Edexcel A-Level Physics AS: 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: 8]

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

Figure for Question 2 — 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: 1]

Which of the following is a vector quantity?

A

efficiency

B

kinetic energy

C

power

D

weight

[Maximum number: 3]

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.

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.

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 =

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

Figure for Question 5 — Edexcel A-Level Physics AS

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

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)

[Maximum number: 1]

Two boats A and B pull a ship. The forces from the boats are F_A and F_B. Which gives the forwards component of the total force?

Figure for Question 6 — Edexcel A-Level Physics AS

A

$F_A\sin31^\circ+F_B\cos27^\circ$

B

$F_A\sin31^\circ+F_B\sin27^\circ$

C

$F_A\cos31^\circ+F_B\cos27^\circ$

D

$F_A\cos31^\circ+F_B\sin27^\circ$

[Maximum number: 4]

P and Q are identical spheres. Sphere P moves along a smooth horizontal surface and collides with sphere Q, which is initially stationary.

After the collision:
- sphere P moves off with a momentum of $0.096 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$ in a direction of $15^{\circ}$ to its initial direction.
- sphere Q moves off with a momentum of $0.14 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$ in a direction of $10^{\circ}$ as shown.

Figure for Question 7 — Edexcel A-Level Physics AS

Use a scaled vector diagram to show that the magnitude of the total momentum of spheres P and Q after the collision is about $0.2 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$ .

Construction of correct vector diagram (parallelogram or triangle) with all 3 directions and $0.096\left(\mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\right)$ and $0.14(\mathrm{~kg}$
(1)
$\mathrm{m} \mathrm{s}^{-1}$ ) labelled
- Momenta correctly scaled (ratio of lengths 0.14 to 0.096 rounds
to between 1.40 and 1.50)
)
- Horizontal resultant (to within a slope of 1 small square)
- Total momentum =0.22 to $0.24\left(\mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\right)$
(Do not award MP4 if this value has been obtained by
calculation or from an incorrect diagram)

[Maximum number: 2]

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.

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.

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 8 — Edexcel A-Level Physics AS

[Maximum number: 4]

The luge is an event at the Winter Olympics. An athlete lies on a small sledge and races down an icy track, feet first.

Figure for Question 9 — Edexcel A-Level Physics AS

An athlete accelerates down a straight section of the track as shown. The track is at an angle $\theta$ to the horizontal.

Draw a free-body force diagram for the sledge and athlete.
You should consider the relative sizes of the forces when drawing your diagram.

[Maximum number: 2]

A lorry has a mass of 4500 kg.
The forward force on the lorry is 6700 N.
The total resistive force on the lorry is 900 N.
Calculate the acceleration of the lorry.

Acceleration =

[Maximum number: 2]

When an object is in contact with a horizontal surface, there is a maximum frictional force F between the object and the surface before sliding occurs.
F is given by the equation

F=\mu N

where $\mu$ is a constant and N is the normal contact force between the object and the surface.
A student investigated this relationship for a rubber block on a concrete surface. She set up the apparatus as shown in the diagram.

Figure for Question 11 — Edexcel A-Level Physics AS

The student varied the mass m placed on top of the rubber block and determined corresponding values of F. Her results are shown in the table.

Table for Question 11 — Edexcel A-Level Physics AS

Explain how the values of N are calculated.

[Maximum number: 7]

A student carries out an experiment to determine a value for g, the acceleration of free fall. A short wooden rod is released above a light gate. A timer connected to the light gate is used to measure the time taken for the wooden rod to pass through the light gate.

The experimental arrangement is shown.

Figure for Question 12 — Edexcel A-Level Physics AS

The student uses the equation $v^{2}=u^{2}+2 a s$ , where u=0, and a graphical method to determine a value for g.

(a)

State the additional measurements the student should take.

[ 2 ]

(b)

Describe how the velocity v of the wooden rod as it passes through the light gate can be determined accurately.

