There are a number of forces that act in a wide variety of cases andhave been given specific names. Some of these, like friction and thenormal force, are so common that we’re hardly aware of them asdistinctive forces. It’s important that you understand how and whenthese forces function, because questions on
SAT II Physics often makeno mention of them explicitly, but expect you to factor them into yourcalculations. Some of these forces will also play an important role inthe chapter on special problems in mechanics.
Weight
Although the words weight and mass areoften interchangeable in everyday language, these words refer to twodifferent quantities in physics. The mass of an object is a property ofthe object itself, which reflects its resistance to being accelerated.The weight of an object is a measure of the gravitational force beingexerted upon it, and so it varies depending on the gravitational forceacting on the object. Mass is a scalar quantity measured in kilograms,while weight is a vector quantity measuring force, and is representedin newtons. Although an object’s mass never changes, its weight dependson the force of gravity in the object’s environment.
For example, a 10 kg mass has a different weight on the moon than it does on Earth. According to Newton’s Second Law, the weight of a 10 kg mass on Earth is
This force is directed toward the center ofthe Earth. On the moon, the acceleration due to gravity is roughlyone-sixth that on Earth. Therefore, the weight of a 10 kg mass on the moon is only about 16.3 N toward the center of the moon.
The Normal Force
The
normal force always actsperpendicular (or “normal”) to the surface of contact between twoobjects. The normal force is a direct consequence of Newton’s ThirdLaw. Consider the example of a 10 kg box resting on the floor. Theforce of gravity causes the box to push down upon the ground with aforce,
W, equal to the box’s weight. Newton’s Third Law dictates that the floor must apply an equal and opposite force,
N = –
W,to the box. As a result, the net force on the box is zero, and, as wewould expect, the box remains at rest. If there were no normal forcepushing the box upward, there would be a net force acting downward onthe box, and the box would accelerate downward
Be careful not to confuse the normal force vector
N withthe abbreviation for newtons, N. It can be a bit confusing that bothare denoted by the same letter of the alphabet, but they are twototally different entities.
Example
A person pushes downward on a box of weight W with a force F. What is the normal force, N, acting on the box?
The total force pushing the box toward the ground is
W +
F. From Newton’s Third Law, the normal force exerted on the box by the floor has the same magnitude as
W +
F but is directed upward. Therefore, the net force on the box is zero and the box remains at rest.
Friction
Newton’s First Law tells us that objects inmotion stay in motion unless a force is acting upon them, butexperience tells us that when we slide coins across a table, or pushboxes along the floor, they slow down and come to a stop. This is notevidence that Newton was wrong; rather, it shows that there is a forceacting upon the coin or the box to slow its motion. This is the forceof
friction, which is at work in every medium but a vacuum, andis the bugbear of students pushing boxes across the sticky floors ofdorm rooms everywhere.
Roughly speaking, frictional forces are causedby the roughness of the materials in contact, deformations in thematerials, and molecular attraction between materials. You needn’tworry too much over the causes of friction, though: SAT II Physicsisn’t going to test you on them. The most important thing to rememberabout frictional forces is that they are always parallel to the planeof contact between two surfaces, and opposite to the direction that theobject is being pushed or pulled.
There are two main types of friction:
static friction and
kinetic friction.Kinetic friction is the force between two surfaces moving relative toone another, whereas static friction is the force between two surfacesthat are not moving relative to one another.
Static Friction
Imagine, once more, that you are pushing a boxalong a floor. When the box is at rest, it takes some effort to get itto start moving at all. That’s because the force of static friction isresisting your push and
holding the box in place.
In the diagram above, the weight and the normal force are represented as
W and
N respectively, and the force applied to the box is denoted by
. The force of static friction is represented by
, where
.The net force on the box is zero, and so the box does not move. This iswhat happens when you are pushing on the box, but not hard enough tomake it budge.
Static friction is only at work when the net force on an object is zero, and hence when
.If there is a net force on the object, then that object will be inmotion, and kinetic rather than static friction will oppose its motion.
Kinetic Friction
The force of static friction will onlyoppose a push up to a point. Once you exert a strong enough force, thebox will begin to move. However, you still have to keep pushing with astrong, steady force to keep it moving along, and the box will quicklyslide to a stop if you quit pushing. That’s because the force ofkinetic friction is pushing in the opposite direction of the motion ofthe box, trying to bring it to rest.
