Pertanyaan

EXERCISE 4.11 Suppose in the same Atwood setup another string is attached to the bottom of m_(1) and a constant force / is applied, retarding the upward motion of m_(1) If m_(1)=5.00kg and m_(1)=10.00kg. what value of fwill reduce the accelera tion of the system by 50% __

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To solve this problem, we need to consider the forces acting on the system and how they affect the acceleration. Let's break down the steps:Step 1: Identify the forces in the systemWithout the retarding force, the only forces acting on the system are the gravitational forces on and , and the tension in the string. The net force causing the acceleration of the system is the difference in the gravitational forces on and , which is .Step 2: Calculate the initial acceleration of the systemUsing Newton's second law, , where is the net force, is the total mass of the system, and is the acceleration. The total mass of the system is . The initial acceleration is given by: Step 3: Introduce the retarding force is applied to retard the upward motion of . This force will act in the opposite direction to the acceleration, thus reducing the net force and the acceleration. The new net force is , and the new acceleration is: Step 4: Determine the retarding force needed to reduce acceleration by 50%We want the new acceleration to be half of the initial acceleration : Substitute the expression for into the equation for and solve for : Step 5: Solve for Multiply both sides by \(2(m_{1} + m_{2})\) to clear the fraction: Distribute the 2 on the right side: Combine like terms: Divide by -1 to get: Subtract from both sides: Factor out : Finally, divide by 2 to solve for : Step 6: Plug in the values for and Given that and , we can plug these values into the equation: **【Answer】: The value of that will reduce the acceleration of the system by 50% is 24.50 N.**