Physics 9702 · AS & A Level · Density and pressure
Density and pressure — practice question
A solid cylinder is hoisted from oil by a wire connected to a motor. Figure 5.1 shows the cylinder at two stages, X and Y, during the lifting. The motor is mounted on an overhead beam. The cylinder has cross-sectional area $0.018\,\text{m}^2$, length $1.2\,\text{m}$ and weight $560\,\text{N}$. The oil density is $940\,\text{kg m}^{-3}$. During the whole lift, the cylinder travels straight upward at a steady $0.020\,\text{m s}^{-1}$. The viscous force from the oil on the cylinder is negligible.
(a)[2]
Determine the density of the cylinder.
(b)[2]
For the cylinder at position X, show that the upthrust from the oil is $200\,\text{N}$.
(c(i))[1]
Calculate, for the moving cylinder at position $X$, the tension in the wire.
(c(ii))[2]
Calculate, for the moving cylinder at position $X$, the power output of the motor.
(d(i))[3]
The cylinder is lifted at constant velocity from position $X$ to position $Y$. State and explain how, if at all, the power output of the motor changes as the cylinder is lifted. Numerical values are not required.
(d(ii))[1]
The motor’s rate of energy output is less than the rate at which the cylinder’s gravitational potential energy increases. Without calculation, explain this difference.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “correct use of $\rho = m/V$” …