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
No they do not there not humans
Answer:
The objects become oppositely charged and have equal amounts of charge.
Explanation:
There are three methods for charging objects:
- Conduction: a charged object is brought in contact with a neutral object. Electrons are transferred from the charged object to the neutral one, which also becomes charged
- Induction: a charged object is brought close (but not in contact) to a neutral object. The charges inside the neutral object redistribute, such that those of opposite sign to the charge in the charged object migrate on the side closer to the charged object, while the charges of same sign migrate towards the opposite side. If the neutral object is then grounded, the charges on the opposite side flow to the ground, leaving the neutral object charged as well
- Friction: two objects initially neutral are rubbed against each other. Electrons move from one object to the other one: therefore, one object becomes positively charged while the other one becomes negatively charged. Since the charge gained by one object is equal to charge lost by the other object, it follows that the two objects have same magnitude of charge, but with opposite sign.
