A cyclotron with a magnetic field of 0.47 t is designed to accelerate protons in a circle with a radius 0.68 m. What is the angu
1 answer:
The angular frequency of the cyclotron is 0.07 x Hz.
- Angular frequency, abbreviated "ω" is a scalar measure of rotation rate in physics.
- It describes the rate of change of the argument of the sine function, the rate of change of the phase of a sinusoidal waveform, or the angular displacement per unit of time.
The cyclotron device is made to accelerate charge particles to extremely high speeds by applying crossed electric and magnetic fields.
<h3>Calculation of angular frequency:</h3>Given,
B = 0.47 T
r = 0.68
mass of proton = 1.6x
q = 1.6 x
so, the frequency is:
f = qB/2m
f = 1.6 x x 0.47/2x3.14x1.6x
f = 0.07 x
Hence, the angular frequency of the cyclotron is 0.07 x Hz.
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Answer:
b) a = -k / m x , c) d²x / dt² = - A w² cos (wt+Ф) , d) and e) T = 2π √m / k
h) a = - A w² cos (wt+Ф)
Explanation:
a) see free body diagram in the attachment
b) We write Newton's second law
Fe = m a
-k x = ma
a = -k / m x
c) the acceleration is
a = d²x / dt²
If x = A cos wt
v = dx / dt = -A w sin (wt +Ф)
a = d²x / dt² = - A w² cos (wt+Ф)
d) we substitute in Newton's second law
d²x / dt² = -k / m x
We call
w² = k / m
e) substitute to find w
-A w² cos (wt+Ф) = -k / m A cos (wt+Ф)
w² = k / m
Angular velocity and frequency are related
w = 2π f
f = 1 / T
We substitute
T = 2π / w
T = 2π √m / k
g) v= - A w sin (wt+Ф)
h) acceleration is
a = - A w² cos (wt+Ф)
Answer:
The escape velocity on the planet is approximately 178.976 km/s
Explanation:
The escape velocity for Earth is therefore given as follows
The formula for escape velocity, , for the planet is
Where;
= The escape velocity on the planet
G = The universal gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²
m = The mass of the planet = 12 × The mass of Earth,
r = The radius of the planet = 3 × The radius of Earth,
The escape velocity for Earth, , is therefore given as follows;
= 16 ×
Given that the escape velocity for Earth, ≈ 11,186 m/s, we have;
The escape velocity on the planet = ≈ 16 × 11,186 ≈ 178976 m/s ≈ 178.976 km/s.