Please help?

2018-06-25 12:51 am
piece if metal, mass 3.6kg is suspended from a spring balance. What is the reading of the balance in N. (a) with the metal in air (b) with the metal in water (c) with the metal in brine (d) what is the density of a liquid in which it gives a reading of 33N? (Density of brine is 1200kgm^-3,density of metal is 9000kgm^-3)

回答 (2)

2018-06-25 1:25 am
✔ 最佳答案
Take g = 9.81 m/s² = 9.81 N/kg
Gravitational force acting on the piece of metal = mg = (3.6 kg) × 9.81 (N kg⁻¹) = 35.3 N
Volume of the metal = (3.6 kg) / (9000 kg m⁻³) = 0.0004 m³

(a)
The density of air is very small, and thus the upthrust acting on the metal is negligible.
Reading of balance = 35.3 N ≈ 35 N (to 2 sig. fig.)

(b)
Density of water = 1000 kg m⁻³
Upthrust acting on the piece of metal = (0.0004 m³) × (1000 kg m⁻³) × (9.81 N/kg) = N
Reading of balance = (35.3 - 3.9) N = 31.4 N ≈ 31 N (to 2 sig. fig.)

(c)
Upthrust acting on the piece of metal = (0.0004 m³) × (1200 kg m⁻³) × (9.81 N/kg) = 4.7 N
Reading of balance = (35.3 - 4.7) N = 30.6 N ≈ 31 N (to 2 sig. fig.)

(d)
Mass of the metal to 2 sig. fig. = 35 N
Upthrust acting on the piece of the metal = (35 - 33) N = 2.3 N ≈ 2 N
Density of the liquid = (2 N) / [(9.81 N kg⁻¹) × (0.0004 m³)] = 510 kg m⁻³
2018-06-25 1:36 am
volume V = m/ρm = 3.6 kg /9.0 kg/dm^3 = 0,400 dm^3 ; g rounded up to 10 m/sec^2

..what is the reading of the balance in N :
(a) with the metal in air
air density ρa = 0.00125 kg/dm^3
reading R1 = m*g*(ρm-ρa) = 3.6*10*(9-0.00125) = 324 N

(b) with the metal in water
water density ρw = 1.00 kg/dm^3
reading R2 = m*g*(ρm-ρw) = 3.6*10*(9-1) = 288 N

(c)with the metal in brine
brine density ρb = 1.20 kg/dm^3
reading R3 = m*g*(ρm-ρb) = 3.6*10*(9-1.2) = 280.8 N

(d) what is the density ρℓ of a liquid if a reading of 33N is achieved?
33 = 3.6*g(9-ρℓ)
36*ρℓ = 36*9-33
ρℓ = 291/36 = 8.083 kg/dm^3


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