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:
4.9 m/s
Explanation:
Since the motion of the ball is a uniformly accelerated motion (constant acceleration), we can solve the problem by using the following suvat equation:
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the distance covered
For the ball in this problem,
u = 0 (it starts from rest)
is the acceleration
s = 3 m is the distance covered
Solving for v,
According to the second law of motion, force is equal to the product of mass and acceleration. This means force is proportional to mass. Hence when mass increases, it is understood that force should increase as well. In this case,the answer to this problem is A.
Explanation:
At the top of the the ball's trajectory, there is only the horizontal component of the initial velocity, which is so the kinetic energy of the ball at this point is
<span>Air at the equator is warmed by the direct rays of the sun while air at the poles is cooled because the suns rays are not so direct. As air warms, it expands and becomes less dense therefore rises, similarly but vice versa for cool air.
Hope this helped </span>