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If you stand on a bathroom scale,the spring inside the scale compresses 0.50 mm, and it tells you your weight is 700 N. Now if you jump on the scale from a height of 1.3 m, what does the scale read at its peak?

Respuesta :

Initially, mg = kx. K = mg/x = 700/0.5x10^-3 = 1400000N/m. From second condition, applying work-energy theorem, potential enery- elastic potential energy = change in kinetic energy. Now change in kinetic energy is 0 since initial and final velocities are 0m/s. Therefore, potential energy = elastic potential energy. mgh = (1/2) * k* x^2. x^2 = 2(mg)h/k = 2 x 700 x 1.3/ 1400000. x = 0.036m. Hope it's clear.

The scale reading at its peak is  0.036m.

What is gravitational potential energy?

If an object is lifted, work is done against gravitational force. The object gains energy.

If you stand on a bathroom scale, the spring inside the scale compresses 0.50 mm, and it tells you your weight is 700 N.

Using Hooke's law, expressed as

Force, F = k (x₂-x₁).

mg = kx.

k= mg/x

Put the values, we get

k = 700/0.5x10^-3

k = 1400000 N/m.

Now if you jump on the scale from a height of 1.3 m,

Applying work-energy theorem,

potential energy =  elastic potential energy

mgh = (1/2) kx²

x = 2(mg)h/k

Plug the values, we get

x = 2 x 700 x 1.3/ 1400000

x = 0.036m.

Thus, the scale reading at its peak is  0.036m.

Learn more about gravitational potential energy.

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