Free Body Diagrams Introduction
From MyMCAT
Contents |
Introduction
In the previous section, Newton's Laws Introduction, we discussed the three fundamental laws of force and how they affect the acceleration of an object. These laws can be used to study complex systems of multiple forces acting on objects to generate free body diagrams which describe just how all the forces are related in a system.
A Freefalling Mass
Consider a block dropped out of a plane. Initially we know there is one force acting on it, gravity, thus the block is being pulled down because the net force is down.
As the block continues to fall however, its acceleration slows. The net force is still down as there is still acceleration, but some other force must be acting in the opposite direction reducing the overall magnitude of the net force. If we think about this, air resistance is the most probable reason as the faster the object goes the stronger the resistance.
At some later time point, the acceleration of the object will reduce all the way to zero. At this point, the object is still falling downwards (as it still has velocity), but its speed will remain constant. In this case, the gravitational force downwards will be exactly equal to the air resistance. Here, we say that the net force is zero, as the internal forces acting on it (gravity and air resistance) are equal and opposite and thus cancel each other out.
A Resting Mass
Now lets consider a box resting on the ground. We already know one force acting on it, gravity. But if this were the only force, what should happen to the box? Well, according to Newton's second law, the net force would be downwards (in the direction of gravity) and the box should accelerate into the ground. But this does not happen, thus there must be a second force acting upwards preventing the box from "falling" into the ground. This force is called the normal force, and is a result of Newton's third law.
Because the box is not accelerating, we know the two forces acting on it are equal in magnitude and opposite in direction.
Friction
Let us consider the same box, only this time it is sliding along the ground. As it slides friction slows the box until it comes to a stop. Again, the box is neither going up or down, thus gravity and the normal force must be equal. The box however is decelerating, thus its net force must be nonzero. In this case, the friction force is causing a deceleration (or an acceleration in the opposite direction of movement).
Interestingly, the force of friction is related to the normal force by the following formula.
This should make sense as heavier objects have a larger mass ( and thus a larger force of gravity and equal normal force) causing a larger friction force. So heavier objects are harder to push along the ground because friction is stronger. Note that kinetic friction always acts in the direction opposite of movement so that the object will eventually slow to a halt if no other forces are applied.
When an object is not moving and resists movement when a force is applied to it, it is the force of static friction which is preventing its movement. Where kinetic friction acts to slow a moving object, static friction acts to keep an object stationary when an external force is applied. Interestingly, static friction is always stronger than kinetic friction, this is why it is often difficult to get an object moving, but once it is in motion it is easier to keep moving.
See the section of friction for a move detailed look at these effects.
An Incline
Now let us consider the same block on a frictionless incline. Gravity still pulls straightdown, but in what direction is the normal force? The normal force always exerts itself perpendicular to the surface which is making contact, thus it is angled up to the side 90 degrees from the incline.
If we now consider what the net force is, well there is clearly an overall force in the direction of the downhill and this is exactly which way the block will slide.
Lets take this a step further now and consider the same system but with friction such that the block is not sliding. All the forces must sum to zero and thus, as we would expect, there must be an extra force preventing the block from sliding down, this extra force is the friction force. The only way for this block to stay motionless is if friction is equal to the force component that was oriented down the slope, which must be some fraction of gravity.
If we draw a right triangle we can determine exactly what the relationships are between the forces. Firstly, we have mg going straight down forming the hypotenuse of the triangle. Thus the component which is perpendicular to the incline is mgcos(x). From the third law, we know that this must be equal to the normal force because they are equal and opposite. Finally, the component in the direction of the incline, mgsin(x), must be equal to that of the static friction holding the block in place because it is not moving. Thus in that direction mgsin(x) = Ff.
Alternatively, we could have determined the force of friction from the normal force if we knew the coefficient of static friction in the above example.
