CAIE A-Level Physics AS 4 Forces Density and Pressure Questions

Practise analysing moments, couples, equilibrium, centres of gravity, density, pressure, hydrostatic relations and upthrust from diagrams and measurements.

Exam points

calculate moments and couples and use the principle of moments to analyse turning effects in rigid bodies
resolve and combine forces, applying equilibrium conditions to supported or suspended systems
use centre of gravity and line-of-action reasoning to assess balance and stability
calculate density and pressure from measured quantities and interpret their units and geometry
apply hydrostatic pressure and upthrust relationships to explain and calculate forces in fluids

Covered syllabus points

4.1 Turning effects of forces 4.2 Equilibrium of forces 4.3 Density and pressure

[Maximum number: 9]

(a)

A cylinder is made from a material of density $2.7 \mathrm{~g} \mathrm{~cm}^{-3}$ . The cylinder has diameter 2.4 cm and length 5.0 cm .

Show that the cylinder has weight 0.60 N .

[ 3 ]

$\rho=m / V$ $V=\pi d^{2} L / 4$ or $\pi r^{2} L$
weight $=2.7 \times 10^{3} \times \pi\left(1.2 \times 10^{-2}\right)^{2} \times 5.0 \times 10^{-2} \times 9.81=0.60 \mathrm{~N}$

(b)

The cylinder in (a) is hung from the end A of a non-uniform bar AB , as shown in Fig. 3.1.

Fig. 3.1

The bar has length 50 cm and has weight 0.25 N . The centre of gravity of the bar is 20 cm from B. The bar is pivoted at P. The pivot is 12 cm from B.

An object X is hung from end B. The weight of X is adjusted until the bar is horizontal and in equilibrium.

[ 3 ]

(i)

Explain what is meant by centre of gravity.

[ 1 ]

(ii)

Calculate the weight of X .
weight of X=

[ 2 ]

$W \times 12$ $(0.25 \times 8)+(0.6 \times 38)$ $\begin{aligned} W =(2+22.8) / 12 =2.1(2.07) \mathrm{N} \end{aligned}$

(c)

The cylinder is now immersed in water, as illustrated in Fig. 3.2.

Fig. 3.2

An upthrust acts on the cylinder and the bar is not in equilibrium.

[ 3 ]

(i)

Explain the origin of the upthrust.

[ 2 ]

(ii)

Explain why the weight of X must be reduced in order to obtain equilibrium for A B.

[ 1 ]

[Maximum number: 5]

(a)

Define the moment of a force.

[ 1 ]

(b)

A thin disc of radius r is supported at its centre O by a pin. The disc is supported so that it is vertical. Three forces act in the plane of the disc, as shown in Fig.2.1.

Fig. 2.1

Two horizontal and opposite forces, each of magnitude 1.2 N , act at points A and B on the edge of the disc. A force of 6.0 N , at an angle $\theta$ below the horizontal, acts on the midpoint C of a radial line of the disc, as shown in Fig. 2.1. The disc has negligible weight and is in equilibrium.

[ 4 ]

(i)

State an expression, in terms of r, for the torque of the couple due to the forces at A and B acting on the disc.

[ 1 ]

2.4 r or $(1.2 \times 2 r)$ or (1.2 r+1.2 r)

(ii)

Friction between the disc and the pin is negligible.

Determine the angle $\theta$ .
$\theta= { }^{\circ}$

[ 2 ]

(anticlockwise moment = ) $6.0 \times r / 2 \times \sin \theta$ $\begin{aligned} 6.0 \times r / 2 \times \sin \theta=2.4 r \theta=53^{\circ} \end{aligned}$

(iii)

State the magnitude of the force of the pin on the disc.
force = N

[ 1 ]

[Maximum number: 4]

(a)

A cylinder is suspended from the end of a string. The cylinder is stationary in water with the axis of the cylinder vertical, as shown in Fig. 2.1.

Fig. 2.1 (not to scale)

The cylinder has weight 0.84 N , height h and a circular cross-section of diameter 0.031 m . The density of the water is $1.0 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ . The difference between the pressures on the top and bottom faces of the cylinder is 520 Pa .

[ 4 ]

(i)

Calculate the height h of the cylinder.

h =m [2

[ 2 ]

$\begin{aligned} (\Delta) p=\rho g(\Delta) h 520=1000 \times 9.81 \times h \end{aligned}$ $h=0.053 \mathrm{~m}$

(ii)

Show that the upthrust acting on the cylinder is 0.39 N .

[ 2 ]

$\begin{aligned} (\text { upthrust } =)(\Delta) p \times A =(\Delta) p \times \pi(d / 2)^{2} \text { or }(\Delta) p \times \pi r^{2} \end{aligned}$ $=520 \times \pi(0.031 / 2)^{2}=0.39(\mathrm{~N})$

[Maximum number: 3]

A pendulum consists of a solid sphere suspended by a string from a fixed point P , as shown in Fig. 3.1.

Fig. 3.1 (not to scale)

The sphere swings from side to side. At one instant the sphere is at its lowest position X , where it has kinetic energy 0.86 J and momentum 0.72 Ns in a horizontal direction. A short time later the sphere is at position Y , where it is momentarily stationary at a maximum vertical height h above position X.

The string has a fixed length and negligible weight. Air resistance is also negligible.

(a)

For the sphere at position Y , calculate the moment of its weight about point P .

moment =

[ 2 ]

$\text { moment }=(0.30 \times 9.81) \times 0.93 \times\left(\sin 47^{\circ} \text { or } \cos 43^{\circ}\right)$

or

moment $=(0.30 \times 9.81) \times\left[0.93^{2}-(0.93-0.29)^{2}\right]^{0.5}$
=2.0 Nm

(b)

State and explain whether the sphere is in equilibrium when it is stationary at position Y .

[ 1 ]

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (i)

Question (ii)

Question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question 3

Question (a)

Question (i)

Question (ii)

Question 4

Question (a)

Question (b)