# Pressure for Edexcel A-level Physics

1. Archimides' principle

Archimides' principle states that an object either partially or fully submerged in a fluid feels an upwards force called upthurst, which is equal to the weight of the fluid displaced by the object. This force arises due to the fact that an object experiences a greater pressure from below in comparison to above. If the upthrust is greater than the weight, the object will float. If it is not, the object will sink.

# 1

Identify and describe the forces which allow a boat to float in water.

By Archimides' principle, since the boat is partially submerged in fluid, it experiences an upwards upthrust force. This upthrust force balances out the downwards weight of the boat. There is no resultant force acting on the boat, therefore by Newton's first law, the boat remains stationary and thus floats, rather than sinking.

Upwards upthrust force balances out the downwards weight.

# 2

A steel ball of radius 3 cm is held fully submerged in a tub of oil. Given that the density of oil is 870 kg/m³ and the density of steel is 8070 kg/m³, find whether the ball sinks or rises to the surface when it is released. Use g = 9.8 m/s² and the fact that the volume of the ball is 0.000113 m³. Density, mass and volume are related using formula ρ = m ÷ V.

By Archimides' principle, upthrust = weight of fluid displaced.
U = ρgV
upthrust = 870 kg/m³ × 9.8 m/s² × 0.000113 m³ = 0.964 (3 s. f.)

The other force acting on the ball is its weight.
ρ = m ÷ V
8070 kg/m³ = mass ÷ 0.000113 m³
mass = 0.913 kg (3 s. f.)
w = mg
weight = 0.913 kg × 9.8 m/s² = 8.94 N (3 s. f.)

Downwards can be taken to be the positive direction.
resultant force = 8.94 N − 0.964 N = 7.98 N downwards (3 s. f.)
By Newton's second law, the ball will move in the direction of the resultant force acting on it, therefore the ball will sink.

The ball will sink.

# 3

An object of mass 2 kg is fully submerged in water of density 1000 kg/m³ and is stationary. Calculate the upthrust acting on the object, given that g = 9.8 m/s².

By Archimides' principle, for stationary submerged objects upthrust = weight.
w = mg
upthrust = 2 kg × 9.8 m/s² = 19.6 N

19.6 N

# 4

A volleyball of radius 20 cm is plunged and held in water of density 1010 kg/m³ such that half of the volleyball is submerged. Given that g = 9.8 m/s² and that the volume of volleyball is 0.0335 m³, calculate the upthrust acting on the volleyball.

By Archimides' principle, the upthrust is equal to the weight of the water displaced by the volleyball. Since half of the volleyball is submerged, half of its volume is used for the calculation of the upthrust.

volume of displaced fluid = 1/2 × 0.0335 = 0.0168 m³ (3 s. f.)
ρ = m/V
mass of displaced fluid = 1010 kg/m³ × 0.0168 m³ = 16.9 kg (3 s. f.)

w = mg
weight of water displaced = 16.9 kg × 9.8 m/s² = 166 N (3 s. f.)
By Archimides' principle, upthrust = 166 N (3 s. f.).

166 N

# 5

A toy block of mass 0.6 kg is held underwater in a bath. The block is a cuboid and its dimensions are 17 cm, 15 cm and 20 cm. Given that the density of water is 1000 kg/m³, deduce whether the block rises to the surface or sinks when released. Use g = 9.8 m/s².

By Archimides' principle, upthrust = weight of fluid displaced.
volume of block = 0.2 m × 0.15 m × 0.17 m = 0.0051 m³
U = ρgV
upthrust = 1000 kg/m³ × 9.8 m/s² × 0.0051 m³ = 49.98 N

The other force acting on the ball is its weight.
w = mg
weight = 0.6 kg × 9.8 m/s² = 5.88 N

Upwards can be taken to be the positive direction.
resultant force = 49.98 N − 5.88 N = 44.1 N upwards (3 s. f.)

By Newton's second law, the ball will move in the direction of the resultant force acting on it, therefore the ball will rise to the surface.

The block will rise to the surface.

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