Answer:
4.0 m/s²
Explanation:
Draw two free body diagrams, one for the cart and one for the hanging mass.
The cart has one force acting on it in the x direction: tension to the right.
The hanging mass has two forces acting on it in the y direction: tension up and weight down.
The hanging mass accelerates downward, so if we take up to be positive, then the acceleration is negative.
Apply Newton's second law to the hanging mass:
∑F = ma
T − m₂g = m₂(-a)
T − m₂g = -m₂a
Apply Newton's second law to the cart:
∑F = ma
T = m₁a
Substitute and solve for a:
m₁a − m₂g = -m₂a
m₁a + m₂a = m₂g
(m₁ + m₂) a = m₂g
a = m₂g / (m₁ + m₂)
Given m₁ = 2.3 kg and m₂ = 1.6 kg:
a = (1.6 kg × 9.8 m/s²) / (2.3 kg + 1.6 kg)
a = 4.0 m/s²
