Answer:
Part a: The force between the tires and the ground is 765 lbf.
Part b: The force between the pallet and the boulder is 1016 lbf.
Explanation:
From the free body diagram on the Truck, boulder and pallet level
is the acceleration of truck which is 1 ft/s2
is the mass of the truck which is 5000 lb or 155.28 slugs
is the mass of the boulder which is 1000 lb or 31.06 slugs
is the mass of the pallet which is 200 lb or 6.211 slugs
is the acceleration of the pallet or boulder which is 0.5 ft/s2
Applying Newton's 2nd Law of Motion on pulley in vertical direction
![2T-(m_a+m_b)g=(m_a+m_b)a_a\\2T-(37.271)(32.2)=(37.271)(0.5)\\T=609.32 lb_f](https://tex.z-dn.net/?f=2T-%28m_a%2Bm_b%29g%3D%28m_a%2Bm_b%29a_a%5C%5C2T-%2837.271%29%2832.2%29%3D%2837.271%29%280.5%29%5C%5CT%3D609.32%20lb_f)
Part a
Applying Newton's 2nd Law of Motion on Truck in horizontal direction
![F-T=m_Ta_T\\F=609.32+(155.28)(1)\\F=765 lb_f](https://tex.z-dn.net/?f=F-T%3Dm_Ta_T%5C%5CF%3D609.32%2B%28155.28%29%281%29%5C%5CF%3D765%20lb_f)
So the force between the tires and the ground is 765 lbf.
Part b
Applying Newton's 2nd Law of Motion on Boulder in vertical direction
![F_{AB}-m_bg=m_ba_b\\F_{AB}=m_b(g+a_b)\\F_{AB}=31.056(32.2+0.5)\\F_{AB}=1016 lb_f](https://tex.z-dn.net/?f=F_%7BAB%7D-m_bg%3Dm_ba_b%5C%5CF_%7BAB%7D%3Dm_b%28g%2Ba_b%29%5C%5CF_%7BAB%7D%3D31.056%2832.2%2B0.5%29%5C%5CF_%7BAB%7D%3D1016%20lb_f)
So the force between the pallet and the boulder is 1016 lbf.
Answer:
lux
Explanation:
I guess because I think I have read it somewhere
Answer:
more speed means that an object has more energy, now if an object's place is something such as a hill, the potential energy will increase meaning an object will have more speed and acceleration. this is because you have the earth's gravity helping you out when the object goes downhill, giving it the higher potential energy
Answer:
![t = 500000\,years](https://tex.z-dn.net/?f=t%20%3D%20500000%5C%2Cyears)
Explanation:
The time constant of the radioactive isotope is:
![\tau = \frac{150000\,years}{\ln 2}](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%5Cfrac%7B150000%5C%2Cyears%7D%7B%5Cln%202%7D)
![\tau = 216404.256\,years](https://tex.z-dn.net/?f=%5Ctau%20%3D%20216404.256%5C%2Cyears)
The isotope decay is predicted by the following model:
![\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7Bm_%7Bo%7D%7D%20%3D%20e%5E%7B-%5Cfrac%7Bt%7D%7B%5Ctau%7D%20%7D)
![\frac{125\,g}{125\,g + 875\,g} = e^{-\frac{t}{216404.256\,years} }](https://tex.z-dn.net/?f=%5Cfrac%7B125%5C%2Cg%7D%7B125%5C%2Cg%20%2B%20875%5C%2Cg%7D%20%3D%20e%5E%7B-%5Cfrac%7Bt%7D%7B216404.256%5C%2Cyears%7D%20%7D)
![0.125 = e^{-\frac{t}{216404.256} }](https://tex.z-dn.net/?f=0.125%20%3D%20e%5E%7B-%5Cfrac%7Bt%7D%7B216404.256%7D%20%7D)
The age of the rock is determined after algebraic handling:
![\ln 0.125 = -\frac{t}{216404.256}](https://tex.z-dn.net/?f=%5Cln%200.125%20%3D%20-%5Cfrac%7Bt%7D%7B216404.256%7D)
![t = 500000\,years](https://tex.z-dn.net/?f=t%20%3D%20500000%5C%2Cyears)
I believe the best answer is B. Waking State