- Speed of ant-V_a=2m/s
- Speed of mirror =v_b=2m/s
We know
Every day a certain amount of water evaporates from Earth’s oceans, lakes, and land surface and forms water vapor and clouds in
1 answer:
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Explanation:
A) To prove the motion of the center of mass of the cylinders is simple harmonic:
System diagram for given situation is shown in attached Fig. 1
We can prove the motion of the center of mass of the cylinders is simple harmonic if
where aₓ is acceleration when attached cylinders move in horizontal direction:
<h3>PROOF:</h3>rotational inertia for cylinders is given as:
-----(1)
Newton's second law for angular motion is:
∑τ = Iα ------(2)
For linear motion in horizontal direction it is:
∑Fₓ = Maₓ ------ (3)
By definition of torque:
τ = RF --------(4)
Put (4) and (1) in (2)
from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate
So above equation becomes
------ (5)
As angular acceleration is related to linear by:
Eq (5) becomes
---- (6)
aₓ shows displacement in horizontal direction
From (3)
∑Fₓ = Maₓ
Fₓ is sum of fs and restoring force that spring exerts:
----(7)
Put (7) in (3)
[/tex] -----(8)
Using (6) in (8)
--- (9)
For spring mass system
----- (10)
Equating (9) and (10)
then (9) becomes
(The minus sign says that x and aₓ have opposite directions as shown in fig 3)
This proves that the motion of the center of mass of the cylinders is simple harmonic.
<h3 /><h3>B) Time Period</h3>Time period is related to angular frequency as:
Answer:
The initial velocity of the water from the tank is 5.42 m/s
Explanation:
By applying Bernoulli equation between point 1 and 2
At the point 1
P₁=0 ( Gauge pressure)
V₁= 0 m/s
Z₁=3 m
At point 2
P₂=0 ( Gauge pressure)
Z₂= 0 m/s
Now by putting the values
V₂= 5.42 m/s
The initial velocity of the water from the tank is 5.42 m/s
Answer:
The y-value of the line in the xy-plane where the total magnetic field is zero
Explanation:
From the question we are told that
The distance of wire one from two along the y-axis is y = 0.340 m
The current on the first wire is
The force per unit length on each wire is
Generally the force per unit length is mathematically represented as
=>
Where is the permeability of free space with a constant value of
substituting values
=>
Let U denote the line in the xy-plane where the total magnetic field is zero
So
So the force per unit length of wire 2 from line U is equal to the force per unit length of wire 1 from line (y - U)
So
substituting values