Please explain normal force?

Question

If I put a static mass on a scale, the weight of the mass will exert a force (mg) on the scale to give a reading. But, at the same time, the scale should also exert the same magnitude of normal force on the mass. Therefore, the resultant force should be zero and so no reading should be obtained. (Obviously, I am wrong)

Anyone please explain to me because it is so confusing.

Answer 1

You are right ... the resultant force in this configuration is zero. However, the scale does not give you the resultant force. It is, by itself, calibrated to measure how much force is being exerted on it .

Answer 2

You are right, the resultant force should be zero or you would keep going down. How ever when you just stepped on the scale, that resultant force was not zero, and you did "fall" down a little bit, enough to make the spring or whatever mechanism of the scale deformed and react to your weight. In fact, a scale does not measure how much you weigh directly, but instead it measures how much its system is deformed, and thereby the reaction it applies on you. As Newton's third law state, once you are in equilibrum (that is when the resultant force equals zero), the reading of the reaction is exactly the measure of your weight.

Answer 3

Let's assume your scale is based on a spring, where W = mg is your weight for a mass m.  F = kdX is the equal but opposite force exerted by the spring.  As you are not accelerating when standing on the scale, we can assert that W = F so that W - F = W - kdX = 0 = ma where a, the acceleration, is zero.

W - kdX = 0 means your weight is offset by the equal and opposite force of the spring.  But the dial on your scale is keyed to the dX, the more dX is compressed the higher your spring based scale will read.  The point is this, yes there is an equal but opposite force, but it's that force that causes the scale to read whatever the weight might be.

Modern scales use electronics to do the same thing the old fashion spring scale did.  But it's still the equal but opposite force that is read.

Answer 4

every force has a equal and opposite reaction right?

so why do things move??

well...

difference in forces result in accelerations. things can be moving at constant velocity, which means forces are balanced.

if you step on a scale you have W acting downwards and R acting upwards. the reaction force (R) is based on elastic tension. (T=-kx) k is a constant, and x is distance displaced and the minus sign means it acts in the opposite direction to the displacement . now when you step on it you have mg working against kx (weight working against tension)

at the start mg > kx you accelerate downwards as the force downwards is greater then the force upwards. (f=ma) when you have moved a certain distance, being x, you will have mg=kx, so acceleration will be 0.

kx never actually is bigger then mg due to being a reaction force

hope this helped. obviously more forces are involved in real life, but this is a basic model of it

Answer 5

The scale measures the force that the weight exerts on the balance pan.  The balance exerts an equal and opposite force on the weight.

The weight itself is subject to two forces, the gravitational pull of the earth and the upward force from the balance pan.  As you correctly state, the result of these is zero.  Otherwise, the weight would be accelerating.  But the cancelling out affects the weight, not the balance.

Hope this helps.