Answer:
a. A = 0.735 m
b. T = 0.73 s
c. ΔE = 120 J decrease
d. The missing energy has turned into interned energy in the completely inelastic collision
Explanation:
a.
4 kg * 10 m /s + 6 kg * 0 m/s = 10 kg* vmax
vmax = 4.0 m/s
¹/₂ * m * v²max = ¹/₂ * k * A²
m * v² = k * A² ⇒ 10 kg * 4 m/s = 100 N/m * A²
A = √1.6 m ² = 1.26 m
At = 2.0 m - 1.26 m = 0.735 m
b.
T = 2π * √m / k ⇒ T = 2π * √4.0 kg / 100 N/m = 1.26 s
T = 2π *√ 10 / 100 *s² = 1.99 s
T = 1.99 s -1.26 s = 0.73 s
c.
E = ¹/₂ * m * v²max =
E₁ = ¹/₂ * 4.0 kg * 10² m/s = 200 J
E₂ = ¹/₂ * 10 * 4² = 80 J
200 J - 80 J = 120 J decrease
d.
The missing energy has turned into interned energy in the completely inelastic collision
Answer:
The value is ![x = 45.99 \ Au](https://tex.z-dn.net/?f=x%20%3D%20%2045.99%20%5C%20%20Au)
Explanation:
From the question we are told that
The period of the asteroid is ![T = 176 \ years = 176 * 365 * 24 * 60* 60 = 5.55*10^{9}\ s](https://tex.z-dn.net/?f=T%20%3D%20%20176%20%5C%20years%20%3D%20176%20%2A%20365%20%2A%2024%20%2A%2060%2A%2060%20%3D%205.55%2A10%5E%7B9%7D%5C%20s)
Generally the average distance of the asteroid from the sun is mathematically represented as
![R = \sqrt[3]{ \frac{G M * T^2 }{4 \pi} }](https://tex.z-dn.net/?f=R%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7BG%20M%20%2A%20T%5E2%20%7D%7B4%20%5Cpi%7D%20%7D)
Here M is the mass of the sun with a value
![M = 1.99*10^{30} \ kg](https://tex.z-dn.net/?f=M%20%20%3D%20%201.99%2A10%5E%7B30%7D%20%5C%20%20kg)
G is the gravitational constant with value ![G = 6.67 *10^{-11} \ m^3 \cdot kg^{-1} \cdot s^{-2}](https://tex.z-dn.net/?f=G%20%20%3D%20%206.67%20%2A10%5E%7B-11%7D%20%20%5C%20%20m%5E3%20%5Ccdot%20kg%5E%7B-1%7D%20%5Ccdot%20%20s%5E%7B-2%7D)
![R = \sqrt[3]{ \frac{6.67 *10^{-11} * 1.99*10^{30} * [5.55 *10^{9}]^2 }{4 * 3.142 } }](https://tex.z-dn.net/?f=R%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B6.67%20%2A10%5E%7B-11%7D%20%20%2A%201.99%2A10%5E%7B30%7D%20%2A%20%5B5.55%20%2A10%5E%7B9%7D%5D%5E2%20%7D%7B4%20%2A%203.142%20%7D%20%7D)
=> ![R = 6.88 *10^{12} \ m](https://tex.z-dn.net/?f=R%20%3D%206.88%20%2A10%5E%7B12%7D%20%5C%20%20m)
Generally
![1.496* 10^{11} \ m \to 1 Au (Astronomical \ unit )](https://tex.z-dn.net/?f=1.496%2A%2010%5E%7B11%7D%20%20%5C%20%20m%20%20%5Cto%20%201%20Au%20%28Astronomical%20%5C%20%20unit%20%29)
So
![R = 6.88 *10^{12} \ m \ \ \ \ \to \ \ x \ Au](https://tex.z-dn.net/?f=R%20%3D%206.88%20%2A10%5E%7B12%7D%20%5C%20%20m%20%5C%20%5C%20%5C%20%5C%20%5Cto%20%5C%20%5C%20%20%20x%20%5C%20%20Au)
=> ![x = \frac{6.88 *10^{12}}{1.496 *10^{11}}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B6.88%20%2A10%5E%7B12%7D%7D%7B1.496%20%2A10%5E%7B11%7D%7D)
=> ![x = 45.99 \ Au](https://tex.z-dn.net/?f=x%20%3D%20%2045.99%20%5C%20%20Au)
The net force of the object is equal to the force applied minus the force of friction.
Fnet = ma = F - Ff
12 kg x 0.2 m/s² = 15 N - Ff
The value of Ff is 12.6 N. This force is equal to the product of the normal force which is equal to the weight in horizontal surface and the coefficient of friction.
Ff = 12.6 N = k(12 kg)(9.81 m/s²)
The value of k is equal to 0.107.
The 120 decibel sound has more amplitude than the 100 decibel sound.
In Physics, the relation between amplitude and intensity is that the intensity of the wave is directly proportional to the square of its amplitude.
To solve the problem, it is necessary the concepts related to the definition of area in a sphere, and the proportionality of the counts per second between the two distances.
The area with a certain radius and the number of counts per second is proportional to another with a greater or lesser radius, in other words,
![A_1*m=M*A_2](https://tex.z-dn.net/?f=A_1%2Am%3DM%2AA_2)
![A_i =Area](https://tex.z-dn.net/?f=A_i%20%3DArea)
M,m = Counts per second
Our radios are given by
![r_1 = 11cm](https://tex.z-dn.net/?f=r_1%20%3D%2011cm)
![R_2 = 20cm](https://tex.z-dn.net/?f=R_2%20%3D%2020cm)
![m = 65cps](https://tex.z-dn.net/?f=m%20%3D%2065cps)
Therefore replacing we have that,
![A_1*m=M*A_2](https://tex.z-dn.net/?f=A_1%2Am%3DM%2AA_2)
![4\pi r_1^2*m = M * 4\pi R_2^2 M](https://tex.z-dn.net/?f=4%5Cpi%20r_1%5E2%2Am%20%3D%20M%20%2A%204%5Cpi%20R_2%5E2%20M)
![r^2*m=MR^2](https://tex.z-dn.net/?f=r%5E2%2Am%3DMR%5E2)
![M = \frac{m*r^2}{R^2}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Bm%2Ar%5E2%7D%7BR%5E2%7D)
![M = \frac{65*11^2}{20^2}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B65%2A11%5E2%7D%7B20%5E2%7D)
![M = 19.6625cps](https://tex.z-dn.net/?f=M%20%3D%2019.6625cps)
Therefore the number of counts expect at a distance of 20 cm is 19.66cps