The supports beneath a building are long concrete cylinders with a pointed end. A pile-driver is a machine used to drive these pointed concrete cylinders into the ground.
Fig. 2.1 shows a pile-driver.
A heavy block with a mass of $2.9 \times 10^4\,\text{kg}$ is raised into the air and then released onto the top of a concrete cylinder. This makes the cylinder sink into the ground.
Fig. 2.2 shows the heavy block.
The block has a height of 2.0 m and a cross-sectional area of $1.8\,\text{m}^2$.
(a)[2]
Calculate the density of the material from which the block is made.
(b(i))[2]
The pile-driver lifts the block from the top of a concrete cylinder through a height of 0.80 m. Take the gravitational field strength $g$ as $10\,\text{N kg}^{-1}$. Calculate the gravitational potential energy gained by the block.
(b(ii))[3]
The block is then released from rest onto the top of the concrete cylinder. Calculate the speed of the block just before it strikes the concrete cylinder.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Density expression: $\rho = m / V$ or $m / (hA)$” …