Question

It's been a long time since I did problems on friction but here's one...

Consider a cuboidal block of dimensions 123 meters with a total mass of 1 kg. There are 3 cases that we need to look at:
Its base of area 1*2 sq. meters is in contact with the surface
Its base of area 1*3 sq. meters is in contact with the surface
Its base of area 2*3 sq. meters is in contact with the surface
for all the above cases, the coefficient of friction (μ) is a constant. the normal force (N) is also the same since the weight of the block is the same and N
has to equal the downward acting force mg since f=μN
, that means the friction force is the same in each of the three cases.
That means the friction force is independent of the orientation of the block!? But that doesn't make sense... with a larger contact area friction should intuitively increase. If friction doesn't, what does? And does the contact area even matter then?

Answer 1

The friction force is independent of the orientation of the block, but the maximum friction force can vary based on the contact area.

Step-by-step explanation:

The force of friction between surfaces depends on several factors, including the coefficient of friction and the normal force. The coefficient of friction is a measure of the roughness or smoothness of the surfaces in contact, and it is different for different combinations of materials. The normal force is the force exerted perpendicular to the surface, which is equal to the weight of the object. In the three cases described, the coefficient of friction and the normal force are the same, so the friction force is the same in each case.

However, the contact area does play a role in determining the maximum friction force that can be exerted. The maximum friction force is given by the equation fs(max) = μsN, where fs(max) is the maximum friction force, μs is the coefficient of static friction, and N is the normal force. As the contact area increases, the normal force increases, and therefore, the maximum friction force also increases. So, while the friction force is the same in each case, the maximum friction force can differ based on the contact area.

In summary, the friction force is independent of the orientation of the block, but the maximum friction force can vary based on the contact area. Other factors, such as the weight of the object and the coefficient of friction, also influence the friction force.