Answer:
The acceleration of 2.0 kg block is 2.7 m/s²
Explanation:
Since, µ₁ < µ₂ acceleration of 2 kg block down the plane will be more than the acceleration of 4 kg block, if allowed to move separately. But, as the 2.0 kg block is behind the 4.0 kg block both of them will move with same acceleration say a. Taking both the blocks as a single system:
<u>Force down the plane on the system</u>
= (4 + 2) g sin30°
= (6)(10)(½)
= 30N
<u>Force up the plane on the system</u>
= µ₁ (2)(g)cos30° + µ₂ (4)(g)cos30°
= (2µ₁ + 4µ₂) g cos30°
= (2 × 0.2 + 4 × 0.3)(10)(√3/2)
≈ 13.76 N
∴ Net force down the plane is F
F = 30 - 13.76
F = 16.24 N
∴Acceleration of both the blocks down the
plane will b a
a = F ÷ (4 + 2)
a = 16.24 ÷ 6
a = 2.7 m/s²
Thus, The acceleration of 2.0 kg block is
2.7 m/s²
<u>-TheUnknownScientist</u>
