Question

Can someone pls explain how to answer these​

Answer 1

Step-by-step explanation:

Hook's law describes the force F a spring exerts on an object that is stretched or compressed by a distance x from its natural length and has spring constant k:

(1)
`F_S = -kx`

The force of gravity of an object with mass m and gravitational acceleration g is given by:

(2)
`F_G=mg`

(a) To find the natural length l of the spring you can use the example 1 and 3 of the spring. Use equations 1 and 2 to get the following system of equations with two unknowns k and l:

`0.02g=(0.14-l)k\\0.03g=(0.16-l)k`

To solve for k you can subtract the equations:

`0.01g=0.02k\\ k=(g)/(2)(N)/(m)`

Now plug in k to solve for l:

`l=0.1m`

(b) Now use Hook's law to find x:

`x=(F)/(k)+l=(mg)/(k)+l=(2mg)/(g)+l=2m+l=0.19m`

(c) Do the same to find the mass m:

`m=(k)/(g) (0.17-l)=(g)/(2g)(0.17-l)=(1)/(2)(0.07)=0.035kg=35g`

(d) Work is given by:

`W=\int\limits^a_b {F}\cdot \, dx=\int\limits^(0.17)_(0.14) {kx} \, dx=(1)/(2)kx^2|^(0.17)_(0.14)=(1)/(2)k(0.17^2-0.14^2)=2.2*10^(-2)J`