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Edexcel GCE
Core Mathematics M1

Dynamics (F=ma)
Materials required for examination
Mathematical Formulae (Green)

Items included with question papers
Nil

Advice to Candidates
You must ensure that your answers to parts of questions are clearly labelled
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Answers
without working may gain no credit
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Figure 4

Two particles P and Q have mass 0
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5
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Initially P is
3
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The particles are released from rest with the string taut and the
hanging parts of the string vertical, as shown in Figure 4
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5 s, it
strikes the ground
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(a) Show that the acceleration of P as it descends is 2
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(3)
(b) Find the tension in the string as P descends
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(4)
(d) State how you have used the information that the string is inextensible
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Particle Q then
moves freely under gravity, without reaching the pulley, until the string becomes taut again
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(6)

2

2
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The particle A lies on a rough horizontal table
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The particle B hangs freely below the pulley, as
shown in Figure 3
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The particles are
released from rest with the string taut
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By writing down separate equations of motion for A and B,

(a) find the tension in the string immediately after the particles begin to move,
(3)
2

(b) show that µ = 3
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Particle A is then a
distance 1 h from P
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(6)
(d) State how you have used the information that the string is light
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A car is towing a trailer along a straight horizontal road by means of a horizontal tow-rope
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The mass of the trailer is 700 kg
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The resistances to motion of the car
and the trailer are assumed to be constant and of magnitude 630 N and 280 N respectively
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Find
(a) the acceleration of the car,
(3)
(b) the tension in the tow-rope
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Assuming that the driving
force on the car and the resistances to motion are unchanged,
(c) find the distance moved by the car in the first 4 s after the tow-rope breaks
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(1)

4

4
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The rope makes an angle of 20° with the ground, as shown in Figure 3
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4
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The tension in the rope is P newtons
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(8)
The tension in the rope is now increased to 150 N
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(6)

5

5
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The horizontal resistances to motion of the car and the trailer
have magnitudes 400 N and 200 N respectively
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Find
(a) the acceleration of the car and trailer,
(3)
(b) the magnitude of the tension in the towbar
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He reduces the force
produced by the engine to zero and applies the brakes
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Given that the resistances to motion are
unchanged and the magnitude of the thrust in the towbar is 100 N,
(c) find the value of F
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Figure 4
Two particles P and Q, of mass 2 kg and 3 kg respectively, are joined by a light inextensible
string
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A constant
force F of magnitude 30 N is applied to Q in the direction PQ, as shown in Figure 4
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The coefficient of friction
between each particle and the plane is µ
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(4)
(d) State how in your calculation you have used the information that the string is inextensible
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(e) Find the time between the instant that the force is removed and the instant that Q comes to
rest

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