Scalar and vector quantities

Which of these is a scalar quantity?

A student has some cupcake cases.

One cupcake case is shown in Figure 7.

The student drops a stack of cupcake cases with the base facing downwards, as shown in Figure 8.

(Source: © Elena Schweitzer/Shutterstock)

Figure 8

The speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

The student also has a stop clock and a metre rule.

Describe an investigation to show how the speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

A stack of cupcake cases has a mass of 0.005 kg.

Calculate the weight, in newtons, of the stack of cupcake cases.

Gravitational field strength = 10 N / kg

Use the equation

W = mg

Figure 9 shows a cupcake case that is falling at a constant velocity.

Draw an arrow on Figure 9 to show the force due to air resistance on the cupcake case.

State the value of the acceleration of the cupcake case when it is falling at a constant velocity

A car travels along a straight road.

The car accelerates at 3 m / s² for a time of 7 s.

Calculate the change in velocity of the car.

Use the equation

change in velocity = acceleration × time taken

change in velocity =_........ m / s

Which of these is a scalar quantity?

A student has some cupcake cases.

One cupcake case is shown in Figure 1.

The student drops a stack of cupcake cases with the base facing downwards, as shown in Figure 2.

(Source: © Elena Schweitzer/Shutterstock)

Figure 2

The speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

The student also has a stop clock and a metre rule.

Describe an investigation to show how the speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

A stack of cupcake cases has a mass of 0.005 kg.

Calculate the weight, in newtons, of the stack of cupcake cases.

Gravitational field strength = 10 N / kg

Use the equation

W = mg

Figure 3 shows a cupcake case that is falling at a constant velocity.

Draw an arrow on Figure 3 to show the force due to air resistance on the cupcake case.

State the value of the acceleration of the cupcake case when it is falling at a constant velocity.

Quantities can be either scalar or vector.

Which of these is a vector quantity?

Figure 7 shows a ball bearing as it falls slowly through a clear, dense liquid.

The apparatus in Figure 7 is used to find the average speed of the ball bearing as it falls.

Devise an experiment to determine the average speed of the ball bearing as it falls through the liquid.

You should include:

• any extra apparatus you would use to take measurements

• the measurements you would take

• how you would calculate the speed.

A student thinks that the ball bearing falls through the liquid at a constant speed.

Explain how you could develop this experiment to determine if the ball bearing falls through the liquid at constant speed.

You may draw a diagram to help your answer.

The ball bearing is now dropped through air.

The initial velocity of the ball bearing is zero.

The acceleration of the ball bearing is 10m/s².

The ball bearing falls 1.5 m.

Calculate the velocity of the ball bearing when it has fallen 1.5 m.

Use the equation

velocity of ball bearing =_........ m/s

Which of these is a vector?

State the equation that relates acceleration to change in velocity and time taken.

A van accelerates from a velocity of 2 m / s to a velocity of 20 m / s in 12 s.

Calculate the acceleration of the van.

acceleration =_........ m / s²

Figure 10 is a velocity / time graph for 15 s of a cyclist’s journey.

Calculate the distance the cyclist travels in the 15 s.

distance =_........ m

*(d) Many factors can affect the stopping distance of a car.

Some of these factors involve the driver and some of these factors involve the car or the road.

Explain how the stopping distance of a car is affected by

• factors involving the driver

• factors involving the car or the road.

You should include examples in your explanations.

Equations

Which of these is a vector?

State the equation that relates acceleration to change in velocity and time taken.

A van accelerates from a velocity of 2 m / s to a velocity of 20 m / s in 12 s.

Calculate the acceleration of the van.

acceleration =_........ m / s²

Figure 2 is a velocity / time graph for 15 s of a cyclist’s journey.

Calculate the distance the cyclist travels in the 15 s.

distance =_........ m

Another cyclist starts from rest, but his acceleration decreases as time increases.

Sketch the velocity / time graph for this cyclist on Figure 2.

The magnitude and direction of a force can be represented by a vector. Figure 13 shows the forces acting on four identical trolleys. The arrows show the magnitude and direction of the forces.

Which diagram shows a pair of forces that will produce zero acceleration?

Figure 14 shows two small boats pulling a much larger ship.

The ship is connected to the boats with ropes.

The tension, T, in each of the ropes has a magnitude of 20 kN.

The ropes are at right angles to each other.

Draw a vector diagram and use it to determine the resultant force that the boats exert on the ship.

magnitude of resultant force on the ship =_........ kN

*(c) Figure 15 shows a wooden block connected to a weight by a string. The string goes over a pulley.

The surfaces of the table and the wooden block are both rough.

wooden block

The wooden block moves across the table at a constant horizontal velocity.

Several vertical and horizontal forces act on the wooden block as it moves.

Explain how the forces keep the wooden block moving across the table at a constant horizontal velocity.

Your answer should refer to all forces acting on the wooden block.

You may add to the diagram to help with your answer.

Which of these speeds would be normal for a person walking?

Figure 1 shows a block hanging from a spring balance.

Use a word from the box to complete the sentence below.

The quantity measured by the spring balance in Figure 1 is

A toy car has a mass of 0.10 kg. The toy car accelerates at 2.0 m/s².

Calculate the force producing this acceleration. State the unit.

Use the equation

F = m × a

force =_........ unit =_........

Use words from the box to complete the sentences below.

Vectors have size and_........ .

Scalars have only_........ .

Which of these forces keeps the Moon moving around the Earth?

Which of these is a scalar quantity?

Figure 4 shows a box at rest on a floor.

The force that the floor exerts on the box is shown by the vector in Figure 4.

Figure 4

Add another vector to the diagram in Figure 4 to show the weight of the box.

Figure 5 shows part of a cart.

When the wheels turn the axles become warm.

Explain why the axles become warm when the wheels turn.

Give one way of reducing the heating of the axles when the wheels turn.

Complete the equation that relates efficiency, useful energy transferred by a device and total energy supplied to the device.

In one second an engine has a total energy input of 7500 J.

In one second 3200 J is transferred to the surroundings as wasted energy.

Calculate the useful energy transferred by the engine.

useful energy transferred =_........ J

Calculate the efficiency of this engine.

efficiency of the engine =_........