A ball of mass 400 grams is immersed in water. The ball is suspended in the water by a rubber band chain which exerts a tension force of 2.5 Newtons on the ball.
What is the weight of the ball?
The weight of the ball is the force exerted on it by gravity. If allowed to fall freely gravity would accelerate it at 9.8 m/s^2 so its weight is weight = F_grav = m * accel_grav = m g weight = .4 kg * 9.8 m/s^2 = 3.92 N.
The weight of the ball is the force exerted on it by gravity. If allowed to fall freely gravity would accelerate it at 9.8 m/s^2 so its weight is
weight = F_grav = m * accel_grav = m g
weight = .4 kg * 9.8 m/s^2 = 3.92 N.
What is the buoyant force on the ball?
The net force on the ball is zero, since it's in equilibrium. Its 3.92 N weight acts downward, and the 2.5 N tension force acts upward. To achieve equlibrium there must be a buoyant force F_bouy such that 2.5 N - 3.92 N + F_buoy = 0 and we conclude that the buoyant force is F_buoy = 1.42 N.
The net force on the ball is zero, since it's in equilibrium. Its 3.92 N weight acts downward, and the 2.5 N tension force acts upward.
To achieve equlibrium there must be a buoyant force F_bouy such that
2.5 N - 3.92 N + F_buoy = 0
and we conclude that the buoyant force is
F_buoy = 1.42 N.
What therefore must be its volume?
By Arcihimedes' Principle the buoyant force on an object is equal to the weight of the water it displaces. The ball must therefore displace an amount of water weighing 1.42 N. Water has a mass density of 1000 kg / m^3, so its weight density is 1000 kg / m^3 * 9.8 m/s^2 = 9800 N / m^3. If V is the water displaced, then its weight is equal to V * 9800 N/m^3 so V * 9800 N/m^3 = 1.42 N and V = 1.42 N / (9800 N/m^3) = .000145 m^3. This is also .145 liters, or 145 cm^3.
By Arcihimedes' Principle the buoyant force on an object is equal to the weight of the water it displaces.
The ball must therefore displace an amount of water weighing 1.42 N.
Water has a mass density of 1000 kg / m^3, so its weight density is 1000 kg / m^3 * 9.8 m/s^2 = 9800 N / m^3.
If V is the water displaced, then its weight is equal to V * 9800 N/m^3 so
V * 9800 N/m^3 = 1.42 N and
V = 1.42 N / (9800 N/m^3) = .000145 m^3.
This is also .145 liters, or 145 cm^3.
What is its density?
The density of the ball is density = mass / volume = 400 grams / (145 cm^3) = 2.8 grams / cm^3, approx. This can also be expressed in kg / m^3 as 2800 kg / m^3.
The density of the ball is
density = mass / volume = 400 grams / (145 cm^3) = 2.8 grams / cm^3, approx.
This can also be expressed in kg / m^3 as 2800 kg / m^3.