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3 years ago

By what factor should the length of the pendulum of a clock be changed if you want it to run 2 times faster?

Physics

2 answers:

Anarel [89]3 years ago

8 0

The period of a simple pendulum is given by $T=2\pi \sqrt{ \frac{l}{g} }$ .

Here $T$ is the period, $l$ length of the pendulum and $g$ acceleration due to gravity. When the pendulum runs 2 times faster, the period gets halved. That is

$\frac{T}{2}=2\pi \sqrt{ \frac{\frac{l}{4}}{g} }$ . The new length of the pendulum is $\frac{l}{4}$ .

That is the length of the pendulum decreases by a factor of 4.

Semenov [28]3 years ago

7 0

You have to decrease the length of the pendulum by 4 times in order to make the clock go 2 times faster

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Answer:

$4.32\cdot 10^5 J$

Explanation:

Power is related to energy by the following relationship:

$P=\frac{E}{t}$

where

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In this problem, we know that

- the power of the fan is P = 120 W

- the fan has been running for one hour, which corresponds to a time of

$t = 1 h \cdot (60 min/h)(60 s/min)=3600 s$

So we can re-arrange the previous equation to find E, the energy (in the form of thermal energy) released by the fan:

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2 years ago

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A sample of helium has a volume of 12.7 m3. The temperature is raised to 323 K at which time the gas occupies 32.5 m3? Assume pr

jasenka [17]

Answer: The original temperature was

$T_{1}=126.51K$

Explanation:

Let's put the information in mathematical form:

$V_{1}=12.7m^{3}$

$T_{1}=?$

$V_{2}=32.5m^{3}$

$T_{2}=323K$

$P_{1}=P_{2}=3atm$

If we consider the helium as an ideal gas, we can use the Ideal Gas Law:

$PV=nRT$

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From this, taking $R=0.08205746\frac{atm.l}{mol.K}$ , we have:

$n=\frac{P_{2}V_{2}}{RT_{2}}$

⇒ $n=3.67mol$

Now:

$T_{1}=\frac{P_{1}V_{1}}{nR}$

⇒ $T_{1}=126.51K$

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2 years ago

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Two identical bodies are sliding toward each other on a frictionless surface. One moves at 1 m/s and the other at 2 m/s. They co

mario62 [17]

Answer:

$V=\dfrac{3}{2}\ m/s$

Explanation:

Two identical bodies are sliding toward each other on a frictionless surface.

Initial speed of body 1, m₁ = 1 m/s

Initial speed of body 2, m₂ = 2 m/s

They collide and stick.

We need to find the speed of the combined mass. Let V is the speed of the combined mass.

Using the conservation of momentum.

$m_1u_1+m_2u_2=V(m_1+m_2)$

We have, m₁ = m₂ = m

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So, the speed of the combined mass is $\dfrac{3}{2}\ m/s$ .

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3 years ago

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shusha [124]

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