Examkin

Soru

Zorluk: Çok zorMeasurement of Mass and Weight

A body is suspended from a spring balance inside an elevator that is accelerating upwards at 2.0 m s−22.0\text{ m s}^{-2} on Earth, giving a scale reading of 60 N60\text{ N}. The body is then taken to a planet where the acceleration due to gravity is 6.0 m s−26.0\text{ m s}^{-2} and placed on an ideal beam balance against standard masses calibrated on Earth. Taking g=10.0 m s−2g = 10.0\text{ m s}^{-2} on Earth, what is the reading obtained on the beam balance?

  1. 5.0 kg5.0\text{ kg}Cevap
  2. B
    6.0 kg6.0\text{ kg}
  3. C
    7.5 kg7.5\text{ kg}
  4. D
    3.0 kg3.0\text{ kg}

Cevap

The reading obtained on the beam balance is 5.0 kg5.0\text{ kg}.
In an upward accelerating elevator, the spring balance registers an apparent weight of Wapp=m(g+a)W_{app} = m(g + a). Substituting the given values gives 60 N=m(10 m s−2+2 m s−2)60\text{ N} = m(10\text{ m s}^{-2} + 2\text{ m s}^{-2}), which yields a true mass m=5.0 kgm = 5.0\text{ kg}. When measured on another planet using an ideal beam balance, the gravitational force on the unknown mass balances against standard masses (m⋅gp=mstandard⋅gpm \cdot g_p = m_{standard} \cdot g_p). Since local gravity gpg_p cancels from both sides, the beam balance measures the invariant mass of 5.0 kg5.0\text{ kg}.

Adım Adım Çözüm

1
Calculate the true mass of the body using the scale reading in the accelerating elevator.
m=5.0 kgm = 5.0\text{ kg}
Inside an upward accelerating elevator, the apparent weight registered by the spring balance is Wapp=m(g+a)W_{app} = m(g + a). Substituting Wapp=60 NW_{app} = 60\text{ N}, g=10.0 m s−2g = 10.0\text{ m s}^{-2}, and a=2.0 m s−2a = 2.0\text{ m s}^{-2} yields 60=m(10+2)60 = m(10 + 2), which gives m=5.0 kgm = 5.0\text{ kg}.
2
Determine the mass reading on a beam balance on the new planet.
The beam balance reads 5.0 kg5.0\text{ kg}.
A beam balance compares the gravitational force on the object with standard masses: m⋅gp=mstandard⋅gp  ⟹  mstandard=mm \cdot g_p = m_{standard} \cdot g_p \implies m_{standard} = m. Because local acceleration due to gravity gpg_p cancels out on both sides, a beam balance measures true invariant mass regardless of location or gravity.

Anahtar Kavram

Mass vs Weight Measurement: Accelerating Frames and Beam Balance Invariance
Tahmini Süre:1m 0s
Bu soruyu puanla

Konular

Measurement of Mass and Weight

Bu konudan daha fazla soru