# Why doesn't weight work perpendicular?

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weight is the force of a body on a surface or on a rope. So why isn't it always perpendiculair to the surface, for example in a slope. When a slope is so steep that it's vertical, there is no weight. But when the slope is a little diagonal you talk about a weight (which faces down(to the center of the earth)) and a perpendiculair component of weight. The perpendiculair weight is equal to the normal force. But if the definition of weight is the force on a surface to remain it's height, why isn't weight (in contrast to gravityforce) always perpendiculair?

this question can also be stated in a different way: is the normal force always eqeal to the weight?

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## Answers and Replies

Merlin3189
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You have a misconception of weight.
Weight means the gravitational force on a mass and it is always vertically down.

Normal force is by definition perpendicular to the surface.

The normal force of a surface on an object is always equal and opposite to the force of the object on the surface. If that is caused by weight, the the force of the object on the surface is equal to the component of weight perpendicular to the surface.

The normal force is only(2) equal to the weight only(1) when the surface is horizontal. [For clarity I use only twice: 1 is grammatically correct, 2 is common usage.]

• PhanthomJay
You have a misconception of weight.
Weight means the gravitational force on a mass and it is always vertically down.

Doesn't that sentence contradict itselve?
because if it means weight is gravitational force on a mass, then it shouldn't always be down. For example on a slope, when a slope is 100% vertical, there is no weight (no gravitational force on mass, only gravity). But when the slope is a little more diagonal, there is a very small force on the slopes surface. This force is weight (gravitational force on mass), the other let's say 99% doesn't make force against the slopes surface, so isn't part of the weight.

It's only a matter of definion, in the same way that aeroplaines don't have weight when flying.

Merlin3189
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No.
Even on a vertical wall, the weight of an object is vertically down.
Aeroplanes have the same weight when flying, just as they have on the ground (except for any burnt fuel!)

Edit: we measure vertical by hanging a mass and seeing which way it is pulled by its weight.

No.
Even on a vertical wall, the weight of an object is vertically down.
Aeroplanes have the same weight when flying, just as they have on the ground (except for any burnt fuel!)

Edit: we measure vertical by hanging a mass and seeing which way it is pulled by its weight.

Not to annoy you, but how do you explain the definition of weight as a force? The definition of weight is (I assume) a force on a mass, thereby weight increases when an elevator goes up and decreases when it's going down. And when there is no surface or rope pulling on you, there is no weight. Thereby calling you weightless (or when a plane drops quickly. I know it's more of a simantic discussion rather than a physical one, but still...

Merlin3189
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No annoyance, you're welcome to ask anything.
You have a false definition of weight.
Look here for a definition of weight in Hyperphysics.

As you say, we are getting into a semantic discussion when we start talking about satellites being weightless or planes diving to give you the sensation of weightlessness. In Physics you are getting into considerations of frames of reference.
From the perspective of Earth, aeroplanes and satellites have weight. To someone moving in the accelerated frame of reference of a satellite or aeroplane accelerating downwards, things may look different. Our mass on a slope is far from that.

• PhanthomJay
SteamKing
Staff Emeritus
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Doesn't that sentence contradict itselve?
because if it means weight is gravitational force on a mass, then it shouldn't always be down. For example on a slope, when a slope is 100% vertical, there is no weight (no gravitational force on mass, only gravity). But when the slope is a little more diagonal, there is a very small force on the slopes surface. This force is weight (gravitational force on mass), the other let's say 99% doesn't make force against the slopes surface, so isn't part of the weight.

It's only a matter of definion, in the same way that aeroplaines don't have weight when flying.

That's news to aeroplanes. They're not weightless; the lift generated by the wings when flying offsets the weight of the aircraft, which allows the plane to stay aloft.

Haven't you ever seen the following diagram? robphy
Science Advisor
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Weight is the gravitational force applied by the earth on the object. It is a force directed towards towards the center of the earth.

A scale that you step on actually measures a normal force, the upward force that must be applied to satisfy Newton's second law.

If your scale is horizontal and you stand in equilibrium on your scale, with no other forces applied on you,
then the scale reading is equal to the magnitude of your weight. Draw free body diagram and use Newton's Second and Third Laws.

If you stood in equilibrium on a scale at the bottom of a pool,
the scale would read less than your weight (since there is an upward buoyant force on you applied by the water).
Your apparent weight is lower than your actual weight.

If you stand on a scale sitting on an elevator, and you are all in equilibrium... the scale reading equals your weight.
If the elevator cable is suddenly cut, then the scale reads zero... since the normal force the scale must apply to satisfy Newton's Second Law is zero.
Your apparent weight is zero... although the earth still applies the same gravitational force on you, directed toward the center of the earth.

• PhanthomJay
All good stuff. In the case of a weight on a slope, that weight (or force) can be broken into two components mathematically. One component of the weight can be resolved as a force perpendicular to the surface of the slope. This is the normal force. There is another component acting parallel to the sloped surface. This is the component that causes a ball to roll down a slope.

So gravity always pulls a mass straight toward the Earth, but that force can be resolved into components the mass isn't sitting on a level surface.

robphy
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All good stuff. In the case of a weight on a slope, that weight (or force) can be broken into two components mathematically. One component of the weight can be resolved as a force perpendicular to the surface of the slope. This is the normal force.

I think it's more correct to say that
the "normal force (applied by the surface)"
balances
this "component of the weight [applied by the earth]... perpendicular to the surface of the slope".

I think simple. The component forces come from the mass of the object sitting on the slope. Either way works as long as your signs (+ or -) are kept straight.

robphy
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I think simple. The component forces come from the mass of the object sitting on the slope. Either way works as long as your signs (+ or -) are kept straight.

I think it's very important to identify the "source of the force" on the object.

ehild
Homework Helper
There are different definitions of weight. One is the force of gravity on the object.
The other, as it is taught in my country, "weight is the force an object exerts on a horizontal support or a vertical suspension.", This definition is related to the way as weight is measured with scales. In this sense, the objects inside a space station are weightless, and you feel weightless in a lift of free fall, although the force off gravity is mg.
The weight is not the normal force in general. The normal force on a slope is not the weight.The normal force is the force the surface exerts on the body. It is equal to the normal component of mg if the slope is in rest.
https://en.wikipedia.org/wiki/Weight