FIGURE 6-12
-Two masses are connected by a string which goes over an ideal pulley as shown in Figure 6-12. Block A has a mass of 3.00 kg and can slide along a smooth plane inclined 30.0° to the horizontal. Block B has a mass of 2.00 kg. What is the acceleration of mass B?

Question

FIGURE 6-12

-Two masses are connected by a string which goes over an ideal pulley as shown in Figure 6-12. Block A has a mass of 3.00 kg and can slide along a smooth plane inclined 30.0° to the horizontal. Block B has a mass of 2.00 kg. What is the acceleration of mass B?

Quizplus · Accepted Answer

Since the inclined plane is smooth, there is no friction. Therefore, both masses experience the same acceleration in opposite directions. Using Newton's Second Law, we have:
m_B*g - T = m_B*a
T - m_A*g*sin(30) = m_A*a
where T is the tension in the string, g is the acceleration due to gravity, and a is the common acceleration of the two masses. Solving for a, we get:
a = (m_B*g - m_A*g*sin(30))/(m_A + m_B)
Substituting the given values, we get:
a = (2*9.81 - 3*9.81*sin(30))/(2 + 3) = 0.981 m/s^2
Therefore, the correct choice is A.

FIGURE 6-12 -Two Masses Are Connected by a String Which Goes Over