maximum force F?

Friction provides the resistive force that opposes the motion of the block. The maximum force F that can be applied without causing slipping is directly related to the frictional force, which is determined by the coefficient of friction (static or kinetic) between the block and the surface, and the normal force acting on the block.

How do you calculate the maximum static friction force?

The maximum static friction force can be calculated using the formula: \( f_s = \mu_s \cdot N \), where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force. This force represents the threshold at which the block will start to slip.

What is the difference between static and kinetic friction in this context?

Static friction is the frictional force that prevents the block from starting to move and is generally higher than kinetic friction. Kinetic friction, on the other hand, is the frictional force acting on the block once it has started moving. The coefficient of static friction (\( \mu_s \)) is typically greater than the coefficient of kinetic friction (\( \mu_k \)).

How do you determine the maximum force F before slipping occurs?

To determine the maximum force F before slipping occurs, you need to calculate the maximum static friction force using \( f_s = \mu_s \cdot N \). The maximum force F is equal to this maximum static friction force. If the applied force exceeds this value, the block will start to slip.

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