Why does the weighing machine show different values when jumping vs standing?

[akshaya]

Weight is defines as the force exerted by the ground on you.
F=ma, and m and a are constant.
But the weighing machine does not show the same value when you simply stand on it and when you jump on it.

So basically my question is, even though force exerted is same, why is there a difference in the value shown in the weighing machine?

 

[member 529879]

The force is greater when you jump on the machine. When you jump in the air and land on the machine the machine or any other surface you land on has to apply a force on you that brings you to rest in a certan amount of time. Let's say you are falling at a rate of 30m/s when you hit the ground and you weigh 75kg. If after you hit the ground it takes 2 seconds for you to come to rest, an average force of about 1,875 Newtons is required compared to about 750 Newtons that is required to keep you at rest.

 

[akshaya]

The force is greater when you jump on the machine. When you jump in the air and land on the machine the machine or any other surface you land on has to apply a force on you that brings you to rest in a certan amount of time. Let's say you are falling at a rate of 30m/s when you hit the ground and you weigh 75kg. If after you hit the ground it takes 2 seconds for you to come to rest, an average force of about 1,875 Newtons is required compared to about 750 Newtons that is required to keep you at rest.

Thank you for the reply, but I'm not sure how you can calculate the force applied by an object on the ground when it falls from a certain height h.
When it's at rest, the force applied is mg, so what about when its in motion?

 

[Isaac0427]

You are correct, your mass is not changing. If I am correct, a scale measures how your body is affected by gravity by testing against it's standard resistance, which calculates your mass if you stand on it. However, as it does not directly calculate your mass, which I think is impossible, by changing the acceleration, therefore changing the force, the reading is altered.

 

[akshaya]

by changing the acceleration, therefore changing the force, the reading is altered.

Yes, i understand what you mean, but how is acceleration changing?

 

[Isaac0427]

Yes, i understand what you mean, but how is acceleration changing?

When you jump you are changing the acceleration.

 

[akshaya]

When you jump you are changing the acceleration.

acceleration is constant though, 9.8m/s^2

 

[Isaac0427]

acceleration is constant though, 9.8m/s^2

From what I understand that is incorrect. When you just stand, the acceleration of the force is just the strength of gravity, right? As you jump and come down, the acceleration increases, and more force is applied. For example, I may be able to hold a 15 kg weight with no problem, but if it is dropped from 3m above my hand and I grab it, my hand will be pushed back due to the extra force.

 

[cpsinkule]

The acceleration due to gravity is constant. Gravity isn't the only force at work here. The normal force is what keeps you from collapsing into the core of the earth. When you jump and hit the ground, the normal force must decelerate you to keep you from falling into the earth. From experience, we know the time required to do this is very small. So when you hit the ground you stop in a fraction of a second. recall that, roughly speaking, acceleration is Δv/Δt. when you hit the ground, your speed is very high. on top of that, the time in which your speed goes to 0 is vanishingly small so from Δv/Δt we see that there is an enormous acceleration imposed on us by the normal force, and hence an enormous force. this is why you see the scale jump so high. the technical term for this is "impulse". you can think of it as the work a force has to do during a period of time.