When Does Normal Force Equal To $mg$
Can someone once and for all explain when does normal force equal to mg?
I know for sure that when there is no friction, normal force will be equal to mg.But, i encountered some questions when there is some mass on an incline with friction, and then the normal force was the y component of mg.
It does not make sense to me, because as i understood when there is friction, we cannot assume that mg will be equal to normal force.
Normal Force arises due to the Newton’s Third law. Normal Force will be always acting opposite to the force falling on the surface.Normal Force is a reaction force. Remember
Normal force is equal to mg only when the object is placed horizontally, and the force is acting in the direction of the gravitational field.
Now your second question
Here you will see that the weight of the body is passing through the Centre of gravity and acting in direction of the centre of the earth.
But the component of weight on the incline is not mg it is cos component.In order to satisfy the Newton’s third law Normal reaction to the object is the cos component$$N=Wg\cos \theta$$ even if friction is there or not there this will be the same
Normal force $F_N$ is just the force between two surfaces. It’s called “normal” because it acts perpendicular to the surfaces.
Gravitational force is completely unrelated. Gravity always acts with $F_g = -mg$. The minus sign indicates that the force points down.
Tension Or Normal Force
One interesting physics conversation this semester has been about how we categorize forces. One future physics teacher in particular kept being concerned about whether to call something a tension force or a normal force. For example, consider the following situations:
- A chain, consisting of many links, hangs vertically. The very top link has a rope wrapped around it, which keeps the whole chain fixed to the ceiling.
- A rope is wrapped around a box and pulled by a person.
What kind of contact forces act on the top link? What kind of contact forces act on the box?
I think many students learn to associate types of forces with kinds of objects. For example, objects like ropes and strings exert tension forces. Objects like walls, ramps, and tables exert Normal forces. Springs, of course, exert spring forces. This kind of object-focused categorization means having to have a category for forces from a hand, like Applied Force
If this is how you think about forces , both the link and the box have tension forces exerted on them by the ropes, because ropes exert tension forces.
Whats interesting is that this is the complete opposite of what Ive often heard said to students. Students are often told that ropes can only pull, not push.
What Is The Line Of Action Of A Force
The line along which a force acts on an object is called the forces line of action . The point where the force is acting on an object is called the point of application of the force. The force which opposes the relative motion between the surfaces of two objects in contact and acts along the surfaces is called the force of friction.
Galileo experimentally proved that objects that are in motion move with constant speed when there is no force acting on it. He could note that when a sphere rolls down an inclined plane, its speed increases because of the gravitational pull acting on it.
When all the forces acting on an object are balanced, the net force acting is zero. But, if all the forces acting on a body result in an unbalanced force, then the unbalanced force can accelerate the body, which means that a net force acting on a body can either change the magnitude of its velocity or change the direction of its velocity. For example, when many forces act on a body, and the body is found to be at rest, we can conclude that the net force acting on the body is zero.
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Television Resting On A Table
When a television rests on a table, a perpendicular force exists on television. As this force is acting perpendicularly to the surface of television, this force will be none other than a Normal Force.
From the above examples, it is clear that when a force acts in a perpendicular direction, it will be termed a Normal Force.
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Applications In Real Life
In an elevator either stationary or moving at constant velocity, the normal force on the person’s feet balances the person’s weight. In an elevator that is accelerating upward, the normal force is greater than the person’s ground weight and so the person’s perceived weight increases . In an elevator that is accelerating downward, the normal force is less than the person’s ground weight and so a passenger’s perceived weight decreases. If a passenger were to stand on a weighing scale, such as a conventional bathroom scale, while riding the elevator, the scale will be reading the normal force it delivers to the passenger’s feet, and will be different than the person’s ground weight if the elevator cab is accelerating up or down. The weighing scale measures normal force , not gravitational force .
When we define upward to be the positive direction, constructing Newton’s second law and solving for the normal force on a passenger yields the following equation:
When we define the center of the ride to be the positive direction, solving for the normal force on a passenger that is suspended above ground yields the following equation:
Normal Force With Examples
Normal Force:Contact objects exert force to each other because of their weights. In this example, book exerts a force to table because of its weight and table also exerts force to the book. We call this force as normal force which is same in magnitude and opposite in direction with the applied force .For different situations, we say that in general normal force is the reaction to the perpendicular force exerting on it. We will deal with different examples of normal force. Look at the given examples below and follow the steps to understand how can we find normal force for different situations.
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Why Is Normal Force At Inclined Plane Defined The Way It Is
So why is normal force at inclined plane is $mg \cos a$ and friction is $mg \sin a$? I mean, why not vice-versa or why not some other ratio? Where does it come from? I can see that the sum squares of friction and normal force under the root should be equal to $mg$ and the angle at which the plane is inclined has something to do with it.
Does it come from some other part of physics or was it just deduced experimentally? I mean, we could slide a sample block from an inclined plane to see what acceleration it has each time we change the angle.
