consider the points p(,,) and q(,,). a. find and state your answer in two forms: and aibjck. b. find the magnitude of .
1 answer:
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Answer:
The maximum speed of the wing tip is 1.25 m/s
Explanation:
In simple harmonic motion, the body experiences a restoring force whose magnitude is directly proportional to the distance from its mean position and its direction is towards the mean position.
The speed in the case of simple harmonic motion is given by the equation :
v = Aωsinωt
Here A is maximum displacement, t is time and ω is the angular frequency of oscillation.
For maximum speed, sinωt = 1 . So, the above equation becomes:
v = Aω
But, ω = 2πf , here f is the frequency of oscillation. So,
v = A x 2πf .....(1)
In this problem,
Frequency of oscillation, f = 40 Hz
Total distance between the upper and lower limits of motion of wing tip is equal to the twice of maximum displacement of the wing tip from the equilibrium position, i.e. ,
2 x A = 1 cm
A = 0.5 cm = 0.5 x 10⁻² m
Substitute the value of f and A in equation (1).
v = 1.25 m/s
Answer:
F = 3.6 kN, direction is 9.6º to the North - East
Explanation:
The force is a vector, so one method to find the solution is to work with the components of the vector as scalars and then construct the resulting vector.
Let's use trigonometry to find the component of the forces, let's use a reference frame where the x-axis coincides with the East and the y-axis coincides with the North.
Wind
X axis
F₁ = 2.50 kN
Tide
cos 30 = F₂ₓ / F₂
sin 30 = F_{2y} / F₂
F₂ₓ = F₂ cos 30
F_{2y} = F₂ sin 30
F₂ₓ = 1.20cos 30 = 1.039 kN
F_{2y} = 1.20 sin 30 = 0.600 kN
the resultant force is
X axis
Fₓ = F₁ₓ + F₂ₓ
Fₓ = 2.50 +1.039
Fₓ = 3,539 kN
F_y = F_{2y}
F_y = 0.600
to find the vector we use the Pythagorean theorem
F =
F =
F = 3,589 kN
the address is
tan θ = F_y / Fₓ
θ = tan⁻¹
θ = tan⁻¹ 0.6 / 3.539
θ = 9.6º
the resultant force to two significant figures is
F = 3.6 kN
the direction is 9.6º to the North - East
Answer:
The distance from the positive plate at which the two pass each other is 0.0023 cm.
Explanation:
We need to find the acceleration of each particle first. Let's use the electric force equation.
<u>For the proton</u>
<u>For the electron</u>
Now we know that the plate separation is 4.26 cm or 0.0426 m. The travel distance of the proton plus the travel distance of the electron is 0.0426 m.
Both of them have an initial speed equal to zero. So we have:
With this time we can find the distance from the positive plate (x(p)).
Therefore, the distance from the positive plate at which the two pass each other is 0.0023 cm.
I hope it helps you!