Answer:
v = 8.90 km/h
Explanation:
In order to calculate the maximum collision speed of the 1200kg car, you take into account that the the kinetic energy of the car when it has a speed v, is equal to the potential elastic energy of the spring when it is maximum compressed.
Then, you use the following equation:
[tex]K=U\\\\\frac{1}{2}Mv^2=\frac{1}{2}kx^2[/tex] (1)
M: mass of the car = 1200kg
v: maximum collision speed of the car = ?
k: spring constant = 1.5MN/m = 1.5*10^6 N/m
x: maximum compression supported by the spring = 7.0cm = 0.070m
You solve the equation (1) for v and replace the values of the other parameters:
[tex]v=x\sqrt{\frac{k}{M}}=(0.07m)\sqrt{\frac{1.5*10^6N/m}{1200kg}}\\\\v=2.47\frac{m}{s}[/tex]
In km/h you obtain:
[tex]v=2.47\frac{m}{s}*\frac{1km}{1000m}*\frac{3600s}{1\ h}=8.90\frac{km}{h}[/tex]
The maximum collision that the car can support is 8.90km/h
