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3 years ago

7

An air-track glider attached to a spring oscillates between the 15.0 cm mark and the 68.0 cm mark on the track. The glider compl

etes 7.00 oscillations in 31.0 s . What is the period of the oscillations?

1 answer:

ipn [44]3 years ago

6 0

Answer:

4.42 s

Explanation:

The frequency of the oscillation is given by the ratio between the number of complete oscillations and the time taken:

$f=\frac{N}{t}$

where for this glider, we have

N = 7.00

t = 31.0 s

Substituting, we find

$f=\frac{7.00}{31.0 s}=0.226 Hz$

Now we now that the period of oscillation is the reciprocal of the frequency:

$T=\frac{1}{f}$

So, substituting f = 0.226 Hz, we find:

$T=\frac{1}{0.226 Hz}=4.42 s$

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Answer:

a) $\Delta T= 100^{\circ}C$

b) $\bigtriangledown T=1^{\circ}C.mile^{-1}$

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d) $\bigtriangledown T_4=1^{\circ}C.mile^{-1}$

Explanation:

Given is the data of variation of temperature with respect to the distance traveled:

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(a)

Total change in temperature from the start till the end of the journey:

$\Delta T= T_f-T_i$ ..............................(2)

where:

$T_f$ = final temperature

$T_i$ = initial temperature

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So, correspondingly we have the eq. (2) & (1) as:

$\Delta T= (100+30)-(0+30)$

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(b)

Now, the average rate of change of the temperature, with respect to distance, from the beginning of the trip to the end of the trip be calculated as:

$\bigtriangledown T=\frac{\Delta T}{\Delta d}$ ......................(3)

where:

$\Delta d$ = change in distance

$\bigtriangledown T=$ change in temperature with respect to distance

putting the respective values in eq. (3)

$\bigtriangledown T=\frac{100}{100}$

$\bigtriangledown T=1^{\circ}C.mile^{-1}$

(c)

comparing the given function of the temperature with the general equation of a straight line:

$y=m.x+c$

We find that we have the slope of the equation as 1 throughout the journey and therefore the rate of change in temperature with respect to distance remains constant.

$\bigtriangledown T_4=1^{\circ}C.mile^{-1}$

(d)

comparing the given function of the temperature with the general equation of a straight line:

$y=m.x+c$

We find that we have the slope of the equation as 1 throughout the journey and therefore the rate of change in temperature with respect to distance remains constant.

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