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Newton's Laws of Motion and Free Body Diagram Objective: Study Newton's laws of motion and free body diagram Procedure: (Keep three (3) significant figures for your calculations and check for proper units) Part 1: Theoretical equation for acceleration As shown in right figure, block of mass $m_1$ and block of mass $m_2$ are moving together with an acceleration $a$. Case i: If the friction between $m_1$ and surface is ignored, the acceleration $a$ is given by equation (1) $a = frac{m_2g}{m_1 + m_2}$ (1) Case ii: If the friction force is considered and the coefficient of kinetic friction is $mu_k$, the acceleration $a$ is given by equation (2) $a = frac{m_2g - mu_k m_1 g}{m_1 + m_2}$ (2) Use Newton's Laws of motion to show how to get equation (1) and (2). (Note: Show your detailed work. Draw free body diagram and write down equations for the net forces on each block in x direction, $sum F_x$, and in y direction, $sum F_y$, respectively.) Case i: Without friction Object $m_1$ free body diagram Net force in x: $sum F_x$ Net force in y: $sum F_y$ Object $m_2$ free body diagram Net force in x: $sum F_x$ Net force in y: $sum F_y$ Work to get equation (1)

          Newton's Laws of Motion and Free Body Diagram
Objective: Study Newton's laws of motion and free body diagram
Procedure: (Keep three (3) significant figures for your calculations and check for proper units)
Part 1: Theoretical equation for acceleration
As shown in right figure, block of mass $m_1$ and block of mass $m_2$ are moving
together with an acceleration $a$.
Case i: If the friction between $m_1$ and surface is ignored, the acceleration $a$
is given by equation (1)
$a = frac{m_2g}{m_1 + m_2}$ (1)
Case ii: If the friction force is considered and the coefficient of kinetic friction is $mu_k$, the
acceleration $a$ is given by equation (2)
$a = frac{m_2g - mu_k m_1 g}{m_1 + m_2}$ (2)
Use Newton's Laws of motion to show how to get equation (1) and (2).
(Note: Show your detailed work. Draw free body diagram and write down equations for the net
forces on each block in x direction, $sum F_x$, and in y direction, $sum F_y$, respectively.)
Case i: Without friction
Object $m_1$ free body diagram
Net force in x: $sum F_x$
Net force in y: $sum F_y$
Object $m_2$ free body diagram
Net force in x: $sum F_x$
Net force in y: $sum F_y$
Work to get equation (1)

$Newton's Laws of Motion and Free Body Diagram Objective: Study Newton's laws of motion and free body diagram Procedure: (Keep three (3) significant figures for your calculations and check for proper units) Part 1: Theoretical equation for acceleration As shown in right figure, block of mass m1 and block of mass m2 are moving together with an acceleration a. Case i: If the friction between m1 and surface is ignored, the acceleration a is given by equation (1) a = fracm2gm1 + m2 (1) Case ii: If the friction force is considered and the coefficient of kinetic friction is muk, the acceleration a is given by equation (2) a = fracm2g - muk m1 gm1 + m2 (2) Use Newton's Laws of motion to show how to get equation (1) and (2). (Note: Show your detailed work. Draw free body diagram and write down equations for the net forces on each block in x direction, sum Fx, and in y direction, sum Fy, respectively.) Case i: Without friction Object m1 free body diagram Net force in x: sum Fx Net force in y: sum Fy Object m2 free body diagram Net force in x: sum Fx Net force in y: sum Fy Work to get equation (1)$

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