A mass M = 5.6 kg on a horizontal table is pulled by a horizontal string that passes over a frictionless pulley to a free-hanging mass m = 3.4 kg.The coefficient of friction between M and the table is 0.28.The acceleration of M is A)3.7 m/s² B)2.0 m/s² C)2.2 m/s² D)0.20 m/s² E)0.49 m/s²

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Quizplus · Accepted Answer

To find the acceleration, we first calculate the net force acting on the system. The force due to gravity on the hanging mass (m) is $F_g = m \cdot g = 3.4 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 33.32 \, \text{N}$. The frictional force opposing the motion on mass M is $F_{\text{friction}} = \mu \cdot N = \mu \cdot M \cdot g = 0.28 \cdot 5.6 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 15.3472 \, \text{N}$. The net force is then $F_{\text{net}} = F_g - F_{\text{friction}} = 33.32 \, \text{N} - 15.3472 \, \text{N} = 17.9728 \, \text{N}$. The total mass of the system is $M + m = 5.6 \, \text{kg} + 3.4 \, \text{kg} = 9 \, \text{kg}$. The acceleration is $a = \frac{F_{\text{net}}}{M + m} = \frac{17.9728 \, \text{N}}{9 \, \text{kg}} = 1.997 \, \text{m/s}^2$, which rounds to $2.0 \, \text{m/s}^2$.

A Mass M = 5