Heavy rains in late July 2010 triggered the mass wasting that occurred in this mountain valley near Durango, Colorado. Heavy equ
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Answer:
a) see attached, a = g sin θ
b)
c) v = √(2gL (1-cos θ))
Explanation:
In the attached we can see the forces on the sphere, which are the attention of the bar that is perpendicular to the movement and the weight of the sphere that is vertical at all times. To solve this problem, a reference system is created with one axis parallel to the bar and the other perpendicular to the rod, the weight of decomposing in this reference system and the linear acceleration is given by
Wₓ = m a
W sin θ = m a
a = g sin θ
b) The diagram is the same, the only thing that changes is the angle that is less
θ' = 9/2 θ
c) At this point the weight and the force of the bar are in the same line of action, so that at linear acceleration it is zero, even when the pendulum has velocity v, so it follows its path.
The easiest way to find linear speed is to use conservation of energy
Highest point
Em₀ = mg h = mg L (1-cos tea)
Lowest point
Emf = K = ½ m v²
Em₀ = Emf
g L (1-cos θ) = v² / 2
v = √(2gL (1-cos θ))
Answer:
Explanation:
<u>Uniform Acceleration </u>
When an object changes its velocity at the same rate, the acceleration is constant.
The relation between the initial and final speeds is:
Where:
vf = Final speed
vo = Initial speed
a = Constant acceleration
t = Elapsed time
It's known a train moves from rest (vo=0) to a speed of vf=25 m/s in t=30 seconds. It's required to calculate the acceleration.
Solving for a:
Substituting:
Answer:
LED bulb = 0.145 A
Incandescent bulb = 0.909 A
CFL bulb = 0.218 A
Explanation:
Given:
Power rating of LED bulb (P₁) = 16 W
Power rating of incandescent bulb (P₂) = 100 W
Power rating of CFL bulb (P₃) = 24 W
Terminal voltage across the circuit (V) = 110 V
We know that, power is related to terminal voltage and current drawn as:
Express this in terms of 'I'. This gives,
Now, calculate the current drawn in each bulb using their respective values.
For LED bulb,
So, current drawn is given as:
For incandescent bulb,
So, current drawn is given as:
For CFL bulb,
So, current drawn is given as:
Therefore, the currents drawn through LED bulb, incandescent bulb and CFL bulb are 0.145 A, 0.909 A and 0.218 A respectively.