LEVEL 2 PHYSICS

Demonstrate understanding of aspects of mechanics

91171

NCEA EXAM and SOLUTIONS 2020

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9:30 a.m. Monday 16 November 2020

6 Credits

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To advance through the show just click

Compiled from the NZQA resources by Jonathan Jaffrey April 2021. Not for commercial use.

Best viewed as a Slide Show since the slides are animated.

Each question was graded from 0 to 8 marks. The marks from each question were then added to give an overall score for the paper. The cut scores for the total gave the final grade :

These statements were reflected in the marking system. the easier, simpler maths and answers are coded A , more difficult ones M and the most complex E in the assessor’s column on the right.

The 2020 schedule judgements are shown underlined here. The equivalents I have used are taken from the 2020 schedules for 91170 & 91173 and not underlined.

Other combinations are also possible. (Using A=1; M=2; E=3) However, for M5 or M6 at least one Merit question needs to be correct. For E7 or E8 at least one Excellence needs to be correct.

You may find the following formulae useful

Where needed use g = 9.8 ms^-2

You are advised to spend 60 minutes answering the questions in this booklet.

Question 1 solutions start on the next slide ……

QUESTION ONE: IN TOWN

Alex and Jo have decided to take a road trip. They start from rest on a straight road, and accelerate at 4.2 m s^–2

a) Show their velocity after 0.60 seconds is 2.5 m s^–1

While waiting at traffic lights, Jo has to put on the handbrake to stop the car rolling down the steep (10^o) slope they are on. The mass of the car and occupants is 1600 kg.

(ii) Complete a labelled vector diagram showing how all three forces add together.

The diagram above shows the friction force acting between the tyres and the road.

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(i) Add labelled arrows to show the other two forces acting on the stationary car.

c) By first working out the force of gravity on the car, show that the value of the friction force required to keep the

car stationary is 2700 N.

d) While travelling at 50 km h^–1, Jo sees a pothole in the road 15 m ahead. She must reduce her speed from 50 km h^–1

to 20 km h^–1 to avoid damaging the car. 

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If the time needed for safe braking from 50 km h^–1 to 20 km h^–1 is 2.3 seconds, show by calculation whether there is

enough time to complete braking before reaching the pothole.

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You should start by showing that 50 km h^–1 = 13.89 m s^–1.

b)

Question 1 solutions continue on the next slides ……

a) Show their velocity after 0.60 seconds is 2.5 m s^–1

(ii) Complete a labelled vector diagram showing how all three forces add together.

Alex and Jo have decided to take a road trip. They start from rest on a straight road, and accelerate at 4.2 m s^–2

2 sig fig

Shows equation and substitution :

A

Correct labelled force diagram:

Correct labelled vector diagram with obvious right angle:

A

M

The diagram above shows the friction force acting between the tyres and the road.

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(i) Add labelled arrows to show the other two forces acting on the stationary car.

b)

While waiting at traffic lights, Jo has to put on the handbrake to stop the car rolling down the steep (10^o) slope they are on. The mass of the car and occupants is 1600 kg.

c)

By first working out the force of gravity on the car, show that the value of the friction force required to keep the car stationary is 2700 N.

d)

While travelling at 50 km h^–1, Jo sees a pothole in the road 15 m ahead. She must reduce her speed from 50 km h^–1

to 20 km h^–1 to avoid damaging the car.  If the time needed for safe braking from 50 km h^–1 to 20 km h^–1 is 2.3 seconds, show by calculation whether there is enough time to complete braking before reaching the pothole.

You should start by showing that 50 km h^–1 = 13.89 m s^–1.

10^o slope, mass of the car and occupants is 1600 kg

This is less than 2.3s so the braking would be unsafe

OR :

This is more than 15 m so the braking would be unsafe

Is there enough time?

Is there enough distance?

Correct F_w :

Correct working :

A

M

Correct answer with explanation / interpretation :

E

ONE correct calculation that could lead to a correct solution, e.g. correctly changes both speeds to m s^–1 :

A

ONE error :

M

Question 1 evidence statement on the next slide ……

There are two ways to tackle this :

Evidence Statement …..

Other combinations are also possible. (Using A=1; M=2; E=3)

However, for M5 or M6 at least one Merit question needs to be correct.

For E7 or E8 at least one Excellence needs to be correct.

Question 2 on the next slide ……………………

Question 2 solutions start on the next slide ……

QUESTION TWO: OPEN ROAD

Jo and Alex continue their drive and take a sharp bend in the road at a constant speed of 12 m s^–1

a) Draw an arrow on the car on the diagram above to show the direction of the

acceleration at this point.

b) Calculate the size of the acceleration if the radius of the bend is 25 m, and explain

what causes this acceleration.

c) State TWO external factors that could change the motion of the car as it travels

around the corner, and explain how these factors would affect the motion

d)

The pair continue on their journey at a constant speed of 12 m s^–1.

