Consider the following:

 

Two objects rest on a wooden plank. One object is twice as heavy as the other.

The heavier object is designated "H" while the lighter object is designated "L."

 

A rope is attached to the center of the plank. A crane hoists the rope.

Obviously, the plank will tilt.

 

Which object will begin to slide first?

 

The answer, which I found via the static friction coefficent formula (below), is that both objects will begin to slide at the same time.

 

However, why is this the case? Doesn't inertia (the tendancy of objects to resist changes in motion) play into this scenario? While mass does not have an effect on friction, it certainly plays a role in inertia (Newton's First Law).

 

 

 

 

 

 

 

u_s = Static Friction Coefficient

F_fs = Force of Static Friction

Fn= Normal Force

 

u_s = | F_fs | / | F_n |

Friction will be proportional to the weight, but then (trivially), so is the weight, a component of which will induce the sliding. So you have an equation that looks something like umg cos(theta)= mg sin(theta) as the condition where sliding begins. mg cancels. The resistance to acceleration is bigger but so is the force inducing the motion. Much like how g can be constant — if mass goes up the force goes up just as fast as the resistance to acceleration.

 

One issue with arguing inertia here is that friction isn't a fixed-value force. If the block is just sitting there, the frictional force has a value. If you push on the block along the plane of the plank (i.e. no change in the normal force), the block may not accelerate, which means you will have a different frictional force. The implied inequality of the net force equation may make it harder to distill the idea of inertia in the problem.

Friction will be proportional to the weight, but then (trivially), so is the weight, a component of which will induce the sliding. So you have an equation that looks something like umg cos(theta)= mg sin(theta) as the condition where sliding begins. mg cancels. The resistance to acceleration is bigger but so is the force inducing the motion. Much like how g can be constant — if mass goes up the force goes up just as fast as the resistance to acceleration.

 

One issue with arguing inertia here is that friction isn't a fixed-value force. If the block is just sitting there, the frictional force has a value. If you push on the block along the plane of the plank (i.e. no change in the normal force), the block may not accelerate, which means you will have a different frictional force. The implied inequality of the net force equation may make it harder to distill the idea of inertia in the problem.

 

Uhhh...

I have no idea what you just said. It was very oddly worded. No offence.