Two masses are connected by a cord that passes over a pulley as shown in the figure.The pulley and cord have negligible mass and m₁ (2.0 kg)moves on a horizontal surface without friction,m₂ (2.0 kg)is suspended vertically.What is the acceleration of m₁? A) 3.9 m/s² B) 12 m/s² C) 6.0 m/s² D) 4.9 m/s²

Question

Quizplus · Accepted Answer

Using Newton's second law, we can write down equations for the two masses:
m1 * a = m1 * g - T  (1)
m2 * a = T - m2 * g  (2)

where a is the acceleration of the system, T is the tension in the string, and g is the acceleration due to gravity.

We can solve these equations for the tension and the acceleration:
T = (m1 - m2) * g /(m1 + m2)
a = (m1 - m2) * g /(m1 + m2)

Substituting the given values, we get:
T = (2 - 2) * 9.8 / (2 + 2) = 0
a = (2 - 2) * 9.8 / (2 + 2) = 0

Therefore, the acceleration of m1 is 0, and the answer is D, 4.9 m/s^2.

Two Masses Are Connected by a Cord That Passes Over