Concepts Of Physics MCQ Edition [Volume 1]PhysicsFriction
Three blocks of masses 2 kg , 3 kg , and 7 kg are stacked one over the other from top to bottom on a horizontal surface. The coefficient of friction between the 2 kg and 3 kg blocks is 0.2 , between the 3 kg and 7 kg blocks is 0.3 , and between the 7 kg block and the horizontal surface is 0.0 . Determine the respective accelerations a₁ , a₂ , and a₃ of the 2 kg , 3 kg , and 7 kg blocks when a horizontal force of 10 N
Options
- Aa₁ = 3 m/s ^2 , a₂ = 0.4 m/s ^2 , a₃ = 0.4 m/s ^2
- Ba₁ = 0 m/s ^2 , a₂ = 10 3 m/s ^2 , a₃ = 0 m/s ^2
- Ca₁ = 5 6 m/s ^2 , a₂ = 5 6 m/s ^2 , a₃ = 5 6 m/s ^2
- Da₁ = 0.5 m/s ^2 , a₂ = 1.5 m/s ^2 , a₃ = 0.5 m/s ^2
Correct answer
C. a₁ = 5 6 m/s ^2 , a₂ = 5 6 m/s ^2 , a₃ = 5 6 m/s ^2
Step-by-step solution
Let the masses of the blocks be m₁ = 2 kg , m₂ = 3 kg , and m₃ = 7 kg . The maximum static friction force between the 2 kg and 3 kg blocks is: f_ 1, = ₁ m₁ g = 0.2 2 10 = 4 N The maximum static friction force between the 3 kg and 7 kg blocks is: f_ 2, = ₂ (m₁ + m₂) g = 0.3 (2 + 3) 10 = 15 N Assume all three blocks move together as a single system. The common acceleration a is given by the total applied force divided by the total mass: a = F m₁ + m₂ + m₃ = 10 2 + 3 + 7 = 10 12 = 5 6 m/s ^2 Now, check the required fr