What is the net force on the block immediately after it starts to slide?

[AIMheels22]

Homework Statement

The coefficient of static friction between a block and a horizontal floor is 0.40, while the coefficient of kinetic friction is 0.15. The mass of the block is 5.0 kg. A horizontal force is applied to the block and slowly increased. What is the value of the applied horizontal force at the instant that the block starts to slide?

What is the net force on the block immediately after it starts to slide?

Homework Equations

The Attempt at a Solution

I am absolutely stumped by this problem! After a FBD i don't really know where to start, Please some one help me!

 

[Kurdt]

The instant the block starts to slide the applied force will be equal to the static friction force. How do you work out the static friction force?

 

[nlightner]

I would first start by identifying the given information and any relevant equations that can be used to solve the problem. In this case, we are given the coefficients of static and kinetic friction, the mass of the block, and the fact that a horizontal force is being applied. The relevant equations for this problem are Newton's second law (F=ma) and the equations for friction (Ff=μN).

Next, I would draw a free-body diagram of the block, labeling all the forces acting on it. The applied horizontal force (F) is the only external force acting on the block, while the normal force (N) and the force of friction (Ff) act within the surface of contact between the block and the floor.

To find the value of the applied horizontal force at the instant the block starts to slide, we need to consider the maximum static friction force (Fs) that can be exerted on the block before it starts to move. This can be calculated by multiplying the coefficient of static friction (μs) by the normal force (N).

Once the applied force (F) exceeds the maximum static friction force (Fs), the block will start to slide. At this point, the net force on the block will be the difference between the applied force and the kinetic friction force (Fk), which is calculated by multiplying the coefficient of kinetic friction (μk) by the normal force (N).

Therefore, the net force on the block immediately after it starts to slide is F-Fk. This can also be written as (μsN)-(μkN), which simplifies to N(μs-μk).

In order to solve for the value of the applied force at this instant, we can set this equation equal to zero and solve for F. This gives us F=N(μs-μk). Plugging in the given values of μs, μk, and N, we can calculate the value of F to be 5.88 N.

In conclusion, the net force on the block immediately after it starts to slide is 5.88 N, which is the difference between the applied force and the kinetic friction force.