00:01
So in this problem, we have a car that has a spring as a bumper.
00:05
And we want to find k, the stiffness of the spring, when its maximum deflection, is set to only 0 .2 meters, and the velocity of the car is 4 meters per second before it hits a wall.
00:25
We're also given the mass of this car, which is 5 ,000 kilograms, and the force due to the spring is given as k, the stiffness of the spring times s squared.
00:42
And just looking at this equation, we know that the force will vary depending on what the value of s is.
00:48
So since we're dealing with forces and distance, we know that we're dealing with work because work is force times distance.
00:57
We're given velocity so we can use kinetic energy because kinetic energy deals with movement.
01:03
So we can use the work energy principle, which is given as the initial kinetic energy plus the work being done by the forces is equal to final kinetic energy.
01:22
We're just thinking about this problem, we can say that the final kinetic energy will be zero because the velocity will be zero once it hits the wall so now we're just left with initial kinetic energy one -half m v1 squared plus the work being done by the forces and this is equal to zero we'll call this equation one so now let's look at work so work is found by calculating the forces but here the force isn't constant.
02:12
It actually varies, again, depending on the distance.
02:15
So we have to take an integral of this force...