Pearson Edexcel IAL Mathematics M1.3.1 Constant-acceleration motion in a straight line

Practise constant-acceleration motion with suvat formulae and motion graphs for cars, trains, projectiles and particles moving in a line.

[Maximum number: 5]

Figure 3

A particle A of mass 4 kg is held at rest on a rough horizontal table. Particle A is attached to one end of a string that passes over a pulley P. The pulley is fixed the the of the table. The other end of the string is attached to a particle B, of mass 3 kg, which hangs freely below P.

The part of the string from A to P is perpendicular to the edge of the table and A, P and B all lie in the same vertical plane.

The string is modelled as being light and inextensible and the pulley is modelled as being small, smooth and light.

The system is released from rest with the string taut. At the instant of release, A is 2 m from the edge of the table and B is 1.4 m above a horizontal floor, as shown in Figure 3.

After descending with constant acceleration for 2 seconds, B hits the floor and does not rebound.

Determine, by calculation, whether or $\operatorname{not} A$ reaches the pulley.

$v^2=2\times0.7\times1.4$ $-\mu\times4g=4a$ $0^2=1.4^2-2\times\frac{5g}{8}s$ $s=0.16\text{ or }0.159$ 0.16+1.4<2

Therefore A does not reach the pulley.

M1 M1 M1 A1 A1 cso

Alternative for the final 3 marks:
$v^2=1.4^2-2\times\frac{5g}{8}\times0.6$ $v^2=-5.39\text{ or }-5.4488$

Since $v^2\ge0$ , A does not reach the pulley.

Marking guidance for this part:
M1 for finding the speed or speed squared of either particle when B hits the floor.
M1 for an equation of motion for A, allowing without the negative sign.
M1 for a complete method to find the distance moved by A until it stops; condone sign error. This independent M mark is M0 if no new deceleration has been found.
A1 for the correct distance.
A1 cso for the correct conclusion, correctly reached, with <2 seen or 2 used in the working.
Alternative: M1 for a complete method to find $v^2$ for the speed with which it would hit the pulley; A1 for the correct value of $v^2$ ; A1 cso for the conclusion.

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M1.3.1 - Constant-acceleration motion in a straight line question 1