Answer:
5.6 m/s²
Explanation:
Draw a free body diagram for each mass. For the mass on the table, there are 3 forces:
Weight force mg pulling down,
Normal force N pushing up,
and tension force T pulling right.
For the hanging mass, there are 2 forces:
Weight force Mg pulling down,
and tension force T pulling up.
The hanging mass accelerates downward, so sum of forces in the -y direction:
∑F = ma
Mg − T = Ma
The mass on the table accelerates to the right, so sum of forces in the +x direction:
∑F = ma
T = ma
Substitute and solve:
Mg − ma = Ma
Mg = (m + M) a
a = Mg / (m + M)
Plug in values:
a = (40 kg) (9.8 m/s²) / (30 kg + 40 kg)
a = 5.6 m/s²
