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

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