Answer:
(a) 
(b) 
(c) K.E. = 21.168 J
(d) 
Explanation:
Given:
- mass of a block, M = 3.6 kg
- initial velocity of the block,
- constant downward acceleration,
That a constant upward acceleration of 
is applied in the presence of gravity.
∴
- height through which the block falls, d = 4.2 m
(a)
Force by the cord on the block,
∴Work by the cord on the block,
We take -ve sign because the direction of force and the displacement are opposite to each other.
(b)
Force on the block due to gravity:
∵the gravity is naturally a constant and we cannot change it
∴Work by the gravity on the block,
(c)
Kinetic energy of the block will be equal to the net work done i.e. sum of the two works.
mathematically:
K.E. = 21.168 J
(d)
From the equation of motion:
putting the respective values:
is the speed when the block has fallen 4.2 meters.
I belive it could be 6.5 but I could be wrong
The time taken by traveler to cover the distance is,
Substitute the known values,
Therefore, the time taken by traveler to cover the distance is 89.3 s.
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>
