The maximum compression of the spring is 0.276 m
Step-by-step explanation:
First of all, we calculate the spring constant of the spring, by using Hooke's law:
![F=kx](https://tex.z-dn.net/?f=F%3Dkx)
where
F = 10 kN = 10,000 N is the force applied
x = 1.25 cm = 0.0125 m is the corresponding compression of the spring
k is the spring constant
Solving for k,
![k=\frac{F}{x}=\frac{10,000}{0.0125}=8\cdot 10^5 N/m](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BF%7D%7Bx%7D%3D%5Cfrac%7B10%2C000%7D%7B0.0125%7D%3D8%5Ccdot%2010%5E5%20N%2Fm)
When the truck impacts with the spring, all the kinetic energy of the truck is converted into elastic potential energy of the spring, so we can write
(1)
where
m is the mass of the truck
v = 2 m/s is the initial speed of the truck
is the spring constant
x is the compression of the spring
The mass of the truck can be found from its weight:
![m=\frac{W}{g}=\frac{150,000 N}{9.81 N/kg}=15,290 kg](https://tex.z-dn.net/?f=m%3D%5Cfrac%7BW%7D%7Bg%7D%3D%5Cfrac%7B150%2C000%20N%7D%7B9.81%20N%2Fkg%7D%3D15%2C290%20kg)
So now we can re-arrange eq.(1) to find the compression, x:
![x=\sqrt{\frac{mv^2}{k}}=\sqrt{\frac{(15,290)(2)^2}{8\cdot 10^5}}=0.276 m](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B%5Cfrac%7Bmv%5E2%7D%7Bk%7D%7D%3D%5Csqrt%7B%5Cfrac%7B%2815%2C290%29%282%29%5E2%7D%7B8%5Ccdot%2010%5E5%7D%7D%3D0.276%20m)
Learn more about kinetic energy:
brainly.com/question/6536722
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320 guests / 5 servings per can = 64 cans required
D. works because if you work it out that means 2n=140 and then divide by 2 which means n=70 and the other number is 71
Answer:
C
Step-by-step explanation:
point-slope equation is y-y1=m(x-x1)
y1=2
x1=6
m=(-5/7)
so the equation is y-2=-5/7(x-6)
hope this helps :3