Answer:
a) K = 0.63 J, b) h = 0.153 m
Explanation:
a) In this exercise we have a physical pendulum since the rod is a material object, the angular velocity is
w² = 
where d is the distance from the pivot point to the center of mass and I is the moment of inertia.
The rod is a homogeneous body so its center of mass is at the geometric center of the rod.
d = L / 2
the moment of inertia of the rod is the moment of a rod supported at one end
I = ⅓ m L²
we substitute
w = 
w = 
w = 
w = 4.427 rad / s
an oscillatory system is described by the expression
θ = θ₀ cos (wt + Φ)
the angular velocity is
w = dθ /dt
w = - θ₀ w sin (wt + Ф)
In this exercise, the kinetic energy is requested in the lowest position, in this position the energy is maximum. For this expression to be maximum, the sine function must be equal to ±1
In the exercise it is indicated that at the lowest point the angular velocity is
w = 4.0 rad / s
the kinetic energy is
K = ½ I w²
K = ½ (⅓ m L²) w²
K = 1/6 m L² w²
K = 1/6 0.42 0.75² 4.0²
K = 0.63 J
b) for this part let's use conservation of energy
starting point. Lowest point
Em₀ = K = ½ I w²
final point. Highest point
Em_f = U = m g h
energy is conserved
Em₀ = Em_f
½ I w² = m g h
½ (⅓ m L²) w² = m g h
h = 1/6 L² w² / g
h = 1/6 0.75² 4.0² / 9.8
h = 0.153 m
Answer:
The volume of water is 139 mL.
Explanation:
Due to the Law of conservation of energy, the heat lost by coffee is equal to the heat gained by the water, that is, the sum of heats is equal to zero.
The heat (Q) can be calculated using the following expression:
where,
c is the specific heat of each substance
m is the mass of each substance
ΔT is the difference in temperature for each substance
The mass of coffee is:
Then,
The volume of water is:
Answer:
<h3>The answer is 500 kg</h3>
Explanation:
The mass of the object can be found by using the formula
v is the velocity
KE is the kinetic energy
From the question we have
We have the final answer as
<h3>500 kg</h3>
Hope this helps you
Answer: n = c / v" "c" is the speed of light in a vacuum, "v" is the speed of light in that substance and "n" is the index of refraction. According to the formula, the index of refraction is the relation between the speed of light in a vacuum and the speed of light in a substance.
Explanation: the relation is the vacuum and the speed of light in a substance.
Answer:
a)30.14 rad/s2
b)43.5 rad/s
c)60633 J
d)42 kW
e)84 kW
Explanation:
If we treat the propeller is a slender rod, then its moments of inertia is
a. The angular acceleration is Torque divided by moments of inertia:
b. 5 revolution would be equals to 
rad, or 31.4 rad. Since the engine just got started
c. Work done during the first 5 revolution would be torque times angular displacement:
d. The time it takes to spin the first 5 revolutions is
The average power output is work per unit time
or 42 kW
e.The instantaneous power at the instant of 5 rev would be Torque times angular speed at that time:
or 84 kW
