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a spring gun initially compressed 2cm fires a 0.01kg dart straight up into the air. if the dart reaches a height it 5.5m determine the spring constant of the gun

Respuesta :

samuelonum1

Answer:

2697.75N/m

Explanation:

Step one

This problem bothers on energy stored in a spring.

Step two

Given data

Compression x= 2cm

To meter = 2/100= 0.02m

Mass m= 0.01kg

Height h= 5.5m

K=?

Let us assume g= 9.81m/s²

Step three

According to the principle of conservation of energy

We know that the the energy stored in a spring is

E= 1/2kx²

1/2kx²= mgh

Making k subject of formula we have

kx²= 2mgh

k= 2mgh/x²

k= (2*0.01*9.81*5.5)/0.02²

k= 1.0791/0.0004

k= 2697.75N/m

Hence the spring constant k is 2697.75N/m

boffeemadrid

The spring constant of given spring is required.

The spring constant is [tex]2697.75\ \text{N/m}[/tex]

Conservation of energy

x = Change in length of spring = 2 cm

m = Mass of object = 0.01 kg

h = Height the dart reaches = 5.5 m

k = Spring constant

g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

The energy balance of the system is given by

[tex]\dfrac{1}{2}kx^2=mgh\\\Rightarrow k=\dfrac{2mgh}{x^2}\\\Rightarrow k=\dfrac{2\times 0.01\times 9.81\times 5.5}{0.02^2}\\\Rightarrow k=2697.75\ \text{N/m}[/tex]

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