Physics, 21.01.2020 03:31 mobslayer88

Gillian buys a pendulum clock at a discount store and discovers when she gets it home that it loses 6.00 minutes each day.

a) should she lengthen or shorten the pendulum in order for it to keep accurate time?
b) if the pendulum has a period of 2.00 s, by how much must the length be changed so that the clock keeps accurate time?

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Answer from: Darkknighta26

a) The pendulum must be shortened to keep accurate time

b) It should be shortened by 0.0082 m or 8.2 mm

Explanation:

Simple Pendulum

A simple pendulum is a system with a point mass that is suspended from a weightless string to a fixed point. It describes a harmonic motion because the oscillations repeat regularly, and kinetic energy is transformed into potential energy, and vice versa.

The equation for the period of a simple pendulum is

$\displaystyle T = 2\pi \sqrt{\frac{L}{ g}}$

where L is the length of the sting and g is the acceleration of gravity .

Note that if we increase the length, the period will also increase, and the oscillations are slower, i.e. take longer to complete

a) Gillian's pendulum is running slow because it loses 6 minutes each day. As shown above, the longer the string, the slower the oscillations, thus he needs to shorten the string to make it move faster and keep up in time .

b) We know the period is 2 seconds. That will give us the actual length of the pendulum, solving the above equation for L .

$\displaystyle L = \frac{gT^2}{4\pi^2}$

$\displaystyle L = \frac{(9.8)2^2}{4\pi^2}$

$\displaystyle L = 0.9929\ m$

The new period should be less than the original. We know that actually, the pendulum's mechanisms make a period of 2 seconds in a measured time of

3600*24+6*60=86760 seconds each day .

This should be shortened to the correct time of 3600*24=86400 seconds per day, so the new period should be

$T'=2\ sec*(86400/86760)=1.9917\ sec$

Which yields to a new length of

$\displaystyle L' = \frac{gT'^2}{4\pi^2}$

$\displaystyle L' = \frac{(9.8)(1.9917)^2}{4\pi^2}$

$L'=0.9847\ m$

Difference of lengths = 0.9929 - 0.9847=0.0082 m

$\boxed{\text{It should be shortened by 0.0082 m or 8.2 mm}}$

Answer from: Quest

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

Answer from: Quest

inverse v=i*r

nice nice

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