What should be the spring constant of a spring designed to bring a 1300 car to rest from a speed of 95 so that the occupants undergo a maximum acceleration of 6.0 ?
Vf^2=Vi+2ax
but a=F/m
0=Vi^2+2ax where a=-6*9.8m/s^2
solve for x.
then, k=f/x= ma/x
To answer this question, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
First, we need to calculate the maximum force required to bring the car to rest from a speed of 95 m/s. The force required is given by:
F = m * a
Where F is the force, m is the mass of the car, and a is the maximum acceleration.
Given:
m = 1300 kg
a = 6.0 m/s^2
F = (1300 kg) * (6.0 m/s^2) = 7800 N
Now, we can input the force into Hooke's Law and solve for the spring constant (k):
F = k * x
Where F is the force, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
Since the car comes to rest, the maximum displacement is when the spring is fully compressed. Let's assume this displacement is represented by x.
Therefore, 7800 N = k * x
To find the spring constant (k), we need to know the maximum displacement (x) of the spring.
Unfortunately, the given information in the question does not provide the maximum displacement of the spring. Therefore, without this information, we cannot determine the spring constant.