Edexcel A-Level Physics Unit 1 Mechanics

[Maximum number: 13]

When water vapour in the atmosphere cools it condenses, forming tiny drops of water. These drops increase in size by colliding with each other and fall back to the ground as rain.

(a)

As a raindrop falls through the air it eventually reaches its terminal velocity. The upthrust on the raindrop can be considered to be negligible.

[ 8 ]

(i)

Explain what is meant by the terminal velocity of the raindrop. Your answer should include a free-body force diagram for the raindrop when terminal velocity has been reached.

[ 4 ]

(ii)

The air resistance F acting on a raindrop travelling at a velocity v, can be determined using the expression

F=0.45 \rho A v^{2}

where A is the cross-sectional area of the raindrop and $\rho$ is the density of the air.
Calculate the terminal velocity of a spherical raindrop of radius $2.0 \times 10^{-3} \mathrm{~m}$ .
density of air $=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$
density of rainwater $=1.0 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$

[ 4 ]

Use of $A=\pi r^{2}$ and $V=\frac{4}{3} \pi r^{3}$

- Use of $\rho=\frac{m}{V}$ and W=m g

- Use of W=F

- $v=6.5-7.0 \mathrm{~m} \mathrm{~s}^{-1}$

(1)

(1)

(1)

(1)

Example of calculation

$A=\pi \times(0.002)^{2}=1.26 \times 10^{-5} \mathrm{~m}^{2}$ $V=\frac{4}{3} \pi \times(0.002 \mathrm{~m})^{3}=3.35 \times 10^{-8} \mathrm{~m}^{3}$ $m=1000 \mathrm{~kg} \mathrm{~m}^{-3} \times 3.35 \times 10^{-8} \mathrm{~m}^{3}=3.35 \times 10^{-5} \mathrm{~kg}$ $W=3.35 \times 10^{-5} \mathrm{~kg} \times 9.81 \mathrm{~N} \mathrm{~kg}^{-1}=3.29 \times 10^{-4} \mathrm{~N}$ $3.29 \times 10^{-4} \mathrm{~N}=0.45 \times 1.2 \mathrm{~kg} \mathrm{~m}^{-3} \times 1.26 \times 10^{-5} \mathrm{~m}^{2} \times v^{2}$ $3.29 \times 10^{-4} \mathrm{~N}=6.80 \times 10^{-6} \times v^{2}$ $v=6.96 \mathrm{~m} \mathrm{~s}^{-1}$

(b)

Some plants have adapted to high rainfall by having a specialised shape and waxy leaves. This allows rain to slide down a leaf and off the end as a series of drops.

[ 5 ]

(i)

A drop of water slides off a leaf as shown.

Add to the diagram to show the position of the drop at regular intervals of time. The first two positions have been drawn for you.

Figure for Question (i) — Edexcel A-Level Physics AS

[ 2 ]

(ii)

Water falls from a leaf at a steady rate of five drops per second.

As each drop reaches the ground, there are four drops above it in the air.
Calculate the height of the leaf from the ground. It can be assumed that the drop at the highest position has just left the leaf.

Height of leaf =

[ 3 ]

Use of $s=u t+1 / 2 a t^{2}$ with u=0

(accept use of t $=0.2 \mathrm{~s}, 0.25 \mathrm{~s}, 0.75 \mathrm{~s}, 1.0 \mathrm{~s}$ )

- See 0.8 s for the time since the drop left the leaf

- $s=3.1 \mathrm{~m}$

(1)

(1)

(1)

Example of calculation
$s=1 / 2 \times 9.81 \mathrm{~N} \mathrm{~kg}^{-1} \times(0.8 \mathrm{~s})^{2}=3.14 \mathrm{~m}$

3

[Maximum number: 4]

A student was given a collection of old coins.
She placed the coins alongside a ruler, as shown, to determine the diameter and thickness of the coins.

Figure for Question Unit 1: Mechanics and Materials question 2 — Edexcel A-Level Physics AS

(a)

The mass of the 20 coins shown is 196 g .

Determine the average density of the coins.

Average density =

[ 2 ]

Use of $\rho=m / V$

- $\rho$ between 8000 and $8600 \mathrm{~kg} \mathrm{~m}^{-3}$

Allow ecf for V from 1(a) for both marks.

Example of calculation

$\rho=m / V$ $\rho=0.0098 \mathrm{~kg} / 1.18 \times 10^{-6} \mathrm{~m}^{3}$ $\rho=8300 \mathrm{~kg} \mathrm{~m}^{-3}$

(b)

Determine whether the coins could be made from brass.
density of brass $=8550 \mathrm{~kg} \mathrm{~m}^{-3} \pm 2 \%$

[ 2 ]

[Maximum number: 8]

A swimmer swims a 100 m race. A simplified displacement-time graph for the swimmer is shown.

Figure for Question Unit 1: Mechanics and Materials question 3 — Edexcel A-Level Physics AS

(a)

Draw a corresponding velocity-time graph for the motion of the swimmer on the axes below. Show all working in the space below.

Figure for Question (a) — Edexcel A-Level Physics AS

[ 4 ]

Use of v=s / t Or use of gradient

- $v=( \pm) 1.1$ to $1.2\left(\mathrm{~m} \mathrm{~s}^{-1}\right)$

- Scaling of the velocity axis so that the graph covers at least 50% of the paper above and below the axes.

(A minimum of 1 number on each axis required e.g. 1 and -1 )

- A positive constant velocity from 0 to 42 s and the same negative constant velocity from 48 s to 90 s with connecting line/curve (tolerance of $\pm 1 \mathrm{~s}$ )

Example of calculation

Initial velocity $=\frac{46 \mathrm{~m}}{40 \mathrm{~s}}=1.15 \mathrm{~m} \mathrm{~s}^{-1}$

(1)

(1)

(1)

(b)

To increase her initial speed, the swimmer began the race by gliding underwater for 15 m and then began to use her arms and legs. This was not represented on the simplified displacement-time graph.

[ 4 ]

(i)

Sketch onto the axes below to show the actual variation of displacement with time for the first 15 m of the race.

Time / s

[ 2 ]

(ii)

Explain one other way in which the motion of the swimmer has been simplified when drawing the displacement-time graph.

[ 2 ]

[Maximum number: 6]

A student determined the viscosity of a liquid using the falling-ball method.

(a)

When the ball is falling at terminal velocity the following equation applies

\text { drag force }=\text { weight of ball }- \text { upthrust }

The density of the liquid was known.
The student used a balance and a digital calliper to make measurements on the ball.
Describe how the student could use her measurements to calculate a value for the drag force acting on the ball.

[ 4 ]

(b)

When falling through the liquid, the ball reached terminal velocity.

The flow of liquid around the ball was laminar.
Calculate the viscosity of the liquid.
terminal velocity of ball $=5.4 \times 10^{-4} \mathrm{~m} \mathrm{~s}^{-1}$
radius of ball $=0.50 \times 10^{-2} \mathrm{~m}$
drag force $=1.1 \times 10^{-2} \mathrm{~N}$

Viscosity of liquid =

[ 2 ]

Edexcel A-Level Physics AS Unit 1 Mechanics and Materials

Covered syllabus points

Covered syllabus points

Unit 1: Mechanics and Materials question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Unit 1: Mechanics and Materials question 2

Question (a)

Question (b)

Unit 1: Mechanics and Materials question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Unit 1: Mechanics and Materials question 4

Question (a)

Question (b)