Scalars & Vectors (AQA AS Physics)

Exam Questions

3 hours45 questions
1a2 marks

Explain the difference between vector and scalar quantities.

1b3 marks

Table 1 contains a number of scalar and vector quantities. 

Place one tick () in each row to show whether each quantity is a scalar or a

Table 1

Quantity

Scalar

Vector

Speed

 

 

Velocity

 

 

Mass

 

 

Weight

 

 

Distance

 

 

Displacement

 

 

1c2 marks

Figure 1 shows a uniform beam supported by two light cables, AB and AC, which are attached to a single steel cable from a crane. The beam is stationary and in equilibrium.

Figure 1

4-1-s-q--q1c-easy-aqa-a-level-physics

State two reasons the beam can be described as ‘in equilibrium’.

1d2 marks

The tension in the cable AB is 3 N and the tension in the cable AC is 4 N. 

Calculate the resultant force required in the beam BC to keep the system in equilibrium.

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2a4 marks

State two vector quantities and two scalar quantities.

2b2 marks

 The helicopter, shown in Figure 1, is moving horizontally through still air. The lift force from the helicopter’s blades is labelled A. 

Figure 1

4-1-s-q--q2b-easy-aqa-a-level-physics

Name the two forces B and C that also act on the helicopter.

2c2 marks

The helicopter is moving at a constant velocity. 

Draw a force vector triangle to show this arrangement.

2d2 marks

The force B has a value of 25 kN and the force C has a value of 40 kN. 

Calculate the value of force A needed to keep the helicopter moving at a constant velocity.

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3a2 marks

State what is meant by a vector quantity and give one example.

3b2 marks

Figure 1 shows a ball is suspended from a cable. The ball is pulled into the position shown by a rope that is kept horizontal.

Figure 1

4-1-s-q--q3b-easy-aqa-a-level-physics

In the position shown, the ball is in equilibrium. 

State the force and component which balance:

  • The force of the rope on the ball.
  • The weight of the ball.
3c2 marks

When in equilibrium, the tension T1 is equal to 10.1 N and the tension T2 is equal to 15.7 N.

Calculate the weight of the ball.

3d1 mark

The ball is then detached from the rope, so it is hanging only by the cable.

4-1-s-q--q3d-easy-aqa-a-level-physics

State the new tension in the cable.

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4a4 marks

Complete Table 1 by stating whether the quantity is a vector or a scalar and by giving the full name of its unit.

Table 1

Quantity

Vector or Scalar

Unit

Force

 

 

Displacement

 

 

Kinetic Energy

 

 

Power

 

 

4b1 mark

Figure1 shows two forces acting on an object at O. The forces have been drawn to scale.

Figure 1

4-1-s-q--q4b-easy-aqa-a-level-physics

State the scale used in Figure 1.

4c3 marks

Complete the scale drawing, in Figure 1, to determine the magnitude of the resultant force.

4d3 marks

The 1.8 N force then begins to act vertically upwards, so the two forces are perpendicular to each other.

Calculate the angle at which the new resultant force acts.

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5a2 marks

A skier travels at constant speed down a slope of 35°, as shown in Figure1. 

Figure1

4-1-s-q--q5a-easy-aqa-a-level-physics

The force labelled P is parallel to the slope. The force labelled Q is perpendicular to the slope. Assume that there is no friction between the skis and the snow.

Identify the forces labelled P and Q.

5b1 mark

State the condition necessary for the skier to be travelling at a constant velocity.

5c4 marks

Figure 2 below shows an arrow representing the weight, W, of the skier. The arrow has been drawn to scale.

Figure 2

4-1-s-q--q5c-easy-aqa-a-level-physics

scale 1 cm: 100 N

By drawing the forces P and Q onto Figure 2, complete the scale diagram and determine the magnitude of the force P.

5d2 marks

Using Figure 2, or otherwise, determine the magnitude of force Q.

