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Wittaler [7]
3 years ago
12

A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is

then pulled down 7.5 cm and released. The ball makes 31 oscillations in 15 s seconds.1) What is its the mass of the ball?Express your answer using two significant figures.m = _____ g2) What is its maximum speed?Express your answer using two significant figures.= _____ cm/s
Physics
1 answer:
olga nikolaevna [1]3 years ago
5 0

Explanation:

It is given that,

Spring constant of the spring, k = 15 N/m

Amplitude of the oscillation, A = 7.5 cm = 0.075 m

Number of oscillations, N = 31

Time, t = 15 s

(a) Let m is the mass of the ball. The frequency of oscillation of the spring is given by :

f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}

Total number of oscillation per unit time is called frequency of oscillation. Here, f=\dfrac{31}{15}=2.06\ Hz

m=\dfrac{k}{4\pi^2f^2}

m=\dfrac{15}{4\pi^2\times 2.06^2}

m = 0.0895 kg

or

m = 89 g

(b) The maximum speed of the ball that is given by :

v_{max}=A\times \omega

v_{max}=A\times 2\pi f

v_{max}=0.075\times 2\pi \times 2.06

v_{max}=0.970\ m/s

v_{max}=97\ cm/s

Hence, this is the required solution.

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The "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper e
Mashcka [7]

Answer:

Explanation:

When the central shaft rotates , the seat along with passenger also rotates . Their rotation requires a centripetal force of mw²R where m is mass of the passenger and w is the angular velocity and R is radius of the circle in which the passenger rotates.

This force is provided by a component of   T , the tension in the rope from which the passenger hangs . If θ be the angle the rope makes with horizontal ,

T cos θ will provide the centripetal force . So

Tcosθ = mw²R

Tsinθ component will balance the weight .

Tsinθ = mg

Dividing the two equation

Tanθ = \frac{g}{\omega^2R}

Hence for a given w , θ depends upon g or weight .

8 0
3 years ago
Read 2 more answers
it is determined that a certain light wave has a wavelength of 3.012x10^-12 m. the light travels at 2.99x10^8 m/s. what is the f
Dahasolnce [82]

Answer:

9.93\times 10^{19}Hz

Explanation:

Speed of light is the product of its wavelength and frequency, expressed as

S=fw

Where s represent speed, f is frequency while w is wavelength

Making f the subject of the formula then

f=s/w

Substituting 2.99x10^8 m/s for s and 3.012x10^-12 m for w then

f=\frac {2.99\times 10^{8}}{3.012\times 10^{-12}}=9.926958831341\times 10^{19}\\f\approx 9.93\times 10^{19}Hz

Therefore, the frequency equals to 9.93\times 10^{19}Hz

4 0
3 years ago
Question 15 of 15
castortr0y [4]

Answer:

a and b

Explanation:

are the correct answers

7 0
3 years ago
Use appropriate units and significant figures.  USE THE LAW OF COSINES AND LAW OF SINES.
N76 [4]

Answer:

The resultant velocity is 86.1 mi/h.    

Explanation:

The law of cosines is given by:

c^{2} = a^{2} + b^{2} - 2abcos(\theta)

Where:

c: is the resultant velocity =?

a: is the velocity of the plane = 75.0 mi/h

b: is the velocity of the wind = 15.0 mi/h  

θ: is the angle between "a" and "b"                          

The angle between "a" and "b" can be found as follows:

\theta = 180.0 - 46.0 = 134.0 ^{\circ}

Now, by using the law of cosines we have:

c^{2} = (75.0)^{2} + (15.0)^{2} - 2*75.0*15.0*cos(134.0) = 7413.0

c = 86.1 mi/h    

Therefore, the resultant velocity is 86.1 mi/h.    

The law of sines is:

\frac{a}{sin(\gamma)} = \frac{b}{sin(\alpha)} = \frac{c}{sin(\theta)}

Where:

γ: is the angle between "b" and "c"

α: is the angle between "a" and "c"

So, if we want to find "c" by using the law of sines, we need to know another angle besides θ (γ or α), and the statement does not give us.

I hope it helps you!        

3 0
3 years ago
A bowling lane is 18 meters long. How long would it take a 1.5 m/s bowling ball to
lara31 [8.8K]

Divide distance by speed:

18 meters / 1.5 meters/ second = 12 seconds

Answer: 12 seconds

5 0
2 years ago
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