UPD:Thank you all guys! What I was ultimately asking just seems to be a matter of philosophy. These all formulas are beautiful and seem to be correct. But they are abstractions. And the confidence that this is true ultimately comes from experiments. Since I am very new to physics, I just wanted to know if my assumptions were true.
In vector notation there is only one equation and no ambiguity. The block is in equilibrium so the net force acting on it must be zero. There are three forces acting on the block – its weight $\vec W$, the normal force $\vec N$ and friction $\vec F$. So we have
$\vec W + \vec N + \vec F = 0$
Since $\vec N$ and $\vec F$ are orthogonal to one another it is convenient to resolve the three vectors into components along an $x$ axis that is parallel to $\vec F$ and a $y$ axis that is parallel to $\vec N$. In component form we have
$\vec F = \\ \vec N = \\ \vec W = , -W \cos )$
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Are Normal Force And Weight Always Equal
Normal force and weight aren’t always equal. They’re equal when:
- There are no other forces exerted in the vertical direction and
- An object is on a flat surface.
Normal force and weight are not equal when:
- There’s an additional force that at least in part works in the vertical direction or
- The object is on an inclined surface.
Common Misconception: Normal Force Vs Newton
In this section we have introduced the quantity normal force, which is represented by the variable N N . This should not be confused with the symbol for the newton, which is also represented by the letter N. These symbols are particularly important to distinguish because the units of a normal force ( N
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First The Normal Force
- A normal force is the name we give to the perpendicular force . It is not equal to $mg\cos$ in general. Maybe it is in this specific scenario but that is just a coincidence.
In your specific case where the object is stationary , if you want to calculate the normal force then you will set up Newton’s 1st law in this perpendicular direction. Since only the normal force $n$ and one component of the weight $w$ acts along this direction, then we get:
$$\sum F=0 \quad\Leftrightarrow\quad n-w_\perp=0 \quad\Leftrightarrow\quad n=w_\perp.$$
Now you just need to find the perpendicular component of the weight. That turns out to include the cosine of the angle due to trigonometry: $w_\perp=mg\cos$. If your question is why this cosine appears here, then let me know in the comments and I’ll adjust the answer. So, now we know that
$$n=mg\cos$$
and this is not a feature of the normal force. This is only an expression that holds true in your specific scenario. If other forces acted or if acceleration was present, then this expression would look very different.
Normal Force With Acceleration
All of our previous examples have had boxes standing still. If a box moves horizontally and the normal force acts vertically, the movement of the box won’t affect the normal force because they are on separate axes. However, what happens if the box moves in the same direction as the normal force? Let’s say our box is in an elevator. The box weighs, and the elevator accelerates down at. What is the normal force?
Free-body diagram of the box in the elevator, StudySmarter Originals
We drew our free-body diagram in the image above. Now we can use Newton’s Second Law in the vertical direction to solve for the normal force, and this time we will include the downward acceleration.
The normal force is
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What Is Normal Force
Normal Force is a perpendicular force that a surface exterts on an object. For Example if we place an object on a table the gravitational force will pull the object donwards. In order to prevent the object from falling the table will exert certain force to prevent it from falling. This force is known as Normal Force and is denoted by FN or N. Normal Force units are Newton.
Notation For Normal Forces
In this course, we will give normal forces a special symbol. Instead of writing F with two subscripts, we will generally write N with two subscripts. The subscripts will still indicate the target and the source of the force, respectively. We will discuss the reason for this special notation when we introduce the full form of the contact force.
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Tension In A Rope And Normal Force
A wooden box with a mass of 22kg and weight of 216N, is pulled at a constant speed with a rope that makes an angle of 37deg with the wooden floor. A frictional force of 100N resists the motion. What is the tension in the rope and the normal force?
The tension, T, has a horizontal component and a vertical component. The horizontal component is equal to the 100 N or T x cos 37 = 100N. Solving for T gives 125 N. The normal force is the weight of the box minus the upward vertical component of the tension. The equation for this is FN = W -T x sin37 where FN is the normal force, W is the weight , and T is the tension previously calculated. I got 141 N for FN.
Normal Force With An External Downward Force
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Normal Force As Constraint
The normal force is a constraint force, as is tension. It takes on whatever value is necessary to ensure that the objects in contact will not move into each other. This implies that the normal force constrains the motions of these objects so that they have the same velocity component perpendicular to the surface and will therefore remain in contact without getting closer or farther from each other. Thus when objects are in contact, the contact force will generate a force to cause the appropriate acceleration to change their velocities so they don’t interpenetrate. Thus there is no “force law” for normal forces – the normal force must be found using Newton’s second law and determining the acceleration of the objects from their motion. To clarify this point, consider the following examples:
Stationary Horizontal Surface Pushing a boxVertically Accelerating Horizontal Surface Box on an elevator accelerating upwards
Horizontally Moving Horizontal SurfaceAn object in contact with a horizontal surface that is moving horizontally like the bed of a moving pickup truck is constrained to have have zero vertical acceleration, but might not have the same horizontal acceleration as the truck . The truck and the object are not required to have the same total acceleration, but will have the same vertical component. |