[Maximum number: 2]

The drag force $F_{\mathrm{D}}$ acting on an object falling through air is given by

F_{\mathrm{D}}=\frac{1}{2} C \rho A v^{2}

where A is the cross-sectional area of the object,
v is the velocity of the object in the air,
$\rho$ is the density of the air and
C is a constant called the drag coefficient.

(a)

Fig. 1.1 shows a sphere falling at terminal velocity in air.

Fig. 1.1

Assume that the upthrust on the sphere is negligible.
On Fig. 1.1, draw and label arrows to show the directions of the two forces acting on the sphere.

[ 2 ]

[Maximum number: 2]

The drag force $F_{\mathrm{D}}$ acting on a sphere falling through a liquid is given by

F_{\mathrm{D}}=6 \pi \eta r v

where r is the radius of the sphere,
v is the speed of the sphere in the liquid and
$\eta$ is a property of the liquid called the viscosity.

(a)

The sphere is shown in Fig. 1.1.

Fig. 1.1

On Fig. 1.1, draw and label arrows to represent the directions of the three forces acting on the sphere as it falls at terminal velocity through the liquid.

[ 2 ]

(a)

Two tugs pull a tanker at constant velocity in the direction XY , as represented in Fig. 1.1.

Fig. 1.1

Tug 1 pulls the tanker with a force $T_{1}$ at $25.0^{\circ}$ to XY . Tug 2 pulls the tanker with a force of $T_{2}$ at $15.0^{\circ}$ to XY . The resultant force R due to the two tugs is $25.0 \times 10^{3} \mathrm{~N}$ in the direction X Y.

[ 4 ]

(i)

By reference to the forces acting on the tanker, explain how the tanker may be described as being in equilibrium.

[ 2 ]

(ii)

1. Complete Fig. 1.2 to draw a vector triangle for the forces $R, T_{1}$ and $T_{2}$ .

Fig. 1.2

2. Use your vector triangle in Fig. 1.2 to determine the magnitude of $T_{1}$ and of $T_{2}$ .

\begin{gathered} T_{1}=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \mathrm{N} \\ T_{2}=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . . \mathrm{N} \\ {[2]} \end{gathered}

[ 2 ]

(a)

A block of wood of weight 25 N is held stationary on a slope by means of a string, as shown in Fig. 1.1.

Fig. 1.1

The tension in the string is T and the slope pushes on the block with a force R that is normal to the slope.

Either by scale drawing on Fig. 1.1 or by calculation, determine the tension T in the string.
T=
N

[ 3 ]

[Maximum number: 4]

stage 1,
2. stage 2.

(a)

Two strings support a load of weight 7.5 N , as shown in Fig. 1.2.

Fig. 1.2

One string has a tension $T_{1}$ and is at an angle $50^{\circ}$ to the horizontal. The other string has a tension $T_{2}$ and is at an angle $40^{\circ}$ to the horizontal. The object is in equilibrium. Determine the values of $T_{1}$ and $T_{2}$ by using a vector triangle or by resolving forces.

\begin{aligned} & T_{1}= \\ & T_{2}= \end{aligned}

[ 4 ]

[Maximum number: 1]

A sphere of radius 2.1 mm falls with terminal (constant) velocity through a liquid, as shown in Fig. 1.1.

Fig. 1.1

Three forces act on the moving sphere. The weight of the sphere is $7.2 \times 10^{-4} \mathrm{~N}$ and the upthrust acting on it is $4.8 \times 10^{-4} \mathrm{~N}$ . The viscous force $F_{\mathrm{V}}$ acting on the sphere is given by

F_{\mathrm{V}}=k r v

where r is the radius of the sphere, v is its velocity and k is a constant. The value of k in SI units is 17 .

(a)

(i)

On the sphere in Fig. 1.1, draw three arrows to show the directions of the weight W, the upthrust U and the viscous force $F_{\mathrm{V}}$ . Label these arrows W, U and $F_{\mathrm{V}}$ respectively.

[ 1 ]

[Maximum number: 1]

A pendulum bob is held stationary by a horizontal force H. The three forces acting on the bob are shown in the diagram.

The tension in the string of the pendulum is T. The weight of the pendulum bob is W.
Which statement is correct?

A

$H=T \cos 30^{\circ}$

B

$T=H \sin 30^{\circ}$

C

$W=T \cos 30^{\circ}$

D

$W=T \sin 30^{\circ}$

[Maximum number: 1]

Two forces act on a circular disc as shown.

Which diagram shows the line of action of the resultant force?

[Maximum number: 1]

An aeroplane is moving at a constant speed in a straight line at an angle $\theta$ to the horizontal.
Four forces act on the aeroplane: thrust force T, weight W, lift force L and resistive force R.

Which two equations must be correct?

A

$L=W \cos \theta$ and $T=R+W \sin \theta$

B

$L=W \sin \theta$ and $T=R+W \cos \theta$

C

$L=W \cos \theta$ and $T=R-W \sin \theta$

D

$L=W \sin \theta$ and $T=R-W \cos \theta$

(a)

An object O of mass 4.9 kg is suspended by a rope A that is fixed at point P . The object is pulled to one side and held in equilibrium by a second rope B, as shown in Fig. 2.1.

Fig. 2.1

Rope A is at an angle $\theta$ to the horizontal and rope B is horizontal. The tension in rope A is 69 N and the tension in rope B is T.

[ 5 ]

(i)

On Fig. 2.1, draw arrows to represent the directions of all the forces acting on object O .

[ 2 ]

(ii)

Calculate
1. the angle $\theta$ ,
2. the tension T.

[ 3 ]