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3 years ago

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A grandfather clock keeps time using a pendulum consisting of a light rod connected to a small heavy mass. With a rod of length

L, the period of oscillation is 2.00 s. What should the length of the rod be for the period of the oscillations to be 1.00 s?

1 answer:

german3 years ago

5 0

Answer:

The length of the rod should be

$\frac{L}{4} \\$

Explanation:

Period of simple pendulum is given by

$T=2\pi\sqrt{\frac{l}{g}} \\$

We have

$\frac{T_1^2}{T_2^2}=\frac{l_1}{l_2}\\\\\frac{2^2}{1^2}=\frac{L}{l_2}\\\\l_2=\frac{L}{4} \\$

The length of the rod should be

$\frac{L}{4} \\$

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The tape in a videotape cassette has a total

xxMikexx [17]

Answer:

$w=19.76 \ rad/s$

Explanation:

<u>Circular Motion </u>

Suppose there is an object describing a circle of radius r around a fixed point. If the relation between the angle of rotation by the time taken is constant, then the angular speed is also constant. If that relation increases or decreases at a constant rate, the angular speed is given by:

$w=w_o+\alpha \ t$

Where $\alpha$ is the angular acceleration and t is the time. If the object was instantly released from the circular path, it would have a tangent speed of:

$\displaystyle v_t=w.r$

We have two reels: one loaded with the tape to play and the other one empty and starting to fill with tape. They both rotate at different angular speeds, one is increasing and the other is decreasing as the tape goes from one to the other. We'll assume the tangent speed is constant for both (so the tape can play correctly). Let's call $w_1$ the angular speed of the loaded reel and $w_2$ that from the empty reel. We have

$w_1=w_{o1}+\alpha_1 \ t$

$w_2=w_{o2}+\alpha_2 \ t$

If $r_f=35\ mm=0.035\ m$ is the radius of the reel when it's full of tape, the angular speed for the loaded reel is computed by

$\displaystyle w_{01}=\frac{v_t}{r_f}$

The tangent speed is computed by knowing the length of the tape and the time needed to fully play it.

$t=1.8\ h=1.8*3600=6480\ sec$

$\displaystyle v_t=\frac{x}{t}=\frac{249\ m}{6480\ sec}=0.0384 \ m/s$

$\displaystyle w_{01}=\frac{0.0384}{0.035}=1,098 \ rad/s$

If $r_e=10\ mm=0.001\ m$ is the radius of the reel when it's empty, the angular speed for the empty reel is computed by

$\displaystyle w_{02}=\frac{0.0384}{0.001}=38.426 \ rad/s$

The full reel goes from $w_{01}$ to $w_{02}$ in 6480 seconds, so we can compute the angular acceleration:

$\displaystyle \alpha_1=\frac{w_{02}-w_{01}}{6480}$

$\displaystyle \alpha_1=\frac{38.426-1.098}{6480}=0.00576 \ rad/sec^2$

The empty reel goes from $w_{02}$ to $w_{01}$ in 6480 seconds, so we can compute the angular acceleration:

$\displaystyle \alpha_2=\frac{1.098-38.426}{6480}=-0.00576 \ rad/sec^2$

So the equations for both reels are

$w_1=1.098+0.00576 \ t$

$w_2=38.426-0.00576 \ t$

They will be the same when

$1.098+0.00576 \ t=38.426-0.00576 \ t$

Solving for t

$\displaystyle t=\frac{38.426-1.098}{0.0115}$

$t=3240 \ sec$

The common angular speed is

$w_1=1.098+0.00576 \ 3240=19.76 \ rad/s$

$w_2=38.426-0.00576 \ 3240=19.76 \ rad/s$

They both result in the same, as expected

$\boxed{w=19.76 \ rad/s}$

6 0

3 years ago

A man weighing 180 lbf pushes a block weighing 100 lbf along a horizontal plane. the dynamic coefficient of friction between the

Talja [164]

The first thing you should know is that the work is defined as:
W = F * d
Where
F = force
d = displacement
We have then
(a) the block
F = (0.2) * (100) = 20
d = 100
W = (20) * (100) = 2000 ft.lbf
(b) the man as the system.
F = (0.2) * (100 + 180) = 56
d = 100
W = (56) * (100) = 5600 ft.lbf
answer:
(a) 2000 ft.lbf
(b) 5600 ft.lbf

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3 years ago

Explain how ozone is both beneficial and detrimental to human health.

Gemiola [76]

The ozone layer is beneficial because it protects us from the ultraviolet (UV) rays from the sun. Without it, survival would be difficult. It is harmful by containing all the pollution and chemicals . That damages our lungs and causes chest pain, coughing,etc.

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How is Venus similar to Earth?

hoa [83]

Answer: D

Explanation: I have my answers VS. Go0gle answers (go0gle answers are pics)

(A) Both have the same day length. Well, Venus doesn't havve the same amount of days. (I already know off the top of my head, but I still searched it up)

(B) Both rotate in the same direction. In school (before Virus) they would always show diagrams of the planets on the projector and Venus doesn't rotate

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5 0

3 years ago

Read 2 more answers

While traveling along a highway a driver slows from 32 m/s and comes to a stop with an acceleration of -6 m/s2. How long did it

diamong [38]

Answer: 6s

Explanation:

Vs=32m/s speed at beginning of slowing down

Vf=0m/s stop speed

a= -6 m/s² acceleration

----------------

Use equation for acceleration :

a=(Vf-Vs)/t

a*t=Vf-Vs

t=(Vf-Vs)/a

t=(0-36)/-6

t=-36/-6

t=6 s

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3 years ago