A block initially at rest is given a quick push by Vrctnid. The block slides across the floor, gradually slows down, and comes to rest. In the spaces provided, draw and label separate free-body diagrams for the block at each of the three instants shown. (Initially at rest) Quick push by Vrctnid The sliding block slows down And is finally at rest Rank the magnitudes of all the horizontal forces in the diagram for each instant. Explain: Are any of the forces that you drew for instant 1 missing from your diagram for instant 2? Explain how you knew. Are any of the forces that you drew for instant 2 missing from your diagram for instant 3? Explain how you knew.
The Correct Answer and Explanation is:
To analyze the forces acting on the block during its motion, let’s break it down into three distinct instants:
Instant 1: Initially at Rest
At this point, the block is at rest before the push by Vrctnid. The forces acting on the block are:
- Normal Force (N): Acts vertically upward, exerted by the surface to counteract gravity.
- Gravitational Force (mg): Acts vertically downward due to the mass of the block.
- Force from Vrctnid (F_push): A horizontal force applied by Vrctnid in the direction of the push.
Since the block is at rest initially, there is no friction force yet acting on it because it hasn’t started to slide.
Horizontal Force Magnitudes:
At this instant, the only horizontal force is the force applied by Vrctnid (F_push).
Instant 2: The Block is Sliding and Slowing Down
At this point, the block has started to slide across the floor but is slowing down, indicating the presence of friction.
- Normal Force (N): The normal force remains the same as in Instant 1, acting upward.
- Gravitational Force (mg): Also remains the same, acting downward.
- Applied Force (F_push): The force from Vrctnid is still acting in the horizontal direction, but it may have decreased in magnitude if the push was not continuous.
- Frictional Force (f_friction): A force of friction is acting opposite to the direction of motion, trying to resist the sliding of the block. This force is responsible for the block slowing down.
In this instant, the horizontal forces are now F_push (acting in the direction of the push) and f_friction (acting opposite to the motion).
Horizontal Force Magnitudes:
The magnitude of F_push is likely smaller than it was in Instant 1, and f_friction has now appeared as a resisting force.
Instant 3: The Block Comes to Rest
At this point, the block has slowed down and finally comes to rest.
- Normal Force (N): The normal force continues to act upward.
- Gravitational Force (mg): Continues acting downward.
- Frictional Force (f_friction): The block is still under the influence of friction, which is now the only horizontal force acting. It has decelerated the block to a stop.
Horizontal Force Magnitudes:
Now, the horizontal force F_push has disappeared since there is no longer any applied push. Only f_friction remains, acting in the opposite direction of motion.
Are any forces missing from the diagrams across the instants?
- From Instant 1 to Instant 2: The frictional force appears in Instant 2 because, as soon as the block starts sliding, friction begins to resist its motion. This force was not present in Instant 1 since the block was at rest.
- From Instant 2 to Instant 3: In Instant 3, the F_push force disappears, as the applied push is no longer acting. The only horizontal force left is f_friction, which has been responsible for stopping the block.
Ranking the Magnitudes of the Horizontal Forces:
- Instant 1: The horizontal force is F_push, which is the largest horizontal force acting at this moment.
- Instant 2: Both F_push and f_friction are present, but F_push is smaller than it was initially, and f_friction has begun to resist the motion.
- Instant 3: Only f_friction remains, which is now the only horizontal force acting.
In summary:
- Instant 1: F_push dominates the horizontal forces.
- Instant 2: F_push and f_friction are in balance, with f_friction gradually increasing.
- Instant 3: f_friction is the only force, as the block comes to rest.
