Question
A block of mass 10 kg is on a horizontal table with
friction coefficient μ = 0.2. A mass of 4 kg is suspended from a frictionless pulley attached to this block. Find the acceleration of the system. (g = 10 m/s²)Solution
- Mass of block on table: M = 10 kg
- Coefficient of friction: μ = 0.2
- Suspended mass: m = 4 kg
- Gravitational acceleration: g = 10 m/s²
- Pulley is frictionless, and the string is light and inextensible
- The 10 kg block is on the table and connected to the 4 kg hanging mass via a pulley.
- Let the entire system move with acceleration a.
- Let the tension in the string be T.
- Downward force: m·g = 4 × 10 = 40 N
- Upward tension: T
- Equation of motion:
m·g – T = m·a
⇒ 40 – T = 4a → (1)
- Horizontal tension pulling right: T
- Friction opposes motion: f = μ·M·g = 0.2 × 10 × 10 = 20 N
- Net force: T – f = M·a
⇒ T – 20 = 10a → (2)
T = 40 – 4a Substitute into (2): (40 – 4a) – 20 = 10a
⇒ 20 – 4a = 10a
⇒ 20 = 14a
⇒ a = 20 / 14 = 10 / 7 ≈ 1.43 m/s² Therefore, the correct answer is option (a).
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