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1a3 marks

Figure 1 shows a uniform beam supported by two light cables, AB and AC, which are attached to a single steel cable from a crane. The beam is stationary and in equilibrium. 

Figure 1

4-1-s-q--q1a-medium-aqa-a-level-physics

The tension in cable AB is equal to T1 and the tension in cable AC is equal to T2. The weight of the beam is 9.5 kN. 

Draw a vector diagram to show the arrangement of the forces, including the angles.

1b2 marks

Write two equations to show the vertical and horizontal components of the forces in part (a).

1c2 marks

Calculate the tension T1 in cable AB.

1d2 marks

Calculate the tension T2 in cable AC. 

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2a2 marks

The helicopter shown in Figure 1 is moving horizontally through still air. The lift force from the helicopter’s blades is labelled A. 

Figure 1

4-1-s-q--q2a-medium-aqa-a-level-physics

The lift force, A, is 12.0 kN and acts at an angle of θ to the horizontal. At any point, the lift force is always four times larger than the drag force. 

Draw a vector diagram to show the arrangement of the forces.

2b3 marks

Show the angle θ is about equal to 76˚.

2c3 marks

Calculate the weight of the helicopter. Give your answer to an appropriate number of significant figures.

2d3 marks

The helicopter begins to descend at a constant speed at an angle of 15° to the horizontal. 

Draw a vector triangle to represent the new forces acting on the helicopter.

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3a1 mark

Figure 1 shows two of the forces acting on a uniform ladder resting against a vertical wall. 

Figure 1

4-1-s-q--q3a-medium-aqa-a-level-physics

Explain how Figure 1 shows that the friction between the ladder and the wall is negligible.

3b2 marks

The forces acting on the ladder are in equilibrium. 

Draw an arrow on Figure 1 to show the direction of the resultant force from the ground acting on the ladder. Label your arrow G.

3c2 marks

The reaction at the ground acts at an angle of 60o to the horizontal. The ladder weighs 140 N. 

Calculate the magnitude of the resultant force G from the ground acting on the ladder.

3d3 marks

If the wall was removed, only the weight W and reaction at the ground G would act, and the ladder would begin to topple. 

State the direction of the resultant force R and calculate its magnitude.

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4a1 mark

Figure 1 shows a uniform steel girder being held horizontally by a crane.

Two cables are attached to the ends of the girder and the tension in each of these cables is T.

Figure 1

4-1-s-q--q4a-medium-aqa-a-level-physics

On Figure 1 draw an arrow to show the line of action of the weight of the girder.

4b2 marks

The tension, T, in each cable is 650 N. 

Calculate the horizontal component of the tension in each cable.

4c2 marks

Calculate the vertical component of the tension in each cable.

4d2 marks

Calculate the weight of the girder.

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5a3 marks

Figure 1 shows a 500 kg iron ball being used on a demolition site. 

Figure 1

4-1-s-q--q5a-medium-aqa-a-level-physics

The ball is suspended from a cable which makes an angle θ with the vertical, and is pulled into the position shown by a rope that is kept horizontal. The tension in the rope is 1600 N. 

Determine the magnitude of the vertical component of the tension in the cable and write an expression relating the angle θ with the vertical and T.

5b3 marks

Determine the magnitude of the horizontal component of the tension in the cable and write an expression relating the angle θ with the vertical and T.

5c3 marks

Determine the angle θ the cable makes with the vertical.

5d2 marks

Determine the magnitude of the tension in the cable.

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1a2 marks

On a construction site, a load, of weight, W, is supported by two strings kept in tension by equal masses, m, hung from their free ends, with each string passing over a frictionless pulley. The arrangement is symmetrical and is shown in Figure 1. 

Figure 1

4-1-s-q--q1a-hard-aqa-a-level-physics

Draw a vector diagram for the three forces acting through the point at which the strings are attached to the load. 

