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A 150-kg crate rests in the bed of a truck that slows from 50 km/h to a stop in 12 s. The coefficient of static friction between the crate and the truck bed is 0.655.(a) Will the crate slide during the braking period? Explain your answer.(b) Give the range of stopping times for the truck that will prevent the crate from sliding.

Respuesta :

Answer:

Explanation:

Given

mass of crate=150 kg

time taken=12 s

coefficient of static friction [tex]\mu _=0.655 [/tex]

velocity of truck[tex]=50 km/h\approx 13.89 m/s[/tex]

deceleration truck experience while braking

v=u+at

[tex]0=13.89+a\times 12[/tex]

[tex]a=-1.15 m/s^2[/tex]

maximum friction force truck can offer to block

[tex]=\mu mg=0.655\times 150\times 9.8=962.85 N[/tex]

actual Force experience by truck ma[tex]=150\times 1.15=172.5[/tex]

Therefore crate will not slide during the braking

(b)range of time

[tex]a_max=6.419[/tex]

therefore

v=u+at

[tex]0=13.89-6.419\times t[/tex]

[tex]t=0.928\approx 0.93 s[/tex]

For time greater than 0.93 s there will be no sliding

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