You devise a wind-up car powered by a spring for trips to the grocery store. The car has an inertia of 540 kg and is 4.7 m long. It should be able to accelerate from rest to 23 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 this length.
In order to meet the acceleration requirement, what must the value of the spring constant be?

Question

You devise a wind-up car powered by a spring for trips to the grocery store. The car has an inertia of  540 kg  and is  4.7 m  long. It should be able to accelerate from rest to  23 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 this length.
In order to meet the acceleration requirement, what must the value of the spring constant be?

anonymous · Answer

I know that the force of the string is -kX and the that it also equals mass times acceleration....but I'm not sure how to find acceleration without time or displacement

anonymous · Answer

@matt101

irishboy123 · Answer

i think you might be looking at this the wrong way

without knowing precisely what you are learning, i'd say that you should look at energy.  if the car accelerates to 23m/s 50 times, it is given $\frac{1}{2}(540)(23^2) J$ worth of energy 50 times.

all of that energy has to be stored in the spring, and the energy in a spring is $U = \frac{1}{2} k x^2$.  here we are told that the spring runs the length of the car and is compressed by a full half length to start with.

that's all we need to know in order to have a go at doing this.