Answer:
(a) α = -0.16 rad/s²
(b) t = 33.2 s
Explanation:
(a)
Applying 3rd equation of motion on the circular motion of the tire:
2αθ = ωf² - ωi²
where,
α = angular acceleration = ?
ωf = final angular velocity = 0 rad/s (tire finally stops)
ωi = initial angular velocity = 5.45 rad/s
θ = Angular Displacement = (14.4 rev)(2π rad/1 rev) = 28.8π rad
Therefore,
2(α)(28.8π rad) = (0 rad/s)² - (5.45 rad/s)²
α = -(29.7 rad²/s²)/(57.6π rad)
<u>α = -0.16 rad/s²</u>
<u>Negative sign shows deceleration</u>
<u></u>
(b)
Now, we apply 1st equation of motion:
ωf = ωi + αt
0 rad/s = 5.45 rad/s + (-0.16 rad/s²)t
t = (5.45 rad/s)/(0.16 rad/s²)
<u>t = 33.2 s</u>
Answer:
v = 2.029 m/s
Explanation:
Given
L = 84.0 cm ⇒ R = 0.5*L = 0.5*84 cm = 42 cm = 0.42 m
m₁ = 0.600 kg
m₂ = 0.200 kg
g = 9.8 m/s²
u₁ = u₂ = 0 m/s
v₁ = ?
v₂ = ?
Due to gravity, the bar oscillates and becomes vertical. The mass that occupies the lower position is the one with the highest torque. The one that reduces the potential energy (the system tends to the position of minimum energy). This is achieved if the mass that goes down is 0.6kg (that goes down 42cm) and the one that goes up is 0.2kg (goes up 42cm).
In this system mechanical energy is conserved, so we can match its value in the horizontal position with the one in the vertical.
then
Ei = Ki + Ui = 0.5*(m₁+m₂)*(0)² + (m₁+m₂)*9.8*(0) = 0 J
Ef = Kf + Uf
⇒ Kf = 0.5*(m₁+m₂)*v² = 0.5*(0.6+0.2)*v² = 0.4*v²
⇒ Uf = m₁*g*h₁ + m₂*g*h₂ = 0.6*9.8*(-0.42) + 0.2*9.8*0.42 = - 1.6464
⇒ Ef = Kf + Uf = 0.4*v² - 1.6464
Since
0 = 0.4*v² - 1.6464 ⇒ v = 2.029 m/s
v is the same value due to the wooden rod is pivoted about a horizontal axis through its center and the masses are on opposite ends.
v₁ = v₂ = v ⇒ ω₁*R₁ = ω₂*R₂ ⇒ ω₁*R = ω₂*R ⇒ ω₁ = ω₂ = ω
⇒ v = ω*R
Answer:
560 m
Explanation:
The speed of sound in air is approximately:
v ≈ v₀ + 0.6T
where v₀ is the speed of sound at 0°C (273 K) in m/s, and T is the temperature in Celsius.
The speed of sound at 20°C at that altitude is:
v ≈ 327 + 0.6(20)
v ≈ 339 m/s
The sound travels from the hikers to the mountain and back again, so it travels twice the distance.
339 m/s = 2d / 3.3 s
2d = 1118.7 m
d = 559.35 m
Rounding, the mountain is approximately 560 m away.
Answer:
Yes, the errors are likely to be relevant
Explanation:
A systematic error occurs as a result of the instrument used in carrying out and experiment. These errors are a result of small fluctuations in the measurement properties of the instrument. This happens when the instrument departs from non-ideal situations, for example as a result of physical expansion or change in temperature. For instance, let the resistance be measured to be up to 10 Ω ± 1 Ω
The error of the resistance, ε = 0.01Ω
Answer:
E = 307667 N/C
Explanation:
Since the object's mass is 1 g, then its weight in newtons is 0.001 * 9.8 = 0.0098 N.
This weight should have the same magnitude of the vertical component of the tension T of the string (T * cos(37)) so we can find the magnitude of the tension T via:
0.0098 N = T * cos(37)
then T = 0.0098/cos(37) N = 0.01227 N
Knowing the tension's magnitude, we can find its horizontal component:
T * sin(37) = 0.007384 N
and now we can obtain the value of the electric field since we know the charge of the ball to be: -2.4 * 10^(-8) C:
0.007384 N = E * 2.4 * 10^(-8) C
Then E = 0.007384/2.4 * 10^(-8) N/C
E = 307667 N/C
