Answer:
a) k = 120 N / m
, b) f = 0.851 Hz
, c) v = 1,069 m / s
, d) x = 0
, e) a = 5.71 m / s²
, f) x = 0.200 m
, g) Em = 2.4 J
, h) v = -1.01 m / s
Explanation:
a) Hooke's law is
F = k x
k = F / x
k = 24.0 / 0.200
k = 120 N / m
b) the angular velocity of the simple harmonic movement is
w = √ k / m
w = √ (120 / 4.2)
w = 5,345 rad / s
Angular velocity and frequency are related.
w = 2π f
f = w / 2π
f = 5.345 / 2π
f = 0.851 Hz
c) the equation that describes the movement is
x = A cos (wt + Ф)
As the body is released without initial velocity, Ф = 0
x = 0.2 cos wt
Speed is
v = dx / dt
v = -A w sin wt
The speed is maximum for sin wt = ±1
v = A w
v = 0.200 5.345
v = 1,069 m / s
d) when the function sin wt = -1 the function cos wt = 0, whereby the position for maximum speed is
x = A cos wt = 0
x = 0
e) the acceleration is
a = d²x / dt² = dv / dt
a = - Aw² cos wt
The acceleration is maximum when cos wt = ± 1
a = A w²
a = 0.2 5.345
a = 5.71 m / s²
f) the position for this acceleration is
x = A cos wt
x = A
x = 0.200 m
g) Mechanical energy is
Em = ½ k A²
Em = ½ 120 0.2²
Em = 2.4 J
h) the position is
x = 1/3 A
Let's calculate the time to reach this point
x = A cos wt
1/3 A = A cos 5.345t
t = 1 / w cos⁻¹(1/3)
The angles are in radians
t = 1.23 / 5,345
t = 0.2301 s
Speed is
v = -A w sin wt
v = -0.2 5.345 sin (5.345 0.2301)
v = -1.01 m / s
i) acceleration
a = -A w² sin wt
a = - 0.2 5.345² cos (5.345 0.2301)
a = -1.91 m / s²
Answer:
it must be helical motion in which the charge particle will move uniformly along z axis and simultaneously it will move in circular path in xy plane.
Explanation:
Magnetic field is along z axis while velocity is in x-z plane
so we will have
so here we can say
so we will have
so here the net force on the charge is perpendicular to its x directional velocity along - Y direction
So due to this component of motion it will move along a circle while other component of the motion will remain uniform always
So here it is combination of two parts
1) Uniform circular motion
2) Uniform motion
So we can say that it must be helical motion in which the charge particle will move uniformly along z axis and simultaneously it will move in circular path in xy plane.
A pulsar, or a pulsing star, is a highly magnetized neutron star that emits a beam of electromagnetic radiation. So they blink when they are rotating because the beam of radiation they emit can only be seen when it is facing the Earth.
Hope this helps.
Weight on any planet is (mass) x (acceleration of gravity there).
Acceleration of gravity on Earth is about 9.8 meters per second² .
So weight of 50 kg on Earth is (50 x 9.8) = <u>490 newtons</u>.
(That's about 110.2 pounds.)
