Answer:
zero or 2π is maximum
Explanation:
Sine waves can be written
x₁ = A sin (kx -wt + φ₁)
x₂ = A sin (kx- wt + φ₂)
When the wave travels in the same direction
Xt = x₁ + x₂
Xt = A [sin (kx-wt + φ₁) + sin (kx-wt + φ₂)]
We are going to develop trigonometric functions, let's call
a = kx + wt
Xt = A [sin (a + φ₁) + sin (a + φ₂)
We develop breasts of double angles
sin (a + φ₁) = sin a cos φ₁ + sin φ₁ cos a
sin (a + φ₂) = sin a cos φ₂ + sin φ₂ cos a
Let's make the sum
sin (a + φ₁) + sin (a + φ₂) = sin a (cos φ₁ + cos φ₂) + cos a (sin φ₁ + sinφ₂)
to have a maximum of the sine function, the cosine of fi must be maximum
cos φ₁ + cos φ₂ = 1 +1 = 2
the possible values of each phase are
φ1 = 0, π, 2π
φ2 = 0, π, 2π,
so that the phase difference of being zero or 2π is maximum
Answer:
3. none of these
Explanation:
The rotational kinetic energy of an object is given by:
where
I is the moment of inertia
is the angular speed
In this problem, we have two objects rotating, so the total rotational kinetic energy will be the sum of the rotational energies of each object.
For disk 1:
For disk 2:
so the total energy is
So, none of the options is correct.
Answer:
As the person moves down the zip wire, her increase in kinetic energy is less than her decrease in gravitational potential energy.
Explanation:
Work is done against the air resistance, causing thermal energy to transfer to the surroundings
Answer:
The cannonball fly horizontally before it strikes the ground, S = 323.25 m
Explanation:
Given data,
The height of the cliff, h = 80 m
The horizontal velocity of the cannonball, Vₓ = 80 m/s
The range of the cannon ball with initial vertical velocity is zero is given by the formula,
S = 323.25 m
Hence, the cannonball fly horizontally before it strikes the ground, S = 323.25 m
(D) The gravitational force between the astronaut and the asteroid.
Reason :
All the other forces given in the options, except (D), doesn't account for the motion of the astronaut. They are the forces that act between nucleons or atoms and neither of them accounts for an objects motion.