[ 2 ]

$\text { - } \quad v=\frac{\text { length of rod }}{\text { time (to pass through light gate) }}$

- Repeat (at each height) and (calculate) an average

(c)

Describe how the student can determine a value for g using a graphical method.

[ 3 ]

[Maximum number: 2]

A steel object is held by an electromagnet. The magnetic force prevents the steel object falling.

State two reasons why the weight of the object and the force from the electromagnet are not a Newton third law pair.
(2)

[Maximum number: 1]

Two objects, R and S, are falling vertically and accelerating due to gravity. Air resistance is negligible.

R has mass m and S has mass 2m. Initially, each object has momentum p.

After time t object R has momentum 2p.

Which of the following gives the momentum of object S after time t?

A

2p

B

3p

C

4p

D

5p

[Maximum number: 2]

P and Q are identical spheres. Sphere P moves along a smooth horizontal surface and collides with sphere Q, which is initially stationary.

After the collision:
- sphere P moves off with a momentum of $0.096 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$ in a direction of $15^{\circ}$ to its initial direction.
- sphere Q moves off with a momentum of $0.14 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$ in a direction of $10^{\circ}$ as shown.

Figure for Question 15 — Edexcel A-Level Physics AS

State the principle of conservation of linear momentum.

[Maximum number: 2]

The photograph shows a ladder that a person can use to climb into the roof space of a building.

Front view

Side view

When not in use, the ladder is stored in the roof space and the opening to the roof space is covered by a board. The board is hinged to the ceiling at one end.

The ladder is attached to the board by a rail, as shown below. A small block prevents the board from rotating into the roof space.

Figure for Question 16 — Edexcel A-Level Physics AS

The weight of the board and rail is 50 N . The weight acts at a distance of 0.45 m from the hinge as shown.

The total length of the ladder is 2.70 m , with 0.85 m to the left of the hinge.

The weight of the ladder is 54 N . Assume the ladder is uniform.

A downward force is required to rotate the board away from the block. This force is applied 0.80 m from the hinge.

Determine the magnitude of this force.

Magnitude of force =

[Maximum number: 6]

The photograph shows a ladder that a person can use to climb into the roof space of a building.

Front view

Side view

When not in use, the ladder is stored in the roof space and the opening to the roof space is covered by a board. The board is hinged to the ceiling at one end.

The ladder is attached to the board by a rail, as shown below. A small block prevents the board from rotating into the roof space.

Figure for Question 17 — Edexcel A-Level Physics AS

(a)

State what is meant by the centre of gravity of an object.

[ 1 ]

(b)

The weight of the board and rail is 50 N . The weight acts at a distance of 0.45 m from the hinge as shown.

The total length of the ladder is 2.70 m , with 0.85 m to the left of the hinge.

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

The weight of the ladder is 54 N . Assume the ladder is uniform.

[ 5 ]

(i)

Explain why the board and ladder remain in the position shown.

[ 5 ]

[Maximum number: 2]

An 'escape lane' can stop cars or trucks safely if the brakes stop working when moving downhill.

The photograph shows an escape lane.

Figure for Question 18 — Edexcel A-Level Physics AS

The escape lane is made of sand and is horizontal, as shown below. The resistive force of the sand on a vehicle reduces the kinetic energy of the vehicle.

As a truck enters the escape lane, the kinetic energy of the truck is $8.0 \times 10^{6} \mathrm{~J}$ .

The sand exerts an average resistive force of $3.5 \times 10^{5} \mathrm{~N}$ on the truck as the truck comes to rest.

Calculate the distance moved by the truck on the escape lane.

Distance =

[Maximum number: 3]

In a high jump competition, athletes jump over a bar.
An athlete has a weight of 680 N .

The athlete moves horizontally as he passes over the bar.

The kinetic energy of the athlete is 409 J .

Show that the athlete has a horizontal speed of about 3.4 m s^-1.

