Welcome to Electro-Online. Our second video shows something slightly different from the first video. The forces applied to the block are no longer horizontal.
Here we have a vertical force and here we have forces applied at an angle. On the vertical force, this is kind of an interesting situation. Obviously the block will not be moving because there's no forces acting in the horizontal direction. We do have a potential for the maximum friction force pushing back this way.
but since there's no forces activating the friction force in this case the friction force actual will be zero even though there's a potential to have the maximum friction force acting on the block which is equal to the normal force times the coefficient of static friction now notice that the normal force is going to be the same as the reaction force because forces only act downward and in this case the normal force is not simply the weight of the block but the weight of the block plus the force acting on the block at the top so the reaction force is simply the sum of those two forces but of course no motion on the block here we have a force acting at a slant at an angle which means there's a horizontal component and a vertical component of the applied force the vertical component will do the same thing as this force right here it will add to the weight acting down on the surface between the block and the the surface here and you can then see that the normal force is going to be equal to the sum of the weight of the block plus the y component of the applied force so the normal force will be bigger than it normally would be if it's only counteracting the weight of the block now you can see that the normal force is no longer equal to the reaction force as it is in this first example that is because there's also a horizontal component which means This will then be counteracted by the friction force pushing in the opposite direction. The reaction force will be the vector sum of the normal force plus the friction force pushing back. Notice that even though the maximum friction force can be this large, the actual friction force is only equal to the x component of the force applied on the block. And so you can see that this will then be the vector sum equal to the reaction force acting on the block. If we draw a diagram like this with all the forces acting on the block, downward we have the weight plus the y-component of the applied force.
In the horizontal direction, we have the x-component of the force, which of course will be counteracted by the friction force right here, which is part of the reaction force, which pushes back this way and pushes back this way, so it's the vector sum of the friction force and the normal force. Again, notice the normal force is the sum of these two components here. Notice on the next example we now have what we call the maximum applied force in the x-direction without the block actually moving.
If the force in the x-direction now equals the maximum friction force, the block will be on the verge of moving. Any additional force applied in the horizontal direction will cause the block to move forward. Now you can see that the friction force pushing back is equal to the maximum friction force, which is equal to the x-component of the applied force.
The y-component is still added to the weight and that's then counteracted by the normal force pushing back in the upward direction the weight plus the y component of that force and the friction force equals the x component of the force and then of course the reaction force is simply the vector sum of those two components notice now that the reaction force has a greater angle because this component is now larger and finally once we get the block moving the maximum friction force can now be not quite as large as before because Instead of having the static coefficient of friction, we now have the kinetic coefficient of friction. Notice here the friction force is the normal force times mu sub s, the static coefficient of friction. Here the friction force equals the normal force times the kinetic coefficient of friction. Notice the angle is now smaller because this component now is smaller as well. Again, f of x, in this case, the x component of the force applied on the block.
equals the friction force equals the maximum friction force that you can have under a moving condition. And so you can see now that this angle then again is smaller. But the big difference here is that the normal force no longer equals simply the weight of the block, but the weight plus the vertical component of the force applied on the block.
And that's how we know the difference.