Question

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.

Answer 1

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

$s=ut+\frac{at^2}{2}$

$2\times 1.4=a\times 7.5^2$

$a=0.0497 m/s^2$

$V_{max}=at=0.373 m/s$

Now Let F be the lift Force

F-mg=ma

F=m(g+a)

$F=1500\times (9.8+0.0497)=14,774.55 N$