Label:

  • The weight of the load, W
  • The tensions in each string, in terms of m and g, the gravitational field strength
  • The angle θ between each string and the vertical
1b3 marks

The mass of the central load is M, as shown in Figure 2. The weight of the central load is still W. 

Figure 2

4-1-s-q--q1b-hard-aqa-a-level-physics

By resolving the forces vertically about point A, determine an expression for: 

(i)         m in terms of W, g and θ. 

(ii)        M in terms of m and θ.

1c4 marks

Figure 3 shows a crane hook in equilibrium under the action of a vertical force of 16.5 kN in the crane cable and tension forces T subscript 1  and begin mathsize 16px style T subscript 2 end style in the sling.

Figure 3

4-1-s-q--q1c-hard-aqa-a-level-physics

By drawing a scale diagram, and stating an appropriate scale, determine the tension forces straight T subscript 1  and begin mathsize 16px style T subscript 2 end style  acting in the sling.

1d3 marks

A crate rests on the inclined load as shown in Figure 4. 

Figure 4

4-1-s-q--q1d-hard-aqa-a-level-physics

Explain the effects on vectors X, Y and Z if the incline becomes steeper.

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2a4 marks

In the leisure activity parascending, a person attached to a parachute is towed over the sea by a tow rope attached to a motorboat. 

Figure 1 shows the directions of the forces acting on a person of weight 0.7 kN when being towed horizontally at a constant speed. The 1.8 kN force is the tension in the tow rope and the force labelled D is the drag force. 

Figure 1

4-1-s-q--q2a-hard-aqa-a-level-physics

Draw a vector triangle relating the forces acting on the person. Hence, or otherwise, determine the magnitude of the drag force.

2b4 marks

Figure 2 shows a different parasailer being towed at a constant velocity. 

Figure 2

 4-1-s-q--q2b-hard-aqa-a-level-physics

The rope towing the parasailer makes an angle of 27° with the horizontal and has a tension of 2.2 kN. The drag force of 2.6 kN acts at an angle of 41° to the horizontal. 

By drawing a scale diagram, and stating an appropriate scale, determine the weight of the parasailer.

2c3 marks

The rope breaks loose from the motorboat, but luckily two of the people on the boat grab it as it reaches an angle of 75° to the horizontal. 

The two people pull the rope with different forces in different directions, as shown in the Figure 3, which shows a bird’s eye view of the parasailer. 

Figure 3

4-1-s-q--q2c-hard-aqa-a-level-physics

The first person pulls the rope with a force of 0.8 kN at an angle of 75.0° to the horizontal. The second person pulls at an angle of 60.0° to the horizontal. 

Calculate the magnitude of the force F that the second person must pull the rope with in order to match the tension of the rope in part (b).

2d1 mark

Determine the magnitude and direction of the force that the boat would have to exert on the rope to make the resultant force equal to zero.

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3a3 marks

An electron is under the influence of two electric fields, E subscript 1  and begin mathsize 16px style E subscript 2 end style, with values 3.0 × 10–8 V m–1 and 6.0 × 10–8 V m–1 respectively, as shown in Figure 1.

Figure 1

4-1-s-q--q3a-hard-aqa-a-level-physics

Determine the magnitude of the resultant field strength E acting on the electron and the angle it makes with the positive horizontal axis.

3b2 marks

The electron has an initial momentum of 4.9 × 10–24 kg m s–1 in the horizontal direction. 

Upon impact, its momentum is 9.8 × 10–24 kg m s–1 at an angle of θ to the horizontal, as shown in Figure 2.

Figure 2

4-1-s-q--q3b-hard-aqa-a-level-physics

Determine the magnitude and direction of the change in momentum relative to the positive horizontal axis.

3c3 marks

A small, charged sphere, suspended from a thread of insulating material, was placed between two vertical parallel plates. 

When a potential difference was applied to the plates, the sphere moved until the thread made an angle of 8.5° to the vertical, as shown in Figure 3. 

