Scalar & vector quantities

Which of these is a scalar quantity?

A student has some cupcake cases.

One cupcake case is shown in Figure 14.

The student drops a stack of cupcake cases with the base facing downwards, as shown in Figure 15.

(Source: © Elena Schweitzer/Shutterstock)

Figure 15

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 16 shows a cupcake case that is falling at a constant velocity.

Draw an arrow on Figure 16 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

Which of these is a scalar quantity?

A student has some cupcake cases.

One cupcake case is shown in Figure 2.

The student drops a stack of cupcake cases with the base facing downwards, as shown in Figure 3.

(Source: © Elena Schweitzer/Shutterstock)

Figure 3

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 4 shows a cupcake case that is falling at a constant velocity.

Draw an arrow on Figure 4 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.

Which of these is a vector?

Figure 17 shows a balanced seesaw with two children on it.

The pivot is at the centre of the seesaw.

The seesaw is balanced with no children sitting on it.

Child P has a weight of 150 N.

Calculate the moment of the weight of child P about the pivot in N m.

Use the equation

moment of a force = forcedistance to pivot

moment =_........

Figure 18 shows the same balanced seesaw, with the distance of child Q to the pivot labelled as well.

Calculate the value of W, the weight of child Q.

Use the idea of moments and the equation

the moment of W = the moment of the weight of child P

Give your answer to 2 significant figures.

*(c) Figure 19 shows a crowbar being used to lift a heavy weight.

Explain how the crowbar enables a person to lift a heavy weight.

You should include the idea of moments in your answer.

It may help to label some distances in Figure 19 and use those distances in your explanation.

Which of these is a vector quantity?

Figure 13 shows a toy that a student makes for a nursery school.

The rod hangs by a string from the ceiling.

weight of S = 2.0 N weight of R = 1.0 N

Figure 13

The moment of C about point P is 0.60 Nm.

Calculate the weight of C.

Use the equation

moment = F × d

weight of C_........

Show that the total moment of S and R about P is 0.70 N m.

Using the data in the question and the principle of moments, determine if the toy shown in Figure 13 is in equilibrium.

The rod is very light so its weight can be ignored.

Figure 14 show a rack and pinion system, used on a mountain railway.

The teeth on the rack are 8.0 cm apart.

Calculate how far along the rack the train moves when the pinion turns through one complete revolution.

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

Complete the following sentences using words from the box below.

The force that keeps the Earth in orbit around the sun is

The force that opposes motion between two surfaces is_........ .

The force that can move small pieces of paper towards a plastic comb

Which of these statements is true for a vector quantity?

Figure 3 shows a force of 200 N acting at the end of a plank of wood.

The force acts at right angles to the plank and at 3.0 m away from a pivot.

Calculate the moment of the 200 N force about the pivot.

State the unit of the moment of the force.

Use the equation

moment of a force = force × distance at right angles to the direction of the force

moment of the force about the pivot =_........ unit_........

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

Calculate the distance the cyclist travels in the 15 s.

*(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.

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

Calculate the distance the cyclist travels in the 15 s.

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

Sketch the velocity / time graph for this cyclist on Figure 3.

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

Use words from the box to complete the sentences below.

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

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

Which row of the table is correct for both force and velocity?

Figure 20 shows a satellite orbiting the Earth.

State the name of the force that keeps the satellite in orbit around the Earth.

Draw an arrow on Figure 20 to show the direction of the force acting on the satellite, that keeps the satellite in orbit around the Earth.

Label this arrow ‘F’.

Satellites are used to gather data about the origin of the Universe.

The Big Bang theory is a theory about the origin of the Universe.

Evidence for the Big Bang theory is provided by red‑shift and CMB radiation.

Describe what is meant by red‑shift.

Explain how red‑shift provides evidence for the Big Bang theory.

The Cosmic Background Explorer (COBE) satellite observed CMB radiation from 1989 to 1993.

State what the ‘M’ in CMB radiation stands for.

State what is meant by ‘cosmic background radiation’.

Explain how the presence of CMB radiation provides evidence for the Big Bang theory.