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;
(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
Answer: 
Explanation:
We are told both planets describe a circular orbit around the star S. So, let's approach this problem begining with the angular velocity 
of the planet P1 with a period 
:
(1)
Where:
is the velocity of planet P1
is the radius of the orbit of planet P1
Finding :
(2)
(3)
(4)
On the other hand, we know the gravitational force 
between the star S with mass 
and the planet P1 with mass 
is:
(5)
Where 
is the Gravitational Constant and its value is 
In addition, the centripetal force 
exerted on the planet is:
(6)
Assuming this system is in equilibrium:
(7)
Substituting (5) and (6) in (7):
(8)
Finding :
(9)
(10)
Finally:
(11) This is the mass of the star S
To reach a vertical height of 13.8 ft against gravity, which has an acceleration of 32 ft/s^2, the required vertical speed can be calculated from the equation:
vi^2 - vf^2 = 2*g*h
Given that it has vf = 0 (it is not moving vertically at its maximum height), g = 32, and h = 13.8, we can solve for vi:
vi^2 = 29.72 ft/s
This is only its vertical speed, so this is equivalent to its original speed multiplied by the sine of the angle:
29.72 ft/s = (v_original)*(sin 42.2<span>°</span>)
v_original = 44.24 ft/s
Converting to m/s, this can be divided by 3.28 to get 13.49 m/s.
The ball should take twice as long to return to its original position as it took to reach its maximum height, so it should return to its original position at 
.
It would take about 4.8 years to travel from earth to Saturn.
<h3>How long would it take?</h3>
We know that speed is expressed as the ratio of distance to time. In this case, we are trying to know ow many years would it take to reach the planet Saturn travelling at 21 thousand miles per hour.
Given that;
Speed = 21 thousand miles per hour
time taken = ???
Distance = 887 million miles
Speed = distance/time
speed * time = distance
time = distance/speed
time = 8.87 * 10^8 miles/2.1 * 10^4 miles per hour
time = 4.22 * 10^4 hours
If 8.766 * 10^3 hours make 1 year
4.22 * 10^4 hours make 4.22 * 10^4 hours * 1 year/8.766 * 10^3
= 4.8 years
Learn more about Saturn:brainly.com/question/12181523
#SPJ1