Figure 3

4-1-s-q--q3c-hard-aqa-a-level-physics

Show that the electrostatic force F on the sphere is given by F = mg tan 8.5°, where m is the mass of the sphere.

3d3 marks

Point charges A and B are placed a distance apart, as shown in Figure 4.

Figure 4

4-1-s-q--q3d-hard-aqa-a-level-physics

The electric field is directed towards the positive charge and away from the negative charge. 

A holds a positive charge and is half the charge of B. B holds a negative charge. Point C is equidistant from the two charges 

(i)
Draw two arrows on Figure 4 at C to represent the directions and relative magnitudes of the components of the electric field at C due to each of the charges. 
(ii)
Hence draw an arrow, labelled E, on Figure 4 at C to represent the direction of the resultant electric field at C.

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4a4 marks

Figure 1 shows a pole being kept vertical to the ground by two taut light ropes. 

The angles between the ropes and the ground are shown in Figure 1. The tension in the left rope is 200 N, and the tension in the right rope is T. 

Figure 1

4-1-s-q--q4a-hard-aqa-a-level-physics

Use a scale diagram to determine the weight of the pole, W and the tension T.

4b3 marks

A canoeist can paddle at a speed of 3.8 m s–1 in still water. 

She encounters a current which opposes her motion. The current has a velocity of 1.5 m s–1 at 30° to her original direction of travel as shown in Figure 2. 

Figure 2

4-1-s-q--q4b-hard-aqa-a-level-physics

By drawing a scale diagram, and stating an appropriate scale, determine the magnitude of the canoeist’s resultant velocity.

4c4 marks

The boat shown in Figure 3 is being towed at constant velocity. The tension force open parentheses F subscript T close parentheses   in the towing rope is 2500 N. The forces resisting the motion can be assumed to be the force of the water on the keel open parentheses F subscript K close parentheses  and the force of the water on the rudder begin mathsize 16px style open parentheses F subscript R close parentheses end style . Figure 3

4-1-s-q--q4c-hard-aqa-a-level-physics

By calculation or by scale drawing, find the size of the force, F subscript R , needed to keep the boat in equilibrium.

4d4 marks

Figure 4 shows a river which flows from West to East at a constant velocity of 35 cm s–1. 

The boat leaves the south bank heading due North at 1.50 m s–1.

Figure 4

4-1-s-q--q4d-hard-aqa-a-level-physics

Using a scale diagram, determine the resultant velocity of the boat, stating both direction and magnitude.

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5a3 marks

A plane flying across the Lake District sets off from base camp to lake Windermere, 28 km away, in a direction of 20.0° north of east. 

After dropping off supplies it flies to lake Coniston, which is 19 km at 30.0° west of north from lake Windermere. 

Determine the distance from lake Coniston to base camp.

5b2 marks

Figure 1 shows the plane flying due north through still air with a speed v.

 Figure 1

4-1-s-q--q5b-hard-aqa-a-level-physics

The plane enters a region where the wind is blowing with a speed u from a direction which makes an angle of θ with due south. 

Write an expression for the time taken for the plane to fly a distance D due north of its current position in this windy region.

5c3 marks

When there is no wind, the aircraft travels 180 km every 30 minutes. When there is a wind blowing 53° south, the aircraft takes an extra 4 minutes to travel the same distance. 

Assuming the orientation of the plane does not change, calculate the speed of the wind in km h–1.

5d3 marks

The pilot wishes to cross the sky in a straight line between two points labelled A and B as shown in Figure 2.

Figure 2

4-1-s-q--q5d-hard-aqa-a-level-physics

The wind is now blowing due south with the same speed as in part (c). The plane continues to travel at the same speed in the wind as in part (c).

To cross from A to B the pilot has to turn the plane at an angle θ to the direction of the wind, as shown in Figure 2. 

Determine the size of the angle θ using a scale drawing.

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