The formula for this problem that we will be using is:
F * cos α = m * g * μs where:F = 800m = 87g = 9.8
cos α = m*g*μs/F= 87*9.8*0.55/800= 0.59 So solving the alpha, find the arccos above.
α = arccos 0.59 = 54 ° is the largest value of alpha
B. Many systems work together to control the internal environment of the body. This process is known as homeostasis.
Answer:
![\tau \approx 7.14 \times 10^{-4}s \approx0.714ms](https://tex.z-dn.net/?f=%5Ctau%20%5Capprox%207.14%20%5Ctimes%2010%5E%7B-4%7Ds%20%5Capprox0.714ms)
Explanation:
In a LC circuit The time constant τ is the time necessary for 60% of the total current (maximum current), pass through the inductor after a direct voltage source has been connected to it. The time constant can be calculated as follows:
![\tau =\frac{L}{R}](https://tex.z-dn.net/?f=%5Ctau%20%3D%5Cfrac%7BL%7D%7BR%7D)
Therefore, the time needed for the current to reach a fraction f = 0.6(60%) of its maximum value is:
![\tau =\frac{1}{1.4\times 10^{3}} =7.142857143 \times 10^{-4} \approx7.14 \times 10^{-4}s](https://tex.z-dn.net/?f=%5Ctau%20%3D%5Cfrac%7B1%7D%7B1.4%5Ctimes%2010%5E%7B3%7D%7D%20%3D7.142857143%20%5Ctimes%2010%5E%7B-4%7D%20%5Capprox7.14%20%5Ctimes%2010%5E%7B-4%7Ds)
The gravitational force between the two objects is given by:
![F=G \frac{m_1 m_2}{d^2}](https://tex.z-dn.net/?f=F%3DG%20%20%5Cfrac%7Bm_1%20m_2%7D%7Bd%5E2%7D%20)
where
![G=8.99 \cdot 10^{-11} m^3 kg^{-1} s^{-2}](https://tex.z-dn.net/?f=G%3D8.99%20%5Ccdot%2010%5E%7B-11%7D%20m%5E3%20kg%5E%7B-1%7D%20s%5E%7B-2%7D)
is the gravitational constant
![m_1 = 1.99 \cdot 10^{30} kg](https://tex.z-dn.net/?f=m_1%20%3D%201.99%20%5Ccdot%2010%5E%7B30%7D%20kg)
is the Sun mass
![m_2 = 3.30 \cdot 10^{23} kg](https://tex.z-dn.net/?f=m_2%20%3D%203.30%20%5Ccdot%2010%5E%7B23%7D%20kg)
is the mass of Mercury
and d is the distance between Sun and Mercury. Since we know the force:
![F=8.99 \cdot 10^{21} N](https://tex.z-dn.net/?f=F%3D8.99%20%5Ccdot%2010%5E%7B21%7D%20N)
we can re-arrange the formula to find d: