A crate sits on the ground. You push as hard as you can on it, but you cannot move it. At any given time when you are pushing, what is the magnitude of the static frictional force exerted on the crate compared to the magnitude of your push

Equal magnitude

Explanation:

Static friction is the friction that exists between the stationary crate and the ground on which it's resting. static friction force is variable and depends on the external forces acting on an object. The higher the external force the higher the static friction until the crate starts moving when kinetic friction takes over.

For a stationary crate;

Static friction = external force exerted on the crate

Fₛ ≤ μₛ×N

Fₛ(max) ≤ μₛ×N

Where;

Fₛ = static friction force

μₛ = coefficient of static friction

N = weight of crate

Therefore,the magnitude of the static frictional force exerted on the stationary crate must be equal to the magnitude of your push.