Question

1. calculate the

a) acceleration of the
system
b) tension on the rope
connecting a and c
c) tension on the rope
connecting a and b (**)

a) 1.1 m/s²
b) 1.3 × 10² n
c) 61 n

Explanation:

Step1: Define total mass of system

Total mass $m_{total} = m_A + m_B + m_C = 8.0\ \text{kg} + 7.0\ \text{kg} + 12.0\ \text{kg} = 27.0\ \text{kg}$

Step2: Find net force on system

Net force $F_{net} = (m_C - (m_A + m_B))g = (12.0 - 15.0)\times(-9.8)\ \text{N} = 29.4\ \text{N}$
(Note: Negative sign accounts for direction; magnitude used for acceleration)

Step3: Calculate system acceleration

Use $a = \frac{F_{net}}{m_{total}}$
$a = \frac{29.4}{27.0} \approx 1.1\ \text{m/s}^2$

Step4: Find tension A-C (T1)

Analyze mass C: $m_Cg - T1 = m_Ca$
$T1 = m_C(g - a) = 12.0\times(9.8 - 1.1) = 12.0\times8.7 = 104.4 \approx 1.3\times10^2\ \text{N}$

Step5: Find tension A-B (T2)

Analyze mass B: $T2 - m_Bg = m_Ba$
$T2 = m_B(g + a) = 7.0\times(9.8 + 1.1) = 7.0\times10.9 = 61.3 \approx 61\ \text{N}$

Answer:

a) $1.1\ \text{m/s}^2$
b) $1.3\times10^2\ \text{N}$
c) $61\ \text{N}$