A block of mass m_b rests on a horizontal surface and is accelerated by means of a horizontal cord that passes over a frictionless peg to a hanging weight of mass m_w. The coefficient of kinetic friction between the block and the horizontal surface is µ and the tension in the cord is T. The acceleration of the block is given by A) T - m_wg)/m_w + m_b). B) T/µm_bg + m_b). C) T - µm_b)/m_b_. D) m_wg - T)/m_w. E) T/m_b - µm_bg.

Question

Quizplus · Accepted Answer

The block and the hanging weight experience opposite forces due to the tension in the cord. The net force on the block due to the tension is T - frictional force, where frictional force = µ*N = µ*m_b*g. The normal force N is equal and opposite to the weight of the block, which is m_b*g. Therefore, the net force on the block is T - µ*m_b*g. By Newton's second law, this force is equal to the mass of the block times its acceleration, so: T - µ*m_b*g = m_b*a Rearranging gives: a = (T - µ*m_b*g)/m_b However, we know that the hanging weight is pulling the block with a force of m_w*g, so: m_b*a = T - µ*m_b*g - m_w*g Solving for a gives: a = (m_w*g - T)/(m_w + m_b)

A Block of Mass Mb Rests on a Horizontal Surface

A Block of Mass M_b Rests on a Horizontal Surface