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The motion of a piston in an auto engine is simple harmonic. If the piston travels back and forth over a distance of 10 cm and the piston has a mass of 1.5 kg, what is the maximum speed of the piston and the maximum force acting on the piston when the engine is running at 4200 rpm?

Respuesta :

Answer:

Maximum force will be 29040 N

Explanation:

We have given mass of the piston m = 1.5 kg

Amplitude A = 10 cm = 0.1 m

Angular speed [tex]\omega =4200rpm=\frac{2\times 3.14\times 4200}{60}=440rad/sec[/tex]

We know that angular speed is given by [tex]\omega =\sqrt{\frac{k}{m}}[/tex]

[tex]440=\sqrt{\frac{k}{1.5}}[/tex]

Squaring both side

[tex]193600=\frac{k}{1.5}[/tex]

k = 290400 N/m

Now force is given by [tex]F=kA=290400\times 0.1=29040N[/tex]

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