Respuesta :
Answer:
spring compressed is 0.724 m
Explanation:
given data
mass = 1.80 kg
spring constant k = 2 × 10² N/m
initial height = 2.25 m
solution
we know from conservation of energy is
mg(h+x) = 0.5 × k × x² ...................1
here x is compression in spring
so put here value in equation 1 we get
1.8 × 9.8 × (2.25+x) = 0.5 × 2× 10² × x²
solve it we get
x = 0.724344
so spring compressed is 0.724 m
There is some gap between the coils under maximum load on the spring. The compressed length of the spring is 0.72 m.
What is the compressed length?
The compressed length of the spring is defined as the axial length of the spring that is subjected to maximum compressive force.
Given that the mass m of the box is 1.80 kg and the spring constant k = 2.00 ✕ 102 N/m. The initial height h of the box is 2.25 m above the top of the spring.
Let's consider that the compressed length of the spring is y. Now as per the law of conservation of energy, the potential energy will be equal to kinetic energy.
[tex]mg (h+y) = \dfrac {1}{2}ky^2[/tex]
[tex]1.80\times 9.8 (2.25+y) = \dfrac {1}{2} \times 2 \times 10^2 \times y^2[/tex]
[tex]17.64(2.25+y) = 100y^2[/tex]
[tex]100 y^2 - 17.64 y - 39.69 = 0[/tex]
[tex]y = 0.72\;\rm m[/tex]
Hence we can conclude that the compressed length of the spring is 0.72 m.
To know more about the compressed length, follow the link given below.
https://brainly.com/question/10310031.
