(i) Newton’s Second Law for \( m_1 \) in terms of weights of the blocks, \( m_1 g \) and \( m_2 g \), or their components in terms of the ramp angle \( \theta \), the tension in the string \( T \), and the normal reaction \( N_1 \) of the table on \( m_1 \), can be written as (use the coordinate axes for signs of different forces):\[\sum F_{x} = \,\,\square\,\, = m_{1}a_{1,x}\]\[\sum F_{y} = \,\,\square\,\, = m_{1}a_{1,y} = 0\](ii) Newton’s Second Law for \( m_2 \) in terms of weights of the blocks, \( m_1 g \) and \( m_2 g \), or their components in terms of the ramp angle \( \theta \) the tension in the string \( T \) and the normal reaction \( N_1 \) of the table on \( m_1 \), can be written as:*Note: The motion of \( m_2 \) is along the y-direction only.*\[\sum F_{y} = \,\,\square\,\, = m_{2}a_{2,y}\](iii) How are the magnitudes of \( a_1 \) and \( a_2 \) related? What are the directions of \( a_1 \) and \( a_2 \)?*Magnitude:*A. \( |a_1| \) is greater than \( |a_2| \) B. \( |a_1| \) is less than \( |a_2| \) C. \( |a_1| \) is equal to \( |a_2| \)*Direction:*A. \( \vec{a_1} \) is in the positive x direction, and \( \vec{a_2} \) is in the positive y-direction. B. \( \vec{a_1} \) is in the positive x direction, and \( \vec{a_2} \) is in the negative y-direction. C. \( \vec{a_1} \) is in the negative x direction, and \( \vec{ **Problem Statement:**1. A block of mass \( m_1 \) and a block of mass \( m_2 \) are connected by a light string as shown; the inclination of the ramp is \( \theta \). Friction is negligible. Assume that \( m_2 > m_1 \).**Diagram Description:** The image depicts two blocks connected by a string over a pulley. Block \( m_1 \) is on an inclined plane with angle \( \theta \), and block \( m_2 \) hangs vertically off the side of the plane. The string runs over a pulley at the top of the incline. Block \( m_1 \) is labeled "1" and is placed on the ramp, while block \( m_2 \) is labeled "2" and hangs freely. The angle \( \theta \) is marked at the base of the incline.**Subpart 1: Draw FBDs (Free Body Diagrams)**In your notebook, draw free body diagrams of \( m_1 \) and \( m_2 \) using the template as shown below. The forces acting on the system are weights of the blocks, \( m_1g \) and \( m_2g \), the tension in the string \( T \), and the normal reaction \( N_1 \) of the table on \( m_1 \). **Note:** The choice of the coordinate axes for the two blocks can be different as shown below:- For \( m_1 \): - Inclined x-y coordinate system with \( x \) parallel to the incline and \( y \) perpendicular.- For \( m_2 \): - Standard x-y coordinate system with \( x \) horizontal and \( y \) vertical.These considerations emphasize analyzing physics problems using different orientations of coordinate axes to simplify calculations based on the system setup.

Name: (i) Newton’s Second Law for \( m_1 \) in terms of weights of the bloc
Uploaded: 2024-03-20T06:57:57.000Z
Channel: Bartleby
Description: (i) Newton’s Second Law for \( m_1 \) in terms of weights of the blocks, \( m_1 g \) and \( m_2 g \), or their components in terms of the ramp angle \( \theta \), the tension in the string \( T \), and the normal reaction \( N_1 \) of the table on \