The work to stretch a spring from its rest position is
(1/2) (spring constant) (distance of the stretch)²
E = 1/2 k x² .
You said it takes 1700 joules to stretch the spring 3 meters from its rest position, so we can write
1700 joules = 1/2 k (3m)²
1 joule = 1 newton-meter
1700 N-m = 1/2 k (3m)²
Multiply each side by 2: 3400 N-m = k · 9m²
Divide each side by 9m² k = 3400 N-m / 9m²
= (377 and 7/9) newton per meter
I don't think that 4m has anything to do with the problem.
anyway. here.
A___________________B_______C
where A is the point that the train was released.
B is where the wheel started to stick
C is where it stopped
From A to B, v=2.5m/s, it takes 2s to go A to B so t=2
AB= v*t = 2.5 * 2 = 5m
The train comes to a stop 7.7 m from the point at which it was released so AC=7.7m
then BC= AC-AB = 7.7-5 = 2.7m
now consider BC
v^2=u^2+2as
where u is initial speed, in this case is 2.5m/s
v is final speed, train stop at C so final speed=0, so v=0
a is acceleration
s is displacement, which is BC=2.7m
substitute all the number into equation, we have
0^2 = 2.5^2 + 2*a*2.7
0 = 6.25 + 5.4a
a = -6.25/5.4 = -1.157
so acceleration is -1.157m/(s^2)
It's the energy your body spends to just keep you breathing and your heart beating ... just being alive, without trying to DO anything.
A motor is built to use all those things and produce mechanical energy.
