Answer:
T = 27.92 N
Explanation:
For this exercise let's use Newton's second law
T - W = m a
The weight
W = mg
The acceleration can be found by derivatives
a = dv / dt
v = 2 t + 0.6 t²
a = 2 + 0.6 t
We replace
T - mg = m (2 + 0.6t)
T = m (g + 2 + 0.6 t) (1)
Let's look for the time for the speed of 15 m / s
15 = 2 t + 0.6 t²
0.6 t² + 2 t - 15 = 0
We solve the second degree equation
t = [-2 ±√(4 - 4 0.6 (-15))] / 2 0.6
t = [-2 ±√40] / 1.3 = [-2 ± 6.325] / 1.2
We take the positive time
t = 3.6 s
Let's calculate from equation 1
T = 2.00 (9.8 + 2 + 0. 6 3.6)
T = 27.92 N
Because one pole of the Earth's axis of rotation (the North one) points
almost exactly toward Polaris.
If Polaris had a pimple or a bump somewhere on its edge, you'd see
the bump rotate around the whole edge, like a clock, once a day. But
the whole star appears to stay in one place, because our axis points to it.
Answer:
22,800 years
Explanation:
Half life equation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is time,
and T is the half life.
0.0625 = (½)^(t / 5700)
log 0.0625 = (t / 5700) log 0.5
4 = t / 5700
t = 22,800
It takes 22,800 years.
