Bathroom scale being compressed but jumping on it

[kavipach]

Homework Statement

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 don't know how to go about this question.

 

[rock.freak667]

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 don't know how to go about this question.

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]

ya hookes law...F=kx.

yes

where k equals spring constant and x equals displacment

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]

according to this the constant equals to 1381818.2 is this right

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]

potential energy?

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]

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

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