Though the force of kinetic friction willalways act in the opposite direction of the force of the push, it neednot be equal in magnitude to the force of the push. In the diagramabove, the magnitude of
is less than the magnitude of
.That means that the box has a net force in the direction of the push,and the box accelerates forward. The box is moving at velocity
v in the diagram, and will speed up if the same force is steadily applied to it. If
were equal to
, the net force acting on the box would be zero, and the box would move at a steady velocity of
v,since Newton’s First Law tells us that an object in motion will remainin motion if there is no net force acting on it. If the magnitude of
were less than the magnitude of
, the net force would be acting against the motion, and the box would slow down until it came to a rest.
The Coefficients of Friction
The amount of force needed to overcome theforce of static friction on an object, and the magnitude of the forceof kinetic friction on an object, are both proportional to the normalforce acting on the object in question. We can express thisproportionality mathematically as follows:
where
is the
coefficient of kinetic friction,
is the
coefficient of static friction, and
Nis the magnitude of the normal force. The coefficients of kinetic andstatic friction are constants of proportionality that vary from objectto object.
Note that the equation for static friction is for the
maximumvalue of the static friction. This is because the force of staticfriction is never
greater than the force pushing on an object. If a boxhas a mass of 10 kg and
= 0.5, then:
If you push this box with a force less than 49 newtons, the box will not move, and consequently the net force on the box must be zero. If an applied force
is less than
, then
= –
.
Three Reminders
Whenever you need to calculate a frictional force on SAT II Physics, you will be told the value of
, which will fall between 0 and 1. Three things are worth noting about frictional forces:
- The smaller µ is, the more slippery the surface. For instance, ice will have much lower coefficients of friction than Velcro. In cases where
, the force of friction is zero, which is the case on ideal frictionless surfaces. - The coefficient of kinetic friction is smaller than the coefficient of static friction.That means it takes more force to start a stationary object moving thanto keep it in motion. The reverse would be illogical: imagine if youcould push on an object with a force greater than the maximum force ofstatic friction but less than the force of kinetic friction. That wouldmean you could push it hard enough to get it to start moving, but assoon as it starts moving, the force of kinetic friction would push itbackward.
- Frictional forces are directly proportional to the normal force.That’s why it’s harder to slide a heavy object along the floor than alight one. A light coin can slide several meters across a table becausethe kinetic friction, proportional to the normal force, is quite small.
Example
A student pushes a box that weighs 15 N with a force of 10 N at a 60ºangle to the perpendicular. The maximum coefficient of static frictionbetween the box and the floor is 0.4.Does the box move? Note that sin60º = 0.866 and cos 60º = 0.500.
In order to solve this problem, we have to determine whether the horizontal component of
is of greater magnitude than the maximum force of static friction.
We can break the
vector into horizontal and vertical components. The vertical componentwill push the box harder into the floor, increasing the normal force,while the horizontal component will push against the force of staticfriction. First, let’s calculate the vertical component of the force sothat we can determine the normal force,
N, of the box:
If we add this force to the weight of the box, we find that the normal force is 15 + 5.0 = 20 N. Thus, the maximum force of static friction is:
The force pushing the box forward is the horizontal component of
, which is:
As we can see, this force is just slightlygreater than the maximum force of static friction opposing the push, sothe box will slide forward.
Tension
Consider a box being pulled by a rope. Theperson pulling one end of the rope is not in contact with the box, yetwe know from experience that the box will move in the direction thatthe rope is pulled. This occurs because the force the person exerts onthe rope is transmitted to the box.
The force exerted on the box from the rope is called the
tensionforce, and comes into play whenever a force is transmitted across arope or a cable. The free-body diagram below shows us a box beingpulled by a rope, where
W is the weight of the box,
N is the normal force,
T is the tension force, and
is the frictional force.
In cases like the diagram above, it’s veryeasy to deal with the force of tension by treating the situation justas if there were somebody behind the box pushing on it. We’ll find theforce of tension coming up quite a bit in the chapter on specialproblems in mechanics, particularly when we deal with pulleys.
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本帖最后由 端木·宇 于 2008-6-19 20:12 编辑 ]
