Answer:
Explanation:Hooke's law states that " if the elastic limit of an elastic material is not exceeded, the extension,e is directly proportional to the applied force or load.
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
Answer is number 2, change in momentum of the object.
The total mechanical energy of the notebook is <u><em>19J</em></u>.
Mechanical energy is the sum of potential energy and kinetic energy. It has no kinetic energy, because it's not moving. So its potential energy is all the mechanical energy it has.
Answer:
k = 5406.88 N/m
Explanation:
Since the initial and final temperatures are constant while the gas expands, the expansion of the gas obeys Boyle's law
Initial gas pressure,
Let the initial gas volume = V
Volume = Length * Area
Since the cross sectional area does not change and the length of the gas-filled chamber is said to double, then the volume also doubles.
The final gas pressure, will be gotten from the Boyle's law equation
The Cross Sectional Area,
R = 5.33 cm = 0.0533 m
= 0.0089 m²
The force exerted on the piston, F = P₂ A
F = 1.145 * 10⁵ * 0.0089
F = 1021.9 N
To get the spring constant, use Hooke's law
F = k Δx
Where Δx = l₂ - l₁
Δx = 2l - l = l ( since the length of the chamber doubles on expansion)
Δx = 18.9 cm = 0.189 m
F = k Δx
1021.9 = k * 0.189
k = 1021.9/0.189
k = 5406.88 N/m