Question

A freely rolling 1200kg car moving at .65m/s is to compress the spring no more than 7 cm beffore stopping. a) what should be the force constant of the spring, and what is the max amount of energy that gets stored in it? b) if the springs that are actually delivered have the proper force constant but can become compressed by only 5 cm, what is the max speed of the given car for which they will provide adequate protection?

Answer 1

First, we need to calculate the potential energy of the car.

When the car impacts the spring, all of the kinetic energy of the car will be stored as potential energy in the spring.

Let's derive the expression for potential energy in a spring. If we make note of the Work-Energy Theorem, we can state that\[W = \Delta PE\] in the case of a spring. (The spring is said to not move here.) Additionally, work can be defined as\[W = \int\limits Fdx \]Noting that the force of a spring is \(F = kx\), then the work done by the spring can be calculated as\[W = \int\limits kx dx = {1 \over 2} kx^2\]From our Work-Energy expression\[{1 \over 2} kx^2 = \Delta PE\]Since all the kinetic energy of the car is converted to potential energy in the spring, \[{1 \over 2} kx^2 = {1 \over 2} m_c v_c^2\]We know all variables except k, which is what we want to solve for. Are you following this okay?

Answer 2

yes so far so good

Answer 3

For part a, we can use the above methodology.

We can use the same equations and thought process for part b. However, here we are solving for \(v_c\).

Answer 4

where i messed up is at \[1/2m_0v_0v\]

Answer 5

i got the right answer thanks a lot. if you ever need help with bio or chem let me know

Answer 6

Great! Will do, however I think I'm past my bio and chem days. Thanks.