Respuesta :
Answer:
(a) 1.042 J
b) 0.108 m
Explanation:
(a)
W = work done to stretch the spring = 2 J
k = spring constant
L₀ = initial length = 30 cm = 0.30 m
L = final length = 42 cm = 0.42 m
x = stretch of the spring = L - L₀ = 0.42 - 0.30 = 0.12 m
Work done to stretch the spring is given as
W = (0.5) k x²
2 = (0.5) k (0.12)²
k = 277.78 N/m
x₀ = initial stretch of the spring = 35 - 30 = 5 cm = 0.05 m
x = final stretch of the spring = 40 - 30 = 10 cm = 0.10 m
W' = work needed to stretch the spring from 35 cm to 40 cm
Work needed to stretch the spring from 35 cm to 40 cm is given as
W' = (0.5) k (x² - x₀²)
W' = (0.5) (277.78) (0.10² - 0.05²)
W' = 1.042 J
b)
x = Stretch of the spring beyond natural length
F = force = 30 N
Spring force is given as
F = k x
30 = (277.78) x
x = 0.108 m
(a) The work is needed to stretch the spring from 35 cm to 40 cm is 1.042 J.
(b) Beyond the length of 0.108 m force of 30 N keep the spring stretched.
what is spring force?
In order to stretch or compress the spring some amount of work has to be done. Which is given as,
[tex]\rm{W=\frac{1}{2} Kx^{2} }[/tex]
where k = spring constant of the spring
x = compression of spring
W= Work required or spring work
Initial length is given by 30 cm = 0.30 m
final length is given by 42 cm = 0.42 m
When spring is stretched change in the length occurs denoted by x
x = final length - initial length =0.42 - 0.30 = 0.12 m
[tex]\rm{W=\frac{1}{2} Kx^{2} }[/tex]
[tex]\rm{2=\frac{1}{2} K(0.12)^{2} }[/tex]
K= 277.78 N/m
(a) work is needed to stretch the spring from 35 cm to 40 cm
stretching length from30cm to 35 is 5 cm which is 0.05 m
stretching length from cm to 30 is 40 cm is 10 cm which is 0.1m
x = final stretch of the spring = 40 - 30 = 10 cm = 0.10 m
Work needed to stretch the spring from 35 cm to 40 cm is given
W = (0.5)K([0.1]² - [0.5]²)
W = (0.5) (277.78) (0.10² - 0.05²)
W = 1.042 J
x is stretch of the spring beyond natural length
F = force = 30 N
Spring force is given as
F = k x
30 = (277.78) x
x = 0.108 m
To learn more about the spring work refer to the link
https://brainly.in/question/18110192
