The Force Diagram provided for a crate shows balanced forces: oppositely-directed forces are of equal strength. This will always be the case for an object that moves with a constant velocity as is the case for this crate that is being pushed by a worker. But you need to determine what the Force Diagram looks like if the worker stops pushing the crate and the leftward-moving crate begins to slow down. To do so, you should first determine the direction of the acceleration. If the acceleration is rightwards, then there is a net, unbalanced force to the right. But if the acceleration is leftwards, then there would be a net, unbalanced force to the left. Read on ...
The Direction of the Acceleration
The direction of an object's acceleration depends on two important features of the object's motion - the direction that the object is moving and whether the object is speeding up or slowing down.
The general rule is: If an object is slowing down, then the direction of the object's acceleration is the
opposite of the direction that the object is moving. On the other hand, if the object is speeding up, then the direction of the object's acceleration is the same as the direction that the object is moving.
Now apply this information to the crate and determine the direction of its acceleration.
Beware of Misconceptions
A common misconception that a Physics student may have is to believe that forces are associated with the direction that an object is moving. That is, students falsely believe that an object that is moving leftward must first of all have a leftward force; and second, that the strength of that leftward force must be greater than any rightward force. But we doubt that you've been taught that way ... at least not by a card-carrying Physics teacher. The fact is that forces are associated with accelerations or changes in the velocity. Forces don't cause objects to move in a given direction. Forces cause objects to change how they are moving in a given direction.
You want to determine the Force Diagram for a crate that is moving leftwards and slowing down. You're probably paying attention to the moving leftwards part ... but don't miss the slowing down part. The slowing down part describes the change that is occuring. Forces when unbalanced cause objects to change the way they are moving. The crate was moving with a constant speed, When it changes to a slowing down motion, you must make sure there is more force against its motion than there is force in the direction of its motion. And don't even presume that there even needs to be a leftward force.
What Happens to the Leftward Force?
When the crate was being pushed, there was a leftward applied force (Fapp). This is the force of the worker pusihing forward on the crate. The force originates from the contact between the worker and the crate. When the worker stops pushing the crate, this forward (i.e., leftward) force is no longer present. Your Force Diagram should not show an applied force (Fapp).
What's the Rub on Friction?
When the crate was being pushed at a constant speed, there was a friction force (Ffrict) acting on it. The friction wasn't caused by the pushing; it was caused by the moving. The fact that the crate's surface was moving across the floor surface caused a frictioni force. We typically refer to this as a sliding friction force and it results when two surfaces that are pressed together (in contact) are moving relative to one another. When the worker stops pushing, the crate continues in motion ... only with a slowing down motion. But the fact that the surfaces -floor and crate bottom - are still moving past one another means that there will still be a friction force (Ffrict) directed opposite of the crate's motion.
Think Interactions ... Always!
Forces result from mutual interactions between two objects. To determine the forces that act upon the crate, ask what objects are the crate interacting with? The crate (as always) interacts with the Earth through gravitational forces between the crate the Earth. The crate pulls up on the Earth and the Earth pulls down on the crate. This is the gravity force (Fgrav). But the crate also interacts with the floor. It presses down on the floor and the floor presses or pushes up on the crate. This is the normal force (Fnorm). Finally, as the crate slides to the left across the floor, it pulls the floor to the left and the floor pulls the crate to the right. This is the rightward friction force (Ffrict) on the crate. Since the crate does not touch or interact with any other object, these are the only forces acting upon the crate.