Question 1
1
The drag force \(F_{\mathrm{D}}\) acting on an object falling through air is given by 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.
structured10 marks
Question 1(b)
1(b)
Fig. 1.1 shows a sphere falling at terminal velocity in air. 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.
Easystructured2 marks
Answer
one arrow vertically downward labelled weight to within \(10^{\circ}\) of the vertical B1 one arrow vertically upwards labelled drag / drag force / \(F_{\mathrm{D}}\) / air resistance / viscous force to within \(10^{\circ}\) of the vertical B1
Question 1
1
The drag force \(F_{\mathrm{D}}\) acting on a sphere falling through a liquid is given by 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.
structured10 marks
Question 1(c)
1(c)
The sphere is shown in 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.
Easystructured2 marks
Answer
one arrow vertically downwards labelled weight / W B1 arrow(s) vertically upwards labelled U / upthrust and drag / \(F_{\mathrm{D}} /\) viscous force B1
Question 1
1
4 marks
Question 1(c)
1(c)
Two tugs pull a tanker at constant velocity in the direction XY , as represented in 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.
structured4 marks
Question 1(c)(i)
1(c)(i)
By reference to the forces acting on the tanker, explain how the tanker may be described as being in equilibrium.
Mediumstructured2 marks
Answer
sum of \(T_{1}\) and \(T_{2}\) equals frictional force these two forces are in opposite directions (allow for 1/2 for travelling in straight line hence no rotation / no resultant torque)
Question 1(c)(ii)
1(c)(ii)
1. Complete Fig. 1.2 to draw a vector triangle for the forces \(R, T_{1}\) and \(T_{2}\). 2. Use your vector triangle in Fig. 1.2 to determine the magnitude of \(T_{1}\) and of \(T_{2}\).
Mediumstructured2 marks
Answer
1. scale vector triangle with correct orientation / vector triangle with correct orientation both with arrows scale given or mathematical analysis for tensions 2. \(\quad T_{1}=10.1 \times 10^{3}\left( \pm 0.5 \times 10^{3}\right) \mathrm{N}\) \(T_{2}=16.4 \times 10^{3}\left( \pm 0.5 \times 10^{3}\right) \mathrm{N}\)
Question 1
1
3 marks
Question 1(b)
1(b)
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. 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
Mediumstructured3 marks
Answer
either triangle / parallelogram with correct shape C1 tension \(=14.3 \mathrm{~N} \quad(\) allow \(\pm 0.5 \mathrm{~N}) \quad\) A2 [3] or \(R=25 \cos 35^{\circ}\) \(T=R \tan 35^{\circ}\) \(T=14.3 \mathrm{~N}\) or \(T=25 \sin 35^{\circ}\) \(T=14.3 \mathrm{~N}\) or \(\quad R\) and T resolved vertically and horizontally leading to \(T=14.3 \mathrm{~N}\)
Question 1
1
stage 1, 2. stage 2.
structured1 marks
Question 1(d)
1(d)
Two strings support a load of weight 7.5 N , as shown in 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.
Mediumstructured4 marks
Answer
either correct shaped triangle M1 correct labelling of two forces, three arrows and two angles A1 or correct resolving: \(T_{2} \cos 40^{\circ}=T_{1} \cos 50^{\circ}\) \(T_{1} \sin 50^{\circ}+T_{2} \sin 40^{\circ}=7.5\) \(T_{1}=5.7(45)(\mathrm{N})\) \(T_{2}=4.8(\mathrm{~N})\) (allow ± 0.2 N for scale diagram)
Question 1
1
A sphere of radius 2.1 mm falls with terminal (constant) velocity through a liquid, as shown in 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 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 .
structured1 marks
Question 1(c)
1(c)
1 marks
Question 1(c)(i)
1(c)(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.
Easystructured1 marks
Answer
W downwards, U upwards, F v upwards B1
Question 2
2
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? \(H=T \cos 30^{\circ}\) \(T=H \sin 30^{\circ}\) \(W=T \cos 30^{\circ}\) \(W=T \sin 30^{\circ}\)
Mediummcq1 marks
Answer
C
Question 3
3
Two forces act on a circular disc as shown. Which diagram shows the line of action of the resultant force?
Mediummcq1 marks
Answer
A
Question 4
4
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? \(L=W \cos \theta\) and \(T=R+W \sin \theta\) \(L=W \sin \theta\) and \(T=R+W \cos \theta\) \(L=W \cos \theta\) and \(T=R-W \sin \theta\) \(L=W \sin \theta\) and \(T=R-W \cos \theta\)
Mediummcq1 marks
Answer
A
Question 2
2
5 marks
Question 2(b)
2(b)
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. 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.
structured5 marks
Question 2(b)(i)
2(b)(i)
On Fig. 2.1, draw arrows to represent the directions of all the forces acting on object O .
Mediumstructured2 marks
Answer
arrow vertically down through O B1 tension forces in correct direction on rope B1
Question 2(b)(ii)
2(b)(ii)
Calculate 1. the angle \(\theta\), 2. the tension T.
Mediumstructured3 marks
Answer
1. weight \(=m g=4.9 \times 9.81(=48.07) \quad\) C1 \(69 \sin \theta=m g \quad\) C1 \(\theta=44 .(1)^{\circ} \quad\) scale drawing allow \(\pm 2^{\circ} \quad\) A1 use of cos or tan 1/3 only 2. \(T=69 \cos \theta\) C1 \(=49.6 / 50 \mathrm{~N} \quad\) scale drawing \(50 \pm 2(2 / 2) \quad 50 \pm 4(1 / 2) \quad\) A1 correct answers obtained using scale diagram or triangle of forces will score full marks cos in 1. then \(\sin\) in 2. (2/2)