2. when a 9.09-kg mass is placed on top of a vertical spring, the spring compresses 0.0418 m. find the…

2. when a 9.09-kg mass is placed on top of a vertical spring, the spring compresses 0.0418 m. find the spring constant of the spring.

2. when a 9.09-kg mass is placed on top of a vertical spring, the spring compresses 0.0418 m. find the spring constant of the spring.

Answer

Explanation:

Step1: Identify the relevant formula

When a mass is placed on a vertical spring and is in equilibrium, the force exerted by the spring (Hooke's law, ( F = kx )) is equal to the weight of the mass (( F = mg )). So we have ( kx = mg ), and we can solve for the spring constant ( k ) as ( k=\frac{mg}{x} ).

Step2: Plug in the values

We know the mass ( m = 9.09\space kg ), the acceleration due to gravity ( g = 9.8\space m/s^{2} ), and the compression ( x = 0.0418\space m ).

Substitute these values into the formula:

( k=\frac{9.09\times9.8}{0.0418} )

First, calculate the numerator: ( 9.09\times9.8 = 9.09\times(10 - 0.2)=90.9 - 1.818 = 89.082 )

Then, divide by the denominator: ( k=\frac{89.082}{0.0418}\approx2131.15\space N/m )

Answer:

The spring constant of the spring is approximately (\boldsymbol{2131\space N/m}) (or more precisely (\boldsymbol{2131.15\space N/m})).