The car is fitted with a crumple zone. Alex says the crumple zone can increase the time of impact

in a collision from 0.2 seconds to 0.8 seconds.

The mass of the car and occupants is 1600 kg.

Use physics principles and appropriate calculation(s) to explain how having a crumple zone can make this

car safer for the occupants during a collision

a)

Draw an arrow on the car on the diagram above to show the direction of the acceleration at this point.

constant speed of 12 m s^–1

b)

Calculate the size of the acceleration if the radius of the bend is 25 m, and explain what causes this acceleration.

c) State TWO external factors that could change the motion of the car as it travels

around the corner, and explain how these factors would affect the motion

Arrow towards the centre :

A

Friction between the tyres and the road give an unbalanced (centripetal) force which causes the acceleration.

Correct calculation OR Unbalanced inward force created by friction causes inward acceleration:

A

BOTH correct :

M

2 sig fig

• If the car hits ice / oil / gravel / wet section of road / or tyre condition changes (eg a rapid puncture or “blow out”)
• this will change the friction forces and either reduce or increase centripetal force
• and so direction will change due to the change in unbalanced forces.

External factor named PLUS

altered friction leads to altered

Fc resulting in altered motion :

M

ONE named factor that causes reduction in friction :

A

Question 2 d) on the next slide ……

• As the acceleration reduces by a factor of 4 the force on the occupants will also reduce by 4 times.

The pair continue on their journey at a constant speed of 12 m s^–1. The car is fitted with a crumple zone. Alex says the crumple zone can increase the time of impact in a collision from 0.2 seconds to 0.8 seconds.

The mass of the car and occupants is 1600 kg.

Use physics principles and appropriate calculation(s) to explain how having a crumple zone can make this car safer for the occupants during a collision

• Assuming the car decelerates by the same amount with or without the crumple zone.
• The crumple zone increasing the impact time by a factor of 4 will reduce the acceleration by the same factor.

Four times less with the crumple zone

Four times less with the crumple zone

Correct values AND

Justifies how crumple zone works, including statement that ∆p is the same in both situations :

Correct momentum change

OR

ONE correct force

OR

Explanation of crumple zone :

Both forces correct :

E

M

A

OR :

• So long as the passengers are securely belted into a seat, and the seat is rigidly fixed in the passenger compartment, losing their momentum over a longer time makes this safer.

A Force / time graph on the next slide …….

Although the momentum change or Impulse is the same, the force exerted in the impact will be less.

same areas

The graph below shows the force of impact over time when the impact time increases :

Question 2 evidence statement on the next slide ……

If we can increase the impact time across which you slow down by 5 times, we decrease the force by 5 times.

Evidence Statement …..

Other combinations are also possible. (Using A=1; M=2; E=3)

However, for M5 or M6 at least one Merit question needs to be correct.

For E7 or E8 at least one Excellence needs to be correct.

Question 3 follows ………

QUESTION THREE: THE BRIDGE

Question 3 c) & d) on the next slide ……

Jo and Alex need to cross a bridge to reach their destination.

The bridge is 30 m long, and has a mass of 30 000 kg.

The supports are 26 m apart, and equal distance from the

centre of the bridge

a) State the two requirements for an object to be in equilibrium.

b) The road is closed as the bridge is under repair. The support column at end B can supply a maximum support

force of 160,000 N

By finding torques about support A, calculate the furthest distance from support A that a 1600 kg mass could be placed before the support at B became overloaded

Question 3 solutions on the next slides ……

The bridge has an earthquake-protection system made up of springs. Before being put in place on the bridge, the springs are tested by being loaded with a mass m. When loaded with a mass m the springs compress by a distance x .

c) Explain, in depth, how the size of the mass on the springs

needs to change in order to compress the springs a distance

2x from the original length

d)

Jo and Alex wonder whether a compressed spring from the bridge could accelerate their car once the spring is

released, as in the diagram below. They decide to determine the effect of the spring on the car’s motion. They

estimate that for this spring, a force of 50 000 N would compress the spring length from 6.0 m to 4.2 m. The total

mass of the car and occupants is 1600 kg

(i)

Calculate the maximum speed to which this spring could accelerate the car and its occupants if it was compressed to 4.2 m

You should start your answer by first determining the spring constant, k

(ii)

What assumption(s) have you made in this calculation ?

a) State the two requirements for an object to be in equilibrium.

b) The road is closed as the bridge is under repair. The support column at end B can supply a maximum support

force of 160,000 N. By finding torques about support A, calculate the furthest distance from support A that a

1600 kg mass could be placed before the support at B became overloaded.

