Answer:
Explanation:
Answer: Let ke = 1/2 IW^2 = 1/2 kMr^2 W^2 be Earth's rotational KE. W = 2pi/24 radians per hour rotation speed and k = 2/5 for a solid sphere M is Earth mass, r = 6.4E6 m.
Then ke = 1/2 2/5 6E24 (6.4E6)^2 (2pi/(24*3600))^2 = ? Joules. You can do the math, note W is converted to radians per second for unit consistency.
Let KE = 1/2 KMR^2 w^2 be Earth's orbital KE. w = 2pi/(365*24) radians per hour K = 1 for a point mass. Note I used 365 days, a more precise number is 365.25 days per year, which is why we have Leap Years.
Find KE/ke = 1/2 KMR^2 w^2//1/2 kMr^2 W^2 = (K/k)(w/W)^2 (R/r)^2 = (5/2) (365)^2 (1.5E11/6.4E6)^2 = 7.81E9 ANS
Explanation:
The electrostatic forces are conservative forces!
The mainly property of the conservative fields is 
In spherical coordinates the field's expression is:

and the curl expression is:

to find the expression for the potential function associated:

Answer:
Vertical Height = 0.784 meter, Speed back at starting point = 10 m/s
Explanation:
Given Data:
V is the overall velocity vector,
and
are its initial vertical and horizontal components

To find:
Max Height
achieved
Calculation:
1) Using the
equation of motion, we know

2) In terms of gravity
height
and the vertical component of Velocity
.
3) As
as at maximum height the vertical component of velocity is zero maximum height achieved

putting values
4) 
5) As for the speed when it reaches back its starting point, it will have a speed similar to its launching speed, the reason being the absence of air friction (Air drag)
(a) 3.5 Hz
The angular frequency in a spring-mass system is given by

where
k is the spring constant
m is the mass
Here in this problem we have
k = 160 N/m
m = 0.340 kg
So the angular frequency is

And the frequency of the motion instead is given by:

(b) 0.021 m
The block is oscillating up and down together with the upper end of the spring. The block will lose contact with the spring when the direction of motion of the spring changes: this occurs when the spring is at maximum displacement, so at
x = A
where A is the amplitude of the motion.
The maximum displacement is given by Hook's law:

where
F is the force applied initially to the spring, so it is equal to the weight of the block:

k = 160 N/m is the spring constant
Solving for A, we find
