Answer:
k = 11,564 N / m, w = 6.06 rad / s
Explanation:
In this exercise we have a horizontal bar and a vertical spring not stretched, the bar is released, which due to the force of gravity begins to descend, in the position of Tea = 46º it is in equilibrium;
let's apply the equilibrium condition at this point
Axis y
W_{y} - Fr = 0
Fr = k y
let's use trigonometry for the weight, we assume that the angle is measured with respect to the horizontal
sin 46 = / W
W_{y} = W sin 46
we substitute
mg sin 46 = k y
k = mg / y sin 46
If the length of the bar is L
sin 46 = y / L
y = L sin46
we substitute
k = mg / L sin 46 sin 46
k = mg / L
for an explicit calculation the length of the bar must be known, for example L = 1 m
k = 1.18 9.8 / 1
k = 11,564 N / m
With this value we look for the angular velocity for the point tea = 30º
let's use the conservation of mechanical energy
starting point, higher
Em₀ = U = mgy
end point. Point at 30º
= K -Ke = ½ I w² - ½ k y²
em₀ = Em_{f}
mgy = ½ I w² - ½ k y²
w = √ (mgy + ½ ky²) 2 / I
the height by 30º
sin 30 = y / L
y = L sin 30
y = 0.5 m
the moment of inertia of a bar that rotates at one end is
I = ⅓ mL 2
I = ½ 1.18 12
I = 0.3933 kg m²
let's calculate
w = Ra (1.18 9.8 0.5 + ½ 11,564 0.5 2) 2 / 0.3933)
w = 6.06 rad / s
0.495 m/s
Explanation
the formula for the terminal velocity is given by:
m is the mass
g is 9.81 m/s²
ρ is density
A is area
C is the drag coefficient
then
Step 1
Let's find the mass
now, replace
hence, the answer is 0.495 m/s
Answer:
3.1 miles
Explanation:
To solve this question it is important to remember that the distance between two mile markers is approximately 1 mile
Once this is known, the question becomes very easy to solve. We make two triangle, which have the following three points
Triangle 1: Hot-Air-Balloon, Ground, Milepost 1 - With angle of depression 20
Triangle 2: Hot-Air-Balloon, Ground, Milepost 2 - With angle of depression 18
As a reminder, the angle of depression is simply the angle the balloonist's head makes with the horizontal plane to be able to see the milepost.
From this we can simply drive two formulas using the Tan function
Equation 1 -
Equation 2 -
Solving them simultaneously we get the value of height (h) to be 3.0852 miles or 3.1 miles
Answer:
this is in the middle of the wheel and helps it rotate it is an axle