Answer:
a) the rotational speed of the clay is 3.45 rad/s
b) the value of A in the equation of motion is 0.15 m
c) the value of ϕi is 90° or π/2 rad.
Explanation:
Given that;
Revolution per minute rpm = 33( 1/3) = 100/3
The frequency f = 100 / 3(60) = 0.55 Hz
a)
Rotational speed W = 2πf
we substitute
W = 2π × 0.55
W = 3.45 rad/s
Therefore, the rotational speed of the clay is 3.45 rad/s
b)
given equation; y(t)=Asin(ωt+ϕi)
given that radius = 0.15 m
y(t)=(0.2)sin(ωt+ϕi)
Therefore, the value of A in the equation of motion is 0.15 m
c)
since y(t) has the maximum value at t =0
so at t=0
y(0) = (0.15)sin(ω(0)+ϕi)
= 0.15sin(ϕi)
this will give maximum value when ϕi = 90°
so
y(0) = (0.15)sin(ω(0)+ϕi)
= 0.15sin(90°)
= 0.15
hence, the value of ϕi is 90° or π/2 rad.
Answer:
I think the Bulb No. 2 will stop emitting light if the bulb No. 1 burns out.
Work needed: 720 J
Explanation:
The work needed to stretch a spring is equal to the elastic potential energy stored in the spring when it is stretched, which is given by
where
k is the spring constant
x is the stretching of the spring from the equilibrium position
In this problem, we have
E = 90 J (work done to stretch the spring)
x = 0.2 m (stretching)
Therefore, the spring constant is
Now we can find what is the work done to stretch the spring by an additional 0.4 m, that means to a total displacement of
x = 0.2 + 0.4 = 0.6 m
Substituting,
Therefore, the additional work needed is
Learn more about work:
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Answer:
The answer to your question is given below.
Explanation:
Mechanical advantage (MA) = Load (L)/Effort (E)
MA = L/E
Velocity ratio (VR) = Distance moved by load (l) / Distance moved by effort (e)
VR = l/e
Efficiency = work done by machine (Wd) /work put into the machine (Wp) x 100
Efficiency = Wd/Wp x100
Recall:
Work = Force x distance
Therefore,
Work done by machine (wd) = load (L) x distance (l)
Wd = L x l
Work put into the machine (Wp) = effort (E) x distance (e)
Wp = E x e
Note: the load and effort are measured in Newton (N), while the distance is measured in metre (m)
Efficiency = Wd/Wp x100
Efficiency = (L x l) / (E x e) x 100
Rearrange
Efficiency = L/E ÷ l/e x 100
But:
MA = L/E
VR = l/e
Therefore,
Efficiency = L/E ÷ l/e x 100
Efficiency = MA ÷ VR x 100
Efficiency = MA / VR x 100
So the equation for angular velocity is
Omega = 2(3.14)/T
Where T is the total period in which the cylinder completes one revolution.
In order to find T, the tangential velocity is
V = 2(3.14)r/T
When calculated, I got V = 3.14
When you enter that into the angular velocity equation, you should get 2m/s
