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A physical quantity X depends on mass, distance, and time. Use dimensional analysis to decide which of these is a possible expression for X, where a is acceleration, v is velocity, and F is force.

A. X=1/2at²
B. X=at
C. X=Ft
D. X=vt

Answers

Answer 1

X=Ft is a possible equation for X because by using SI units its final term became Kg metre per second

Answer 2

The correct expression for a physical quantity depending on mass, distance, and time is C. X = Ft, as it has the dimensions MLT⁻¹ and includes all three: mass (M), distance (L), and time (T).

In order to determine which expression for a physical quantity X that depends on mass m, distance s, and time t, is possible using dimensional analysis, we examine the provided options. Using the dimensions given [m] = M, [s] = L, [v] = LT⁻¹, [a] = LT⁻², and [t] = T:

X = 1/2at² has dimensions of L( T⁻² )( T² ) = L which does not involve mass.

X = at has dimensions of L( T⁻² )( T ) = LT⁻¹ which is velocity, not involving mass.

X = Ft has dimensions of ( M LT⁻² )( T ) = MLT⁻¹ which represents impulse or momentum, and it involves mass, length, and time.

X = vt has dimensions of L( T⁻¹ )( T ) = L which is distance, but it does not involve mass.

The correct option that includes dimensions of mass, distance, and time is C. X = Ft which represents impulse or momentum.


Related Questions

many musical instruments use "boxes" as a part of an instrument. Some examples are acoustic guitars and pianos. From your experience in this lab on building your own musical instrument, write a brief essay on the purpose of these "boxes". Include description of a xylophone and what is uses of for the purpose of the box.

Answers

Answer :

Essay on Sound instruments/sound boxes:

Musical instruments also some times called "sound box",  because the box modifies the sound of an instrument. It also helps in transfer of sound to the surrounding air.

The box is the open chamber in the body of musical instrument

The sound box responds more strongly to vibrations at certain frequencies created by playing instrument. This phenomena is known as resonance.

The resonance impacts on the tone quality.

For example xylophone, which is a musical instrument with wooden bars. These wooden bars are arranged similar to the piano. under each bar of the xylophone there is a resonator tube, which amplifies the sound.


Final answer:

The 'boxes' or 'bodies' of musical instruments like guitars and pianos serve as resonators, amplifying and enhancing the tone quality of the instrument. In the case of a xylophone, the boxes or tubes beneath the wooden bars act as amplifiers of the initial sound produced.

Explanation:

In the field of music, 'boxes' are components of many musical instruments, often called the instrument's 'resonating box' or 'body'. They contribute significantly to the amplification and tone quality of the instrument. For instance, in an acoustic guitar, the sound box amplifies the vibrations of the strings and projects the sound.

When playing a piano, the sound is created by hammers striking strings. These vibrations are then transmitted to the soundboard, basically a large 'box', which increases the surface area that vibrates to project the sound throughout the room.

In relation to a xylophone, the utility of the 'box' is a bit different. In a xylophone, the wooden bars produce sound which is amplified by resonator tubes or boxes below. Instead of acting as the primary sound source like in a guitar or piano, the tubes or boxes under a xylophone amplifies the initial sound created by the strike of the mallet.

Learn more about Boxes in Musical Instruments here:

https://brainly.com/question/34611241

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At an auto race, a member of the pit crew stands beside the track. A car approaches him at 100 m/s and emits a sound at frequency 1100Hz. The air is still and the speed of sound is 340mls. What frequency will the pit crew member hear? A.1560Hz
B.1420Hz
C.1640Hz
D.850Hz

Answers

As per the formula of Doppler's effect we know that

[tex]f = f_o\frac{v}{v - v_s}[/tex]

now we know that

v = 340 m/s

[tex]v_s = 100 m/s[/tex]

[tex]f_o = 1100 Hz[/tex]

now we will have

[tex]f = 1100(\frac{340}{340 - 100})[/tex]

[tex]f = 1560 Hz[/tex]

so the frequency heard by the crew will be approx 1560 Hz

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