Answer:
The average speed of the earth in its orbit is ![29.86km/s](https://tex.z-dn.net/?f=29.86km%2Fs)
Explanation:
The average distance between the Earth and the Sun is
.
The average speed of the earth in its orbit can be found by the next equation :
(1)
Where r is the radius and T is the period.
In this case, the orbit of the Earth can be considered as a circle
(
) instead of an ellipse.
It takes 1 year to the Earth to make one revolution around the Sun. Therefore, its period will be 365.25 days.
Notice that to express the period in terms of seconds, the following is needed:
⇒ ![31557600s](https://tex.z-dn.net/?f=31557600s)
Then, equation 1 can be used:
![v = \frac{2 \pi (1.50x10^{8}km)}{31557600s}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B2%20%5Cpi%20%281.50x10%5E%7B8%7Dkm%29%7D%7B31557600s%7D)
![v = 29.86km/s](https://tex.z-dn.net/?f=v%20%3D%2029.86km%2Fs)
Answer:
(a) The spring constant is 59.23 N/m
(b) The total energy involved in the motion is 0.06 J
Explanation:
Given;
mass, m = 240 g = 0.24 kg
frequency, f = 2.5 Hz
amplitude of the oscillation, A = 4.5 cm = 0.045 m
The angular speed is calculated as;
ω = 2πf
ω = 2 x π x 2.5
ω = 15.71 rad/s
(a) The spring constant is calculated as;
![\omega = \sqrt{\frac{k}{m} } \\\\\omega ^2 = \frac{k}{m} \\\\k = m\omega ^2\\\\where;\\\\k \ is \ the \ spring \ constant\\\\k = (0.24) \times (15.71)^2\\\\k = 59.23 \ N/m](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D%20%5C%5C%5C%5C%5Comega%20%5E2%20%3D%20%5Cfrac%7Bk%7D%7Bm%7D%20%5C%5C%5C%5Ck%20%3D%20m%5Comega%20%5E2%5C%5C%5C%5Cwhere%3B%5C%5C%5C%5Ck%20%5C%20is%20%5C%20the%20%5C%20spring%20%5C%20constant%5C%5C%5C%5Ck%20%3D%20%280.24%29%20%5Ctimes%20%2815.71%29%5E2%5C%5C%5C%5Ck%20%3D%2059.23%20%5C%20N%2Fm)
(b) The total energy involved in the motion;
E = ¹/₂kA²
E = (0.5) x (59.23) x (0.045)²
E = 0.06 J
Explanation:
(1) Every object moves in a straight line unless acted upon by a force. (2) The acceleration of an object is directly proportional to the net force exerted and inversely proportional to the object's mass. (3) For every action, there is an equal and opposite reaction.
Answer: ![1.54m^3](https://tex.z-dn.net/?f=1.54m%5E3)
Explanation:
Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.
The combined gas equation is,
where,
= initial pressure of gas at STP = 1 atm
= final pressure of gas = 2.67 atm
= initial volume of gas =
= final volume of gas = ?
= initial temperature of gas at STP =
= final temperature of gas =
Now put all the given values in the above equation, we get:
![V_2=1.54m^3](https://tex.z-dn.net/?f=V_2%3D1.54m%5E3)
Thus the final volume will be ![1.54m^3](https://tex.z-dn.net/?f=1.54m%5E3)
goU 234 = 234.04095amu & mass of He4 = 4.002602 amu)