Physics

Physics

Problem

An iron block of volume 2.0×10−4 m32.0 \times 10^{-4}\,\text{m}^3 hangs from a spring balance and is completely immersed in oil of density 800 kg m−3800\,\text{kg m}^{-3}. The container of oil and the balance are inside a lift that is accelerating upward at 2.0 m s−22.0\,\text{m s}^{-2}. Determine the reading of the spring balance. (ρiron=7.9×103 kg m−3\rho_{\text{iron}} = 7.9 \times 10^{3}\,\text{kg m}^{-3}, g=9.8 m s−2g = 9.8\,\text{m s}^{-2})
Intuitive explanation

The spring balance reads the normal force on the iron block, which depends on both gravity and the upward acceleration of the lift. You need to account for two forces: the block's weight in the accelerating frame (which increases due to the lift's acceleration) and the buoyant force from the displaced oil (which also increases because the effective gravity is stronger). The key is to use the effective acceleration geff=g+ag_{\text{eff}} = g + a in both the weight and buoyancy calculations, then find the net upward force the spring must provide.

Intuitive explanation

The spring balance reads the normal force on the iron block, which depends on both gravity and the upward acceleration of the lift. You need to account for two forces: the block's weight in the accelerating frame (which increases due to the lift's acceleration) and the buoyant force from the displaced oil (which also increases because the effective gravity is stronger). The key is to use the effective acceleration geff=g+ag_{\text{eff}} = g + a in both the weight and buoyancy calculations, then find the net upward force the spring must provide.

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