An object is attached to a vertical spring and slowly lowered to its equilibrium position. this stretches the spring by an amount d. if the same object is attached to the same vertical spring but permitted to fall instead, through what maximum distance does it stretch the spring? show all work. step by step.

2d

Explanation:

For any instance equivalent force acting on the body is

Where

m is the mass of the object

k is the force constant of the spring

d is the extension in the spring

and

d/dt(dx/dt)=  is the acceleration of the object

solving the above equation we get

where

A is the amplitude of oscillation from the mean position.

k= spring constant , T= time period

Here  we are assuming  that at t=T/4

x= 0   since, no extension in the spring

then

A=- d

Hence

x=- d sin wt + d

now, x is maximum when sin wt=- 1

Therefore,

x(maximum)=2d

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min