Answer:
c) 2.02 x 10^16 nuclei
Explanation:
The isotope decay of an atom follows the equation:
ln[A] = -kt + ln[A]₀
<em>Where [A] is the amount of the isotope after time t, k is decay constant, [A]₀ is the initial amount of the isotope</em>
[A] = Our incognite
k is constant decay:
k = ln 2 / Half-life
k = ln 2 / 4.96 x 10^3 s
k = 1.40x10⁻⁴s⁻¹
t is time = 1.98 x 10^4 s
[A]₀ = 3.21 x 10^17 nuclei
ln[A] = -1.40x10⁻⁴s⁻¹*1.98 x 10^4 s + ln[3.21 x 10^17 nuclei]
ln[A] = 37.538
[A] = 2.01x10¹⁶ nuclei remain ≈
<h3>c) 2.02 x 10^16 nuclei</h3>
<span>
as we know that the velocity vectors are at right angles
magnitude = ?
hypotenuse of a right
triangle.
v^2 = 90^2 + 4^2
v^2 = 8116
Taking the square root of both sides here we get,
v = 90.1 m/s
hope it helps
</span>
Let's call the constant acceleration a.
At a time t, its speed will thus be v(t)=a*t+v0 where v0 is its initial speed, here 10 m/s. Hence v(t)=a*t+10.
From there we can deduce the position P(t)=a*t^2/2+10t+p0 where p0 is the initial position, here 0.
Hence P(t)=a*t^2/2+10t
Let's call T the time at which it's at 50 m/s, we know that P(T)=225m and that v(T)=50 m/s hence a*T+10=50 thus a=40/T and P(T)=(40/2+10)T=30T
Hence T=225/30=7.5
It took 7.5 seconds
So, <u>the value of the work is approximately 84.65 J</u>.
<h2>Introduction</h2>
Hi ! Here I will help you to discuss the subject about work that caused by force in amount value of angle. Work is affected by the force and displacement.
- If related to the magnitude of the force, the amount of work will be proportional to the magnitude of the applied force. Thats mean, if the value of the force that applied on it is greater, then the value of the work will be greater.
- If related to the magnitude of shift, the amount of work will be proportional to the magnitude of shift of object. Thats mean, if the value of the shift on it is greater, then the value of the work will be greater.
<h3>Formula Used</h3>
The work done by a moving object can be expressed in the equation:
If the Angle Is Ignored

If the Angle Effect on Work

With the following condition:
- W = work that done by object (J)
- F = force that applied (N)
- s = shift or distance (m)
= angle of elevation (°)
<h3>Solution</h3>
We know that :
- F = force that applied =
N - s = shift or distance = 84.9 m
= angle of elevation = 45°
What was asked ?
- W = work that done by object = ... J
Step by step :






<h3>Conclusion</h3>
So, the value of the work is approximately 84.65 J.
To solve this exercise we need the concept of Kinetic Energy and its respective change: Initial and final kinetic energy.
Let's start considering that the angular velocity is given by,

Where,
V = linear speed
R = the radius
In the case of the initial kinetic energy:

Where I is the moment of inertia previously defined.

In the case of the final kinetic energy, we have to,


For conservation of Energy we have, that
, then (canceling the mass and the radius)




