Do the adding up on the chart
Answer:
0.00050, 0.000000000406, 36513
Answer:
a) A = 4.0 m
, b) w = 3.0 rad / s
, c) f = 0.477 Hz
, d) T = 20.94 s
Explanation:
The equation that describes the oscillatory motion is
x = A cos (wt + fi)
In the exercise we are told that the expression is
x = 4.0 cos (3.0 t + 0.10)
let's answer the different questions
a) the amplitude is
A = 4.0 m
b) the frequency or angular velocity
w = 3.0 rad / s
c) angular velocity and frequency are related
w = 2π f
f = w / 2π
f = 3 / 2π
f = 0.477 Hz
d) the period
frequency and period are related
T = 1 / f
T = 1 / 0.477
T = 20.94 s
e) the phase constant
Ф = 0.10 rad
f) velocity is defined by
v = dx / dt
v = - A w sin (wt + Ф)
speed is maximum when sine is + -1
v = A w
v = 4 3
v = 12 m / s
g) the angular velocity is
w² = k / m
k = m w²
k = 1.2 3²
k = 10.8 N / m
h) the total energy of the oscillator is
Em = ½ k A²
Em = ½ 10.8 4²
Em = 43.2 J
i) the potential energy is
Ke = ½ k x²
for t = 0 x = 4 cos (0 + 0.1)
x = 3.98 m
j) kinetic energy
K = ½ m v²
for t = 00.1
²
v = A w sin 0.10
v = 4 3 sin 0.10
v = 1.98 m / s
Answer:
the distance that the dice is under the monkey 6 m
Explanation:
This is a projectile throwing exercise for the dart and free fall for the monkey, as we are asked for the distance when the dart passes under the monkey, so by that time the dice is 100 m away from the monkey, let's calculate how long it takes for the dart to reach this point
X = Vox t
t = X / Vox
t = 100/32
t = 3,125 s
With this time let's calculate the height of the dart and height that the monkey has descended
Dart
Y = Voy t - ½ g t²
Y = 10.88 3.125 - ½ 9 3125² = 34 - 43.94
Y = - 9.94 m
Monkey
Let's calculate how much descended in this time, see that the monkey is 40 m higher than the dart
Ym = Yo + Vot - ½ g t²
We assume that the monkey is released so that its Vo is zero
Ym = Yo - ½ g t²
Ym = 40 - ½ 9 3,125² = 40 -43.94
Ym = -3.94 m
We already have the distances of each one, the difference between them is the subtraction of the two
ΔDY = Yd -Ym
ΔY = 9.94 -3.94
ΔY = 6 m
This is the distance that the dice is under the monkey