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Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0∘ and the coefficient of rolling friction is 0.38. Use work and energy to find the length of a ramp that will stop a 15,000 kg truck that enters the ramp at 35 m/s.

Respuesta :

davidlcastiblanco

Answer:

d=16537m

Explanation:

The energy kinetic of the motion and the work of the friction determinate the length of the ramp

Kinetic energy

[tex]K=\frac{1}{2}*m*(v)^{2}[/tex]

Work friction

[tex]W=F_{f}*d[/tex]

[tex]K-W=0[/tex]

[tex]\frac{1}{2}*m*(v)^{2}=[u*m*g*cos(6)]*d[/tex]

[tex]d=\frac{v^{2}}{2*u*g*cos(6)}[/tex]

[tex]d=\frac{35^{2}}{2*0.38*9.8*cos(6)}[/tex]

[tex]d=165.37m[/tex]

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