A television channel is assigned the frequency range from 54 MHz to 60 MHz. A series RLC tuning circuit in a TV receiver resonat
1 answer:
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A) 320 count/min
B) 40 count/min
C) 80 count/min, 11400 years
Explanation:
A)
The activity of a radioactive sample is the number of decays per second in the sample.
The activity of a sample is therefore directly proportional to the number of nuclei in the sample:
where A is the activity and N the number of nuclei.
As a consequence, since the number of nuclei is proportional to the mass of the sample, the activity is also directly proportional to the mass of the sample:
where m is the mass of the sample.
In this problem:
- When the mass is , the activity is
- When the mass is , the activity is
So we can find A2 by using the rule of three:
B)
The equation describing the activity of a radioactive sample as a function of time is:
(1)
where
is the initial activity at time t = 0
t is the time
is the decay constant, which gives the probability of decay
The decay constant can be found using the equation
where is the half-life, which is the amount of time it takes for the radioactive sample to halve its activity.
In this problem, carbon-14 has half-life of
So its decay constant is
We also know that the tree died
t = 17,100 years ago
and that the initial activity was
(value calculated in part A, corresponding to a mass of 20 g)
So, substituting into eq(1), we find the new activity:
C)
We know that a sample of living wood has an activity of
per 1 g of mass.
Here we have 5 g of mass, therefore the activity of the sample when it was living was:
Moreover, here we have a sample of 5 g, with current activity of : it means that its activity per gram of mass is
We know that the activity halves after every half-life: Here the activity has became 1/4 of the original value, this means that 2 half-lives have passed, because:
- After 1 half-life, the activity drops from 16 count/min to 8 count/min
- After 2 half-lives, the activity dropd to 4 count/min
So the age of the wood is equal to 2 half-lives, which is:
Answer:
La velocidad con la que se debe lanzar el trineo es aproximadamente 9.96 m/s
Explanation:
La masa del trineo, m = 2 kg
El ángulo de inclinación del trineo, θ = 30 °
El coeficiente de fricción, μ = 0,15
La altura a la que debe ascender el trineo, h = 4 m
La reacción normal del trineo en la rampa, N = m · g · cos (θ)
La fuerza de fricción = N × μ
Dónde;
g = Th aceleración debida a la gravedad ≈ 9.81 m/s²
∴ = 0.15 × 2 kg × 9.81 m/s² × cos (30°) ≈ 2.55 N
La longitud de la rampa que se mueve el trineo, l = h/(sin(θ))
∴ l = 4/(sin(30°)) = 8
La longitud de la rampa que se mueve el trineo, l = 8 m
El trabajo realizado sobre la fricción, =
× l
= 2.55 × 8 ≈ 20.4
El trabajo realizado sobre la fricción, ≈ 20.4 Julios
El trabajo realizado para levantar el trineo a 4 metros de altura, P.E. = m·g·h
∴ P.E. = 2 kg × 9.81 m/s² × 4 m ≈ 78.48 Joules
El trabajo realizado para levantar el trineo a 4 metros de altura, P.E. ≈ 78.48 Joules
El trabajo total requerido para levantar el trineo 4 metros por la rampa, =
+ P.E.
= 20.4 J + 78.84 J ≈ 99.24 J
Energía cinética, K.E. = 1/2 × m × v²
La energía cinética necesaria para mover el trineo por la rampa, K.E. se da de la siguiente manera;
K.E. = 1/2 × 2 kg × v² ≈ 99.24 J
∴ v² ≈ 99.24 J/(1/2 × 2 kg)
La velocidad con la que se debe lanzar el trineo para que ascienda 4 metros por la rampa, v ≈ 9.96 m/s