Question

A 57.0 kg cheerleader uses an oil-filled hydraulic lift to hold four 130 kg football players at a height of 1.20 m.If her piston is 19.0 cm in diameter, what is thediameter of the football players' piston?

Answer 1

F_cheerleader/ Area_cheerpiston = F_football/ Area_{football piston}

F_cheerleader= 57 kg

F_football= 4players(130 kg)=520 kg

Area_{cheer piston}=πr²=π(.095m)²⁼.0283 (can add more decimal places if needed)

Area_{football piston}= F_football x Area_{cheer piston}/ Fcheerleader

= (520kg)(.0283m²)/(57kg)

= .258 m²

Area=πr²

radius=√(Area/π)

=√(.258/π)=.286 m

diameter=2radius=2(.286)=.572 m=57.2 cm

**note some rounding error may be present Xp **

Answer 2

A 54.0 kg cheerleader uses an oil-filled hydraulic lift to hold four 130 kg football players at a height of 1.30 m. If her piston is 15.0 cm in diameter,what is the diameter of the football players' piston?

The pressure inside the hydraulic lift is the same everywhere.
Pressure = force ÷ area
Force = weight
Pressure = weight ÷ area

For the cheerleader,
Weight = 54 * 9.8 = 529.2 N
P = 529.2 ÷ (p * 0.15^2) = 23520 ÷ p

For the football players,
Weight = 4 * 130 * 9.8 = 5096 N
P = 5096 ÷ (p * r^2)

23520 ÷ p = 5096 ÷ (p * r^2)
Multiply both sides by p
23520 = 5096 ÷ r^2
r^2 = 5096 ÷ 23520
r = (5096 ÷ 23520)^0.5 = 0.465 m
Radius of football players' piston = 46.5 cm

Answer 3

A 54.0 kg cheerleader uses an oil-filled hydraulic lift to hold four 130 kg football players at a height of 1.30 m. If her piston is 15.0 cm in diameter,what is the diameter of the football players' piston?

The pressure inside the hydraulic lift is the same everywhere.
Pressure = force ÷ area
Force = weight
Pressure = weight ÷ area

For the cheerleader,
Weight = 54 * 9.8 = 529.2 N
P = 529.2 ÷ (p * 0.15^2) = 23520 ÷ p

For the football players,
Weight = 4 * 130 * 9.8 = 5096 N
P = 5096 ÷ (p * r^2)

23520 ÷ p = 5096 ÷ (p * r^2)
Multiply both sides by p
23520 = 5096 ÷ r^2
r^2 = 5096 ÷ 23520
r = (5096 ÷ 23520)^0.5 = 0.465 m
Radius of football players' piston = 46.5 cm