Bathroom scale being compressed but jumping on it

kavipach

1. The problem statement, all variables and given/known data
If you stand on a bathroom scale, the spring inside the scale compresses 0.55mm, and it tells you your weight is 760N.
Now if you jump on the scale from a height of 1.3 m, what does the scale read at its peak?

rock.freak667

What are your thoughts on the question? Post your attempt.

kavipach

well i tried a few things... i found the persons mass which is 77.55kg.Since F=ma,and we have m, i tired using kinamatics to find a but finding the velocity of the person just before impact. Then i got stuck. I dont know how to go about this question.

rock.freak667

So when the person stands on the scale, they weigh 760N. This means that the spring compresses. Do you know a formula that relates force and extension?

kavipach

ya hookes law...F=kx.

kavipach

where k equals spring constant and x equals displacment

rock.freak667

yes

good.


So can you find the spring constant,k using the information in the first line of the question?

kavipach

according to this the constant equals to 1381818.2 is this right

rock.freak667

1381818.2 N/m yes, remember to put in your units.


So second line now. If the person is at 1.3m in the air, what type of energy does he have? This energy is converted into the energy needed to compress the spring a displacement,x, at the peak.

kavipach

potential energy?

rock.freak667

yes. What is the formula for gravitational potential energy? And what is the formula for the energy stored by a spring?

kavipach

The formula for gravitational potential energy is U=mgy where u equals the p.e, m equals mass and y is the displacement. the formula for the energy storedd in a spring is U=1/2kx^2

rock.freak667

So if all the gravitational energy is converted to energy stored in the spring, that makes

gravitational p.e. = energy stored in the spring.


Can you find the compression,x for the scale now?

kavipach

ya i think i can..thanks for all the help..your a life saver