State the meaning of work done.
A diver lets go of a solid sphere with radius $16\,\text{cm}$ from the sea bed. The sphere rises vertically towards the sea surface. Its weight is $20\,\text{N}$. The upthrust on the sphere is $170\,\text{N}$ and stays constant while the sphere rises. Calculate the density of the material of the sphere.
Briefly explain where the upthrust on the sphere comes from.
Calculate the acceleration of the sphere just after it is released.
The viscous (drag) force $D$ on the sphere is defined by $D = kr^2v^2$, where $r$ is the sphere’s radius and $v$ is its speed. The constant $k$ has value $810\,\text{kg m}^{-3}$. Find the sphere’s constant (terminal) speed.
A diver releases another sphere, which travels at a constant speed of $6.30\,\text{m s}^{-1}$ straight towards a stationary ship. The sphere emits sound at frequency $4850\,\text{Hz}$. As it approaches, the ship measures the sound at frequency $4870\,\text{Hz}$. Determine, to three significant figures, the speed of sound in the water.
The sphere experiences a viscous (drag) force $D$ given by $D = kr^2v^2$, with $r$ as the sphere’s radius and $v$ as its speed. Here $k = 810\,\text{kg m}^{-3}$. Determine the sphere’s constant (terminal) speed.
A diver lets go of a separate sphere moving directly towards a stationary ship at a constant speed of $6.30\,\text{m s}^{-1}$. It emits sound with frequency $4850\,\text{Hz}$, and the ship receives a frequency of $4870\,\text{Hz}$ while the sphere is approaching. Determine, to three significant figures, the speed of sound in the water.