Answer:
(a) 4.4 m/s²
(b) 27 N
Explanation:
Draw a free body diagram for each block. There are four forces on the sliding block:
Tension force T pulling to the right,
Weight force mg pulling down,
Normal force N pushing up,
and friction force Nμ pulling left.
There are two forces on the hanging block:
Tension force T pulling up,
and weight force mg pulling down.
Sum of forces on the sliding block in the +y direction:
∑F = ma
N − mg = 0
N = mg
Sum of forces on the sliding block in the +x direction:
∑F = ma
T − Nμ = ma
T − mgμ = ma
Sum of forces on the hanging block in the -y direction:
∑F = ma
mg − T = ma
T = mg − ma
(a) Substitute:
mg − ma − mgμ = ma
g − a − gμ = a
g (1 − μ) = 2a
a = g (1 − μ) / 2
Plug in values:
a = (9.8 m/s²) (1 − 0.11) / 2
a = 4.4 m/s²
(b) Substitute:
T − mgμ = mg − T
2T = mg (1 + μ)
T = mg (1 + μ) / 2
Plug in values:
T = (5.0 kg) (9.8 m/s²) (1 + 0.11) / 2
T = 27 N
