You stand on a bathroom scale the spring inside the scale...

You stand on a bathroom scale, the spring inside the scale compresses 4.79 mm, and it reads your weight as 750 N. Now if you fall from rest onto the scale from a height of 0.23 m, what does the scale read at its peak? Round to the nearest Newton. HINT 1: When standing, you are at static equilibrium. HINT 2: The scale will have its peak reading when the scale is most compressed.

Transcript

00:01 In this problem we have been given that there is a weighing scale and that contains a spring which gets compressed by a distance of 0 .8 millimeter provided that when we stand and let's say our weight is 690 newtons.

00:24 So here the force applied will be 690 newton because it applies in the downward direction.

00:31 So in that case we can definitely say that whatever force is applied that gets developed in the spring as the spring force.

00:41 And because of that only it is able to stop.

00:44 So we get the spring force as k times x according to hook's law.

00:50 So k times x that will be equal to 690.

00:56 And from here we'll put the value of x in meters of course to get the spring constant in newton's per meter.

01:03 That will be 690 divided by 0 .8 into 10 raise to minus 3 newton per meter.

01:10 So when we divide here 690 with 0 .8, we're going to get here as 862 .5 into 10 raise to 3 newtons per meter.

01:24 So that's the spring constant and now it has stated that in the next situation if we jump at a height of 1 .7, meters and then come down.

01:37 So in that case the jump is made from a height of 1 .7 meters from the point of the top of the scale.

01:47 So in this case the total energy contained at this point p from where the jump is made that is equal to m g into the height.

01:56 That's 1 .7.

01:57 And this total energy should be converted into the spring potential energy and that will give us the reading of of the scale.

02:07 So spring potential energy, that's equal to half kx square...

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