Two particles P and Q have mass 0.5 kg and m kg respectively, where m < 0.5 - Edexcel - A-Level Maths Mechanics - Question 6 - 2007 - Paper 1

Applying Newton's second law for particle P:

$0.5g - T = 0.5a$

Where:

• $g$ = 9.8 m/s²
• $a$ = 2.8 m/s²

Substituting known values:

$0.5 \times 9.8 - T = 0.5 \times 2.8$

This leads us to:

$T = 4.9 - 1.4 = 3.5 \text{ N}$

Using Newton's second law for particle Q:

$T - mg = -m a$

Substituting in our earlier findings:

$3.5 - mg = -m \times 2.8$

Now, rearranging gives us:

$mg = 3.5 + 2.8m$

We can substitute (m = \frac{5}{18}) and solve for mass to confirm that the equality holds.

Since the string is inextensible, both particles must have the same magnitude of acceleration during their motion. Therefore, the acceleration of particle P is equal to that of particle Q.

When P strikes the ground, it stops instantly, and Q continues moving under gravity:

Using:

$v^2 = u^2 + 2as$

Letting $u = 0$, and s = 3.15 m for Q:

$v^2 = 0 + 2 \times 9.8 \times 3.15$

Thus, calculating:

$v^2 = 61.74 \Rightarrow v = \sqrt{61.74} \approx 7.85 \text{ m/s}$

We can then find the time $t$ to reach this speed:

$t = \frac{v}{g} = \frac{7.85}{9.8} \approx 0.8 \text{ s}$