A group of 25 particles have the following speeds:
two have speed 11 m/s, seven have 17 m/s, four have 19 m/s, three have 27 m/s, six have 32 m/s, one has 33 m/s, and two have 40 m/s.

(a) Determine the average speed.
(b) Determine the RMS speed.
(c) Determine the most probable speed.

[tex]v_{avg}=\frac{(2 \times 11) +(7 \times 17)+(4 \times 19)+(3 \times 27) +(6 \times 32) +(1 \times 33)+(2 \times 40) }{25}\\v_{avg}=\frac{22+119+76+81+192+33+80}{25}\\v_{avg}=\frac{603}{25}\\v_{avg}=24.12 m/s[/tex]

So the average speed is 24.12 m/s

Part b

RMS Speed

[tex]v_{rms}=\frac{\sum v^2}{n}[/tex]

[tex]v_{rms}=\sqrt{\frac{(2 \times 11^2) +(7 \times 17^2)+(4 \times 19^2)+(3 \times 27^2) +(6 \times 32^2) +(1 \times 33^2)+(2 \times 40^2) }{25}} \\v_{rms}=\sqrt{\frac{242+2023+1444+2187+6144+1089+3200}{25}}\\\\v_{rms}=\sqrt{\frac{16329}{25}}\\v_{rms}=\sqrt{653.16}\\v_{rms}=25.55 m/s[/tex]

So the rms speed is 25.55 m/s

Part c

Most Probable Speed

As 7 particles have speed of 17 m/s i.e. 7 is the highest frequency so 17 m/s is the most probable speed.

A group of 25 particles have the following speeds: two have speed 11 m/s, seven have 17 m/s, four have 19 m/s, three have 27 m/s, six have 32 m/s, one has 33 m/s, and two have 40 m/s. (a) Determine the average speed. (b) Determine the RMS speed. (c) Determine the most probable speed.

Respuesta :

Otras preguntas

A group of 25 particles have the following speeds:
two have speed 11 m/s, seven have 17 m/s, four have 19 m/s, three have 27 m/s, six have 32 m/s, one has 33 m/s, and two have 40 m/s.

(a) Determine the average speed.
(b) Determine the RMS speed.
(c) Determine the most probable speed.