Answer:
y = -19.2 sin (23.15t) cm
Explanation:
The spring mass system is an oscillatory movement that is described by the equation
y = yo cos (wt + φ)
Let's look for the terms of this equation the amplitude I
y₀ = 19.2 cm
Angular velocity is
w = √ (k / m)
w = √ (245 / 0.457
w = 23.15 rad / s
The φ phase is determined for the initial condition t = 0 s
, the velocity is negative v (0) = -vo
The speed of the equation is obtained by the derivative with respect to time
v = dy / dt
v = - y₀ w sin (wt + φ)
For t = 0
-vo = -yo w sin φ
The angular and linear velocity are related v = w r
v₀ = w r₀
v₀ = v₀ sinφ
sinφ = 1
φ = sin⁻¹ 1
φ = π / 4 rad
Let's build the equation
y = 19.2 cos (23.15 t + π/ 4)
Let's use the trigonometric ratio π/ 4 = 90º
Cos (a +90) = cos a cos90 - sin a sin sin 90 = 0 - sin a
y = -19.2 sin (23.15t) cm
Answer:
A 3 feet radius snowball will melt in 54 hours.
Explanation:
As we can assume that the rate of snowball takes to melt is proportional to the surface area, then the rate for a 3 feet radius will be:
T= A(3 ft)/A(1 ft) * 6 hr
A is the area of the snowballs. For a spherical geometry is computing as:
A=4.pi.R^2
Then dividing the areas:
A(3 feet)/A(1 foot) = (4 pi (3 ft)^2)/(4 pi (1 ft)^2) = (36pi ft^2)/(4pi ft^2)= 9
Finally, the rate for the 3 feet radius snowball is:
T= 9 * 6 hr = 54 hr
<h2>
Answer: Gravitational attraction will be the same</h2>
According to the law of universal gravitation, which is a classical physical law that describes the gravitational interaction between different bodies with mass:
(1)
Where:
is the module of the force exerted between both bodies
is the universal gravitation constant.
and 
are the masses of both bodies.
is the distance between both bodies
Now, if we double both masses and the distance also doubles, this means:
and will be now 
and 
will be now 
Let's rewrite the equation (1) with this new values:
(2)
Solving and simplifying:
(3)
As we can see, equation (3) is the same as equation (1).
So, if the masses both double and the distance also doubles the <u>Gravitational attraction between both masses will remain the same.</u>
Answer:
A = 1.4 m/s²
B = -0.10493 m/s³
a = 1.29507 m/s²
T = 28095.8271 N
T = 1.13198 W
Explanation:
t = Time taken
g = Acceleration due to gravity = 9.81 m/s²
The equation
Differentiating with respect to time
At t = 0
Hence, A = 1.4 m/s²
B = -0.10493 m/s³
At t = 5 seconds
a = 1.29507 m/s²
T = 28095.8271 N
Weight of rocket
T = 1.13198 W
Answer:
The poem, Going Down the Hill on a Bicycle, written by Henry Charles Beeching describes the thrilling ride of a boy going downhill. ... The poet mentions how he lifts his feet from the pedals and keeps his hands still so that he would not lose his balance and fall off the bicycle, while it is dashing down the hill.
