 #1
Jaccobtw
 162
 31
 Homework Statement:
 You devise a wound up car powered by a spring for trips to the grocery store. The car has an inertia of 500 kg and is 4.2 m long. It should be able to accelerate from rest to 20 m/s at least 50 times before the spring needs winding. The spring runs the length of the car, and a full winding compresses it to half of its length In order to meet the acceleration requirement, what must the value of the spring constant be?
 Relevant Equations:

F = ma
F = kd
"It should be able to accelerate from rest to 20 m/s at least 50 times before the spring needs winding"
So F = kd = k(2.1)  d is 2.1 because it is the compression length
Now, since we know the d, divide it by 50, 2.1/50 = 0.042m
Basically, the spring unwinds 0.042 m 50 times for a total distance of 2.1m.
Now, calculate acceleration:
v(f)^2 = v(i)^2 * 2 * a * d
We know our final velocity is 20 m/s, our initial is 0.
Solving for a we get, 4,762 m/s^2
Back to our original equations
F = kd = ma
Solve for k and we get : 5.7 * 10^7 N/m
But I got this wrong :(
So F = kd = k(2.1)  d is 2.1 because it is the compression length
Now, since we know the d, divide it by 50, 2.1/50 = 0.042m
Basically, the spring unwinds 0.042 m 50 times for a total distance of 2.1m.
Now, calculate acceleration:
v(f)^2 = v(i)^2 * 2 * a * d
We know our final velocity is 20 m/s, our initial is 0.
Solving for a we get, 4,762 m/s^2
Back to our original equations
F = kd = ma
Solve for k and we get : 5.7 * 10^7 N/m
But I got this wrong :(