[Maximum number: 2]

The diagram shows a system used to move a stone block up a ramp. A team of people uses a rope to pull the block at a constant speed.

Figure for Question 20 — Edexcel A-Level Physics AS

height of ramp $=4.35 \mathrm{~m}$
angle of ramp to horizontal $=6.0^{\circ}$
mass of block $=2.10 \times 10^{3} \mathrm{~kg}$
speed of block up ramp $=0.450 \mathrm{~m} \mathrm{~s}^{-1}$
total power of team $=6.25 \mathrm{~kW}$

Show that the useful work done on the block is about 90 kJ.

[Maximum number: 5]

The luge is an event at the Winter Olympics. An athlete lies on a small sledge and races down an icy track, feet first.

Figure for Question 21 — Edexcel A-Level Physics AS

After the finish line there is a straight, uphill section of track for the sledge to decelerate in. The maximum permitted gradient of this section is 20%.

An athlete reaches the finish line at a velocity of $33 \mathrm{~m} \mathrm{~s}^{-1}$ . She then applies a minimum braking force of 240 N as she moves along the uphill section of track to help her come to a stop.

Calculate the minimum uphill length of track L that should be available for braking. You should ignore all frictional forces other than those applied by the athlete.
mass of sledge and athlete $=95 \mathrm{~kg}$

Either (energy)

Use of $E_k=\frac{1}{2}mv^2$ .

Use trigonometry to determine the component of weight along the slope or the vertical height in terms of L.

Use of $E_{grav}=mg\Delta h$ to determine gravitational energy, or use of W=Fs.

Use of $E_k=E_{grav}+W$ to determine $L=120\,\mathrm{m}$ .

Or (forces)

Use trigonometry to determine the component of weight along the slope or the vertical height in terms of L.

Use of resultant force = $mg\sin 11.3^{\circ}+240\,\mathrm{N}$ .

Use F=ma to determine a.

Use of $v^2=u^2+2as$ with their a (not 9.81) to determine s.

$L=120\,\mathrm{m}$ . Example: $L=122\,\mathrm{m}$ .

[Maximum number: 2]

The diagram shows a system used to move a stone block up a ramp. A team of people uses a rope to pull the block at a constant speed.

Figure for Question 22 — Edexcel A-Level Physics AS

height of ramp $=4.35 \mathrm{~m}$
angle of ramp to horizontal $=6.0^{\circ}$
mass of block $=2.10 \times 10^{3} \mathrm{~kg}$
speed of block up ramp $=0.450 \mathrm{~m} \mathrm{~s}^{-1}$
total power of team $=6.25 \mathrm{~kW}$

Show that the total force that the team exerts on the block is about 14 kN .
(2)

Use of P=W / t and $\Delta W=F \Delta s$

Force = 13.9(kN)

Example of calculation

In 1 second $W=6250 \mathrm{~J}$ and distance travelled $=0.450 \mathrm{~m}$ $F=6250 \mathrm{~W} \div 0.450 \mathrm{~m} \mathrm{~s}^{-1}=13.9 \mathrm{kN}$

(1)

(1)

[Maximum number: 2]

The diagram shows a system used to move a stone block up a ramp. A team of people uses a rope to pull the block at a constant speed.

Figure for Question 23 — Edexcel A-Level Physics AS

height of ramp $=4.35 \mathrm{~m}$
angle of ramp to horizontal $=6.0^{\circ}$
mass of block $=2.10 \times 10^{3} \mathrm{~kg}$
speed of block up ramp $=0.450 \mathrm{~m} \mathrm{~s}^{-1}$
total power of team $=6.25 \mathrm{~kW}$

Determine the efficiency of the system.

Efficiency =

Edexcel A-Level Physics AS 1.3 Mechanics Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question (a)

Question (b)

Question (c)

Question 13

Question 14

Question 15

Question 16

Question 17

Question (a)

Question (b)

Question (i)

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23