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aleksklad [387]

3 years ago

15

A train station bell gives off a fundamental tone of 500 Hz as the train approaches the station at a speed of 30.0 m/s. If the s

peed of sound in air is 339 m/s, what will be the apparent frequency of the bell to an observer riding the train?

1 answer:

TiliK225 [7]3 years ago

3 0

Answer:

548.5 Hz

Explanation:

We are given that

Frequency of source=500 Hz

Speed of train=30m/s

Speed of sound in air=339m/s

We have to find the frequency of the bell to an observer riding the train.

The apparent frequency for the listener

$f=\frac{v_0}{v_0-v_s}f_1$

Where $f_1=$ Frequency of source

$v_0$ =Speed of sound

$v_s$ =Speed of source

Using the formula

The apparent frequency of the bell to an observer riding the train= $\frac{339}{339-30}\times 500=548.5 Hz$

Hence, the apparent frequency of the bell to an observer riding the train=548.5 Hz

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A child whose weight is 287 N slides down a 7.20 m playground slide that makes an angle of 31.0Â° with the horizontal. The coeff

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Answer:

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$H =212.6 \ J$

b

$v = 7.647 \ m/s$

Explanation:

From the question we are told that

The child's weight is $W_c = 287 \ N$

The length of the sliding surface of the playground is $L = 7.20 \ m$

The coefficient of friction is $\mu = 0.120$

The angle is $\theta = 31.0 ^o$

The initial speed is $u = 0.559 \ m/s$

Generally the normal force acting on the child is mathematically represented as

=> $N = mg * cos \theta$

Note $m * g = W_c$

Generally the frictional force between the slide and the child is

$F_f = \mu * mg * cos \theta$

Generally the resultant force acting on the child due to her weight and the frictional force is mathematically represented as

$F =m* g sin(\theta) - F_f$

Here F is the resultant force and it is represented as $F = ma$

=> $ma = m* g sin(31.0) - \mu * mg * cos (31.0)$

=> $a = g sin(31.0)- \mu * g * cos (31.0)$

=> $a = 9.8 * sin(31.0) - 0.120 * 9.8 * cos (31.0)$

=> $a = 4.039 \ m/s^2$

So

$F_f = 0.120 * 287 * cos (31.0)$

=> $F_f = 29.52 \ N$

Generally the heat energy generated by the frictional force which equivalent tot the workdone by the frictional force is mathematically represented as

$H = F_f * L$

=> $H = 29.52 * 7.2$

=> $H =212.6 \ J$

Generally from kinematic equation we have that

$v^2 = u^2 + 2as$

=> $v^2 = 0.559^2 + 2 * 4.039 * 7.2$

=> $v = \sqrt{0.559^2 + 2 * 4.039 * 7.2}$

=> $v = 7.647 \ m/s$

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