At what angle will a box start to slide

In summary, the problem involves two boxes of nails, one weighing 20 kg and the other 10 kg, being lifted at a construction site. The plank tilts towards the heavier box and the coefficient of static friction is 0.4. The equation |Fs| = µs|mg| is used to calculate the force of static friction, which is 78.4 N for the 20 kg box and 39.2 N for the 10 kg box. However, when the board is at an angle, the normal reaction force will change in size and must be taken into account. It is unclear if the situation is any different than having the boxes on a ramp, assuming they are traveling at a steady speed.
  • #1
TheronSimon
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0

Homework Statement



So there 2 boxes of nails being lifted at a construction site and one box is 20 kg and the other 10 kg. and the plank tilts towards the heavier box. if the coeficient of static friction is 0.4 draw a FBD for each box of nails and use it to calculate the angle at which each box begins to slide.

Homework Equations





The Attempt at a Solution



|Fs| = µs|mg|

20 Kg box is 78.4 N
10 kg Box is 39.2 N

And now I am not sure how to continue...
 
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  • #2
TheronSimon said:

Homework Statement



So there 2 boxes of nails being lifted at a construction site and one box is 20 kg and the other 10 kg. and the plank tilts towards the heavier box. if the coeficient of static friction is 0.4 draw a FBD for each box of nails and use it to calculate the angle at which each box begins to slide.

Homework Equations





The Attempt at a Solution



|Fs| = µs|mg|

20 Kg box is 78.4 N
10 kg Box is 39.2 N

And now I am not sure how to continue...


When the board is at an angle, the normal reaction force will no longer equal mg in size, so you need to account for that.

Question: is this situation really any different to having the boxes of nails on a ramp? It certainly would be if the crane lifting them was causing them to accelerate up or down, but if they are traveling at steady speed?
 

FAQ: At what angle will a box start to slide

What factors affect the angle at which a box will start to slide?

The angle at which a box will start to slide is affected by the weight of the box, the material of the surface it is resting on, the coefficient of friction between the box and the surface, and the force applied to the box.

How does the weight of the box affect the sliding angle?

The heavier the box, the higher the sliding angle will be. This is because the weight of the box creates a greater downward force, increasing the normal force between the box and the surface and therefore increasing the frictional force.

What is the coefficient of friction and how does it impact the sliding angle?

The coefficient of friction is a measure of the roughness or smoothness of the surface. A higher coefficient of friction means there is more resistance to motion, therefore a higher sliding angle is needed for the box to start sliding. On the other hand, a lower coefficient of friction means there is less resistance, requiring a lower sliding angle.

How does the force applied to the box affect the sliding angle?

The greater the force applied to the box, the lower the sliding angle will be. This is because the force applied creates a greater horizontal force, overcoming the frictional force and causing the box to slide at a lower angle.

Can the sliding angle be accurately predicted?

The sliding angle cannot be accurately predicted as it depends on various factors such as the weight of the box, the surface material, and the force applied. However, it can be estimated by considering these factors and conducting experiments to determine the sliding angle for a specific scenario.

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