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Answer:
W= 4.4 J
Explanation
Elastic potential energy theory
If we have a spring of constant K to which a force F that produces a Δx deformation is applied, we apply Hooke's law:
F=K*x Formula (1): The force F applied to the spring is proportional to the deformation x of the spring.
As the force is variable to calculate the work we define an average force
Formula (2)
Ff: final force
Fi: initial force
The work done on the spring is :
W = Fa*Δx
Fa : average force
Δx : displacement
:Formula (3)
: final deformation
:initial deformation
Problem development
We calculate Ff and Fi , applying formula (1) :


We calculate average force applying formula (2):

We calculate the work done on the spring applying formula (3) : :
W= 11N*(0.7m-0.3m) = 11N*0.4m=4.4 N*m = 4.4 Joule = 4.4 J
Work done in stages
Work is the change of elastic potential energy (ΔEp)
W=ΔEp
ΔEp= Epf-Epi
Epf= final potential energy
Epi=initial potential energy




W=ΔEp= 5.39 J-0.99 J = 4.4J
:
The rate at which the height is changing is ( 5 / x ) m / hr
We know that,
Area of an equilateral triangle A =
/ 4
h =
x / 2
Where,
x = Side
h = Height
Given that,
dA / dt = 5
/ hr
h =
x / 2
Differentiate both sides with respect to t
dh / dt = (
/ 2 ) ( dx / dt )
dx / dt = ( 2 /
) ( dh / dt )
A =
/ 4
Differentiate both sides with respect to t
dA / dt = (
/ 4 ) ( 2x ) ( dx / dt )
5 = (
/ 4 ) ( 2x ) ( 2 /
) ( dh / dt )
dh / dt = ( 5 / x ) m / hr
Rate of change of height is defined as the rate at which height of an object changes with respect to time. It is represented as dh / dt
Therefore, the rate at which the height is changing is ( 5 / x ) m / hr
To know more about Rate of change of height
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