AS-Level Maths| Connected Particles

a) $T = 33.6$ N

b) $a = 1.4$ ms⁻²

a) $T = \dfrac{12g}{7} = 16.8$ N

b) $m = 1.2$

a) Using $s = \frac{1}{2}at^2$: $2.5 = \frac{1}{2} \times a \times 1.25^2 \implies a = 3.2$ ms⁻²

b) $T = 39.0$ N

c) For $A$: $mg - T = ma \implies m(9.8-3.2) = 39 \implies m = \dfrac{65}{11}$

a) $T = 2mg$

b) For $P$: $T - kmg = km \cdot \dfrac{g}{3} \implies 2mg = \dfrac{4kmg}{3} \implies k = 1.5$

a) $a = 2.0$ ms⁻²

b) $T = 14.0$ N

a) Net force $= 1200 - 200 - 100 = 900$ N, total mass $= 1200$ kg, $a = \dfrac{900}{1200} = 0.75$ ms⁻²

b) $T = 325$ N

a) $a = 0.7$ ms⁻²

b) $T = 770$ N

a) i) $a \approx 2.84$ ms⁻²

a) ii) $T = 1.5g - 1.5a = 1.5(9.8) - 1.5(2.84) \approx 10.4$ N

a) iii) $k \approx 3.32$ N

a) $a = 3.2$ ms⁻²

b) $T = 5.28$ N

c) $F = 3.68$ N