When the child pushes the heavy couch with all her strength for 15 seconds, the couch does not move because of the strong static friction between the couch and the floor, the weight of the couch, the couch's inertia, and the possibility of insufficient force to overcome these factors.
When the small child pushes on the large couch with all her strength for a period of 15 seconds and it doesn't move, there are a few reasons why this might be happening:
1. Friction: The couch and the floor exert a force called friction, which opposes the motion between them. In this case, the static friction between the couch and the floor is greater than the force applied by the child. Static friction is the friction force between two surfaces that are not moving relative to each other. So, despite the child's effort, the couch remains stationary due to the strong static friction acting against her push.
2. Weight of the couch: The couch is heavier than the child, which means it has a greater gravitational force pulling it downwards. The weight of the couch adds to the force of static friction, making it more difficult to overcome.
3. Inertia: The couch has inertia, which is the tendency of an object to resist changes in its motion. Since the couch is initially at rest, it requires a greater force to overcome its inertia and start moving. The force applied by the child may not be sufficient to overcome the couch's inertia.
4. Insufficient force: It is possible that the force applied by the child is simply not strong enough to move the couch. Pushing with all her strength may still not be enough to overcome the static friction and move the heavy couch.