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It takes 15 s to raise a 1200-kg car and the supporting 300-kg hydraulic car-lift platform to a height of 2.8 m. The velocity of the lift increases uniformly from zero to its maximum value at mid-height in 7.5 s and then decreases uniformly to zero in 7.5 s. Knowing that the peak power output of the hydraulic pump is 6 kW when the velocity is maximum, determine the maximum lift force provided by the pump.

Respuesta :

Answer:14.774 kN

Explanation:

Given

mass of car=1200 kg

mass of Hydraulic lift=300 kg

total time t=15 s

it covers s=1.4 in t=7.5 s

thus acceleration

[tex]s=ut+\frac{at^2}{2}[/tex]

[tex]2\times 1.4=a\times 7.5^2[/tex]

[tex]a=0.0497 m/s^2[/tex]

[tex]V_{max}=at=0.373 m/s[/tex]

Now Let F be the lift Force

F-mg=ma

F=m(g+a)

[tex]F=1500\times (9.8+0.0497)=14,774.55 N[/tex]

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