Respuesta :
Answer:
the work required for the loading of second dart is 64 times greater as work required for loading the first dart.
Explanation:
k = spring constant of the spring loaded toy dart gun
x₁ = compression of spring to load the first dart = d
x₂ = compression of spring to load the second dart = 8 d
E₁ = Work required to load the first dart
E₂ = Work required to load the second dart
Work required to load the first dart is given as
E₁ = (0.5) k x₁² = (0.5) k d²
Work required to load the second dart is given as
E₂ = (0.5) k x₂² = (0.5) k (8d)² = (64) (0.5) k d²
E₂ = 64 E₁
So the work required for the loading of second dart is 64 times greater as work required for loading the first dart
The work required for the loading of the second dart is 64 times the work required for loading the first dart.
What is spring work?
In order to stretch or compress the spring some amount of work has to be done. Which is given by
[tex]\RM{W=\frac{1}{2} K\times{x}}[/tex]
where k = spring constant of the spring
x = compression of spring
W= Work required or spring work
case 1,
x₁ = Compression of spring to load the first dart = d
W₁ = Work required to load the first dart
Work required to load the first dart is given as
W₁ = (0.5) k x₁² = (0.5) k d²
case 2,
x₂ = Compression of spring to load the second dart = 8 d
W₂ = Work required to load the second dart
Work required to load the second dart is given as
W₂ = (0.5) k x₂² = (0.5) k (8d)² = (64) (0.5) k d²
It is observed that the work required for the loading of the second dart is 64 times the work required for loading the first dart.
To learn more about the spring work refer to the link
https://brainly.in/question/18110192
