In a car lift, compressed air exerts a force F, on a small piston having a radius of 5.0 cm . This pressure is transmitted to a second piston of radius 15 cm. If the mass of the car to be lifted is 1350 kg, calculate F.

Question

In a car lift, compressed air exerts a force F, on a small piston having a radius of 5.0 cm . This pressure is transmitted to a second piston of radius 15 cm. If the mass of the car to be lifted is 1350 kg, calculate F. (A) 1 × 103 N (B) 1.5 × 103 N (C) 2 × 103 N (D) 2.5 × 103 N

Tardigrade Admin · Accepted Answer

Since pressure is transmitted undiminished throughout the fluid, F1=A1((F2/A2)) =(π(5 × 10-2 m )2 ×(1350 kg × 9.8 ms -2)/π(15 × 10-2 m )2) =1470 N =15 × 103 N

Q. In a car lift, compressed air exerts a force $F$ , on a small piston having a radius of $5.0 c m .$ This pressure is transmitted to a second piston of radius $15 c m$ . If the mass of the car to be lifted is $1350 k g$ , calculate $F$ .

$1 \times 1 0^{3} N$

$1.5 \times 1 0^{3} N$

$2 \times 1 0^{3} N$

$2.5 \times 1 0^{3} N$

Since pressure is transmitted undiminished throughout the fluid,
$F_{1} = A_{1} (\frac{F _{2}}{A _{2}})$
$= \frac{π ( 5 \times 1 0 ^{- 2} m ) ^{2} \times ( 1350 k g \times 9.8 m s ^{- 2} )}{π ( 15 \times 1 0 ^{- 2} m ) ^{2}}$
$= 1470 N = 15 \times 1 0^{3} N$

Q. In a car lift, compressed air exerts a force F, on a small piston having a radius of 5.0cm. This pressure is transmitted to a second piston of radius 15cm. If the mass of the car to be lifted is 1350kg, calculate F.

1×103N

1.5×103N

2×103N

2.5×103N