Scalar & vector quantities

Figure 1 shows a floating hot air balloon attached to the ground by a rope.

The hot air balloon is stationary.

The wind is exerting a force on the hot air balloon in Figure 1.

Which arrow shows the direction of the force of the wind in Figure 1 ?

Tick (✓) one box.

Which force causes the hot air balloon to float?

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Air resistance

Gravity

Upthrust

The hot air balloon in Figure 1 is stationary.

What is the resultant force on the balloon?

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The resultant force is the tension in the rope.

The resultant force is the weight.

The resultant force is zero.

The mass of the hot air balloon is 350 kg.

Calculate the weight of the hot air balloon.

gravitational field strength = 9.8 N/kg

Use the equation:

_ weight = mass × gravitational field strength

The hot air balloon exerts a force of 200 N on the rope.

The force causes the rope to stretch by 1.60 m.

The rope behaves like a spring.

Calculate the spring constant of the rope.

Use the equation:

Choose the unit from the box.

Figure 11 shows a floating hot air balloon attached to the ground by a rope.

The hot air balloon is stationary.

The wind is exerting a force on the hot air balloon in Figure 11.

Which direction is the force of the wind acting?

What is the name of the upwards force on the hot air balloon?

The weight of the hot air balloon is 3.43 kN.

gravitational field strength = 9.8 N/kg

Calculate the mass of the hot air balloon.

Use the Physics Equations Sheet.

The resultant force on the balloon is zero.

What is meant by ‘resultant force’?

Figure 12 shows a vector diagram of the force of the rope on the hot air balloon.

Scale 1 cm = 50 N

Complete the vector diagram to determine the magnitude of the horizontal and vertical components of the force.

A student investigated how the extension of a spring varied with the force applied to the spring.

Figure 13 shows the equipment used.

This is the method used.

1. Measure the length of the unstretched spring.

2. Hang the spring from the clamp stand.

3. Hang a mass from the spring.

4. Calculate the weight of the mass.

5. Measure the new length of the spring.

6. Calculate the extension of the spring.

7. Repeat steps 3 to 6 for additional masses.

A spring can be elastically or inelastically deformed.

What does ‘elastically deformed’ mean?

Figure 14 shows the results.

The student concluded:

‘The extension of the spring is directly proportional to the weight up to a point called the limit of proportionality.’

What was the extension of the spring when the spring reached its limit of proportionality?

Determine the spring constant of the spring used by the student.

Use the Physics Equations Sheet.

The mass on the spring is stationarity after the spring has extended.

The force that the mass exerts on the spring is represented by the vector diagram in Figure 15.

Draw an arrow on Figure 15 to show the magnitude and direction of the tension in the spring.

Figure 10 shows a boat on the sea.

The boat is travelling at a constant speed.

Draw an arrow on Figure 10 to show the size and direction of the force of the water on the propeller.

A quantity can be a scalar quantity or a vector quantity.

Identify which quantities are scalar quantities and which quantities are vector quantities.

Tick (✓) one box in each row.

Which equation links distance (s), speed (v) and time (t)?

Tick (✓) one box.

The speed of the boat is 12 m/s.

Calculate the time taken to travel 6000 m.

Use the Physics Equations Sheet.

Figure 11 shows the forces acting on the boat when it is moving at a constant speed.

The engine of the boat is turned off. The boat slows down and stops.

Explain what happens to the forces acting on the boat.

Figure 2 shows a boat on the sea.

The boat is travelling at a constant speed.

Draw an arrow on Figure 2 to show the size and direction of the force of the water on the propeller.

A quantity can be a scalar quantity or a vector quantity.

Identify which quantities are scalar quantities and which quantities are vector quantities.

Tick (✓) one box in each row.

Which equation links distance (s), speed (v) and time (t)?

Tick (✓) one box.

The speed of the boat is 12 m/s.

Calculate the time taken to travel 6000 m.

Use the Physics Equations Sheet.

Figure 3 shows the forces acting on the boat when it is moving at a constant speed.

The engine of the boat is turned off. The boat slows down and stops.

Explain what happens to the forces acting on the boat.

Figure 1 shows a boat pulling a person parasailing.

A rope attaches the person to the boat.

What type of force is the weight?

Tick (✓) one box.

Contact force

Magnetic force

Non-contact force

The mass of the person is 75 kg.

Calculate the weight of the person.

gravitational field strength = 9.8 N/kg

Use the equation:

weight = mass × gravitational field strength

The resultant force acting on the person is zero.

Which of the following describes the motion of the person?

Tick (✓) one box.

Velocity decreasing

Moving at constant velocity

Velocity increasing

The horizontal force on the person is 4300 N.

Calculate the work done by this force in moving the person a horizontal distance of 500 m.

Use the equation:

work done = force × distance

Choose the unit from the box.

The speed of the boat changes.

The height of the person above the water decreases by 18 m.

Calculate the decrease in gravitational potential energy of the person.

mass of person = 75 kg

gravitational field strength = 9.8 N/kg

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

A scalar quantity has size, but no direction.

Distance is a scalar quantity.

Which of the following is a scalar quantity?

Tick (✓) one box.

Acceleration

Speed

Velocity

Weight

Figure 6 shows the route a car travelled from town P to town Q.

The displacement of the car is the straight-line distance from town P to town Q.

Determine the displacement of the car when the car has travelled from town P to town Q.

Include the direction from north.

At one point in the journey the car had an acceleration of 0.12 m/s².

The car has a mass of 800 kg.

Calculate the resultant force on the car.

Use the equation:

resultant force = mass × acceleration

Figure 7 shows a distance-time graph for a different part of the car’s journey.

Determine the speed of the car.

Figure 5 shows a car travelling at a constant speed on a straight, level road.

Draw an arrow on Figure 5 to show the direction of the force of air resistance on the car.

The mass of the car is 850 kg

Calculate the weight of the car.

Use the equation:

weight = mass × gravitational field strength

gravitational field strength = 9.8 N/kg

What is the direction of the normal contact force of the road on the wheels?

Tick (✓) one box.

The car is travelling at constant speed.

The resultant force on the car is zero.

How does the size of the normal contact force of the road on the wheels compare with the weight of the car?

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A car is travelling at a constant speed.

A constant braking force of 5100 N is applied by the brakes.

The car decelerates and stops.

The braking distance is 38 m

Calculate the work done by the braking force.

Choose the unit from the box.

Use the equation: work done = force × distance

Which two factors affect braking distance?

Tick (✓) two boxes.

The distance a car travels during the driver’s reaction time is called the thinking distance.

Which factor affects thinking distance?

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Figure 6 shows a sketch graph of how thinking distance varies with speed.

Which term describes the relationship between thinking distance and speed?

Tick (✓) one box.