The force of friction on the crate is equal to the amount of horizontal force you are applying to it, up to a certain limit known as the static friction threshold.
When you apply a horizontal force to the crate, it experiences both your pushing force and the frictional force. The friction force acts in the opposite direction to counteract your push and prevent the crate from sliding. If the crate does not move, it means that the force you are applying is not exceeding the maximum static friction force.
Static friction adjusts in response to the applied force, which means if you are pushing on the crate but it remains stationary, the force of friction is exactly equal to your applied force. For instance, if you are pushing with a force of 10 Newtons, and the crate doesn’t slide, the static friction force is also 10 Newtons.
However, if the pushing force exceeds the maximum static friction force, then the crate will begin to slide, and kinetic friction would take over. The key takeaway here is that as long as the crate remains stationary, the friction force matches the applied force, ensuring that the crate does not move.