All torques and all forces are balanced or

the sum of all the forces is zero and the sum of all the torques is zero

A

Bridge 30 m, mass 30 000 kg. Supports 26 m apart, equidistant from the centre.

Question 3 b) solution on the next slide ……

b) The road is closed as the bridge is under repair. The support column at end B can supply a maximum support

force of 160,000 N. By finding torques about support A, calculate the furthest distance from support A that a

1600 kg mass could be placed before the support at B became overloaded.

b) The road is closed as the bridge is under repair. The support column at end B can supply a maximum support

force of 160,000 N. By finding torques about support A, calculate the furthest distance from support A that a

1600 kg mass could be placed before the support at B became overloaded.

Bridge 30 m, mass 30 000 kg. Supports 26 m apart, equidistant from the centre.

Taking torques around A we have two weights F_car F_W acting clockwise and F_B anticlockwise.

If we set F_B to its maximum value F_B = 160,000 N

160000 x 26 = (30000 x 9.8 x 13) + (1600 x 9.8)d

4.16 x 10⁶ = 3.822 x 10⁶ + 15680d

4.16 x 10⁶ - 3.822 x 10⁶ = 15680d

d = 21.556 = 22 m

2 sig fig

Correct distance :

A correct torque :

A

M

Question 3 c) & d) on the next slides ……

Question 3 d) solution on the next slide ……

The bridge has an earthquake-protection system made up of springs. Before being put in place on the bridge, the springs are tested by being loaded with a mass m. When loaded with a mass m the springs compress by a distance x .

c) Explain, in depth, how the size of the mass on the springs

needs to change in order to compress the springs a distance

2x from the original length

The force of gravity on mass m is F = mg.

This compresses the spring by x.

For a spring we have F = kx

where k is the spring constant.

So to double x , F and m must also double.

Double m fully justified :

Double m :

A

M

d)

Jo and Alex wonder whether a compressed spring from the bridge could accelerate their car once the spring is

released, as in the diagram below. They decide to determine the effect of the spring on the car’s motion. They

estimate that for this spring, a force of 50 000 N would compress the spring length from 6.0 m to 4.2 m. The total

mass of the car and occupants is 1600 kg

(i)

Calculate the maximum speed to which this spring could accelerate the car and its occupants if it was compressed to 4.2 m.

You should start your answer by first determining the spring constant, k

(ii)

What assumption(s) have you made in this calculation ?

We can find the maximum speed a number of ways.

First we are told to find k

F = kx

50000 = k(6.0 – 4.2)

k = 27,777.8 = 28 kNm^-1

If the potential energy stored in the spring becomes kinetic energy of the car :

We can find the speed by looking at energy :

Another method looks at force and acceleration:

If the spring is linear the average force is half the maximum:

We know the car starts from rest so :

We assume the spring is linear (elastic)

All the E_P becomes E_K of the car none is lost

2 sig fig

Correct answer with assumption :

E

v found

OR Energy found and assumption stated :

M

k found OR

“Energy is conserved” :

A

Question 3 evidence statement on the next slide ……

Evidence Statement …..

The marks from each question are then added to give an overall score for the paper. The cut scores for the total gave the final grade :

The examiners’ comments in the assessment report follow …….

Cut Scores …..

General Remarks:

• Candidates who achieved higher grades used correct physics terminology.
• All calculated answers should be given with an appropriate SI unit.
• Candidates should ensure they completely answer the question. Many candidates after completing a calculation of force failed to give the direction of the force.

2020 Level 2 Report for 91171 Mechanics :

More comments follow ……..

Candidates who were awarded Achievement commonly:

Candidates who were assessed as Not Achieved commonly:

• knew the appropriate formulae to apply in different contexts
• performed single-step calculations accurately
• drew free-body force diagrams
• understood the concept of centripetal force
• stated the necessary conditions for equilibrium
• applied Hooke’s law.

• were unable to attempt to answer many questions
• solved very simple numerical problems
• drew diagrams inaccurately
• used physics terminology very imprecisely
• confused physics concepts, particularly energy with momentum, and force with momentum.

More comments follow ……..

2020 Level 2 Report for 91171

Candidates who were awarded Achievement with Merit commonly: 

• read questions sufficiently carefully to understand what was required in response
• drew vector diagrams
• completed multi-step calculations correctly
• explained phenomena using correct physics terminology
• showed thoughtful consideration of more than one physics concept in an answer.

Candidates who were awarded Achievement with Excellence commonly:

• read questions very carefully so that their response addressed exactly what was being asked.

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• drew vector diagrams carefully and accurately.

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• completed multi-step solutions of numerical problems based on different topics in a clear, elegant and economical manner.

Compiled from the NZQA resources by Jonathan Jaffrey April 2021.

For educational use only, not for commercial use

Good Luck with your revision!