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The motor of a four wheeler traveling along a muddy trail generates an average power of 7.05 104 W when moving at a constant speed of 15 m/s. When pulling a log along the trail at the same speed, the engine must generate an average power of 8.15 104 W. What is the tension in the tow rope pulling the log?

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davidlcastiblanco

Answer:

[tex]F=733.33 N[/tex]

Explanation:

Power is the work to make a motion in a determine time also the al the work is the force make in a distance so:

[tex]P=\frac{W}{t}[/tex]

[tex]W=F*d[/tex]

Replacing

[tex]P=F*\frac{d}{t}[/tex]

Knowing that the velocity is:

[tex]v=\frac{d}{t}[/tex]

So:

[tex]P=F*v[/tex]

Solve to F to determinate the tension that in this case is the force in the rope

[tex]F=\frac{P}{v}[/tex]

The power is the total power so:

[tex]P=8.15x10^4W-7.05x10^4W=11x10^3W[/tex]

[tex]F=\frac{3kW}{15\frac{m}{s}}=733.33 N[/tex]

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