UniGeniusA-level Maths · Edexcel 9MA0

L20 · M6.1

Mechanics units and signed quantities

The lessonTwo exam questions, then a review

4 marksCore techniqueM6.1, M8.3

A cyclist of mass 65 kg rides at 90 km h−1^{-1} down a hill.
(a)
Write the cyclist's speed in m s−1^{-1}.
(1 mark)

Use ^ for powers and sqrt( ) for roots.

(b)
Find the weight of the cyclist.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(c)
State the SI unit of acceleration.
(1 mark)

Use ^ for powers and sqrt( ) for roots.

4 marksCore techniqueM6.1, M8.3

In this question take g=10g = 10 m s−2^{-2} on Earth. A rock sample has mass 3.2 kg.
(a)
Find the weight of the rock on Earth.
(1 mark)

Use ^ for powers and sqrt( ) for roots.

(b)
On the Moon the acceleration due to gravity is 1.6 m s−2^{-2}. Find the weight of the rock on the Moon.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(c)
Explain why the mass of the rock on the Moon is still 3.2 kg.
(1 mark)

Use ^ for powers and sqrt( ) for roots.

5 marksUnfamiliar problemM6.1

The air resistance on a car is modelled as F=cv2F = c v^2, where FF is in newtons and vv is the speed in m s−1^{-1}.
(a)
Find the SI units of cc, in terms of kg, m and s.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
With c=0.4c = 0.4 in these units, find the air resistance at 25 m s−1^{-1}.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(c)
A student uses v=90v = 90 in the formula for a speed of 90 km h−1^{-1}. Explain the effect of this mistake.
(1 mark)

Use ^ for powers and sqrt( ) for roots.

3 marksUnfamiliar problemM6.1, M9.1

A spanner is 25 cm long. A student pushes at the end of the spanner, perpendicular to it, with a force of 40 N, and writes: 'moment =40×25=1000= 40 \times 25 = 1000'.
(a)
Find the moment of the force about the bolt, with its SI unit.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
Explain what is wrong with the student's answer.
(1 mark)

Use ^ for powers and sqrt( ) for roots.

4 marksUnfamiliar problemM6.1

A 600 kg van slows uniformly from 108 km/h to rest in 5 s. Take its initial direction of motion as positive.
(a)
Find the acceleration in SI units.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
Find the magnitude of the resultant braking force.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

4 marksUnfamiliar problemM6.1

A 800 kg van slows uniformly from 144 km/h to rest in 5 s. Take its initial direction of motion as positive.
(a)
Find the acceleration in SI units.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
Find the magnitude of the resultant braking force.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

4 marksUnfamiliar problemM6.1

A force of 3 kN acts perpendicular to a lever at distance 40 cm from its pivot.
(a)
Find its moment in N m.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
Find the perpendicular force in newtons giving the same moment at 0.8 m.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

4 marksUnfamiliar problemM6.1

A force of 4 kN acts perpendicular to a lever at distance 40 cm from its pivot.
(a)
Find its moment in N m.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
Find the perpendicular force in newtons giving the same moment at 0.8 m.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

4 marksUnfamiliar problemM6.1

A runner moves east at 3 m/s for 40 s, then west at 2 m/s for 20 s. Take east as positive.
(a)
Find displacement and total distance.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
Find the average speed for the whole trip. Give exact answers.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

4 marksUnfamiliar problemM6.1

A runner moves east at 4 m/s for 40 s, then west at 2 m/s for 20 s. Take east as positive.
(a)
Find displacement and total distance.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

(b)
Find the average speed for the whole trip. Give exact answers.
(2 marks)

Use ^ for powers and sqrt( ) for roots.

Independent practice for Pearson Edexcel A-level Mathematics (9MA0), not endorsed by Pearson.

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