ECollogriboard

AP PHYSICS $1$

Test Booklet

Unit $4$ Progress Check: FRQ $4$

Show all your work for each part of the question. The parts within the question may not have equal weight.

Note: Figure not uravil tw aven.

Two blocks are on a horizontal tabletop, as shown in the figure. Block A of mass $m_A$ is initially moving with speed $v_0$ to the right toward Block $B$ of mass $m_B,$ which is initially at rest. The blocks can slide with negligible friction on the tabletop, which is a height $h$ above the floor. The blocks collide and stick together, moving to the right and beyond the edge of the table. The blocks remain together as they fall to the floor, landing with their center of mass a horizontal distance $x_{AB}$ from the table's edge.

Block B is then returned to its initial position, and Block A is replaced with Block C $.$ Block C has mass $2m_A$ and is given an initial speed $\frac{v_0}{2}$ to the right. As before, the blocks collide, stick together, and remain together as they fall to the floor. Blocks $B$ and $C$ land with their center of mass a horizontal distance $x_{BC}$ from the table's edge.

$($a$)$ Indicate the correct relation between $x_{AB}$ and $x_{BC}.$

$(a)$ Indicate the correct relation between

$q,x_{AB}>x_{BC}$

$x_{BC}>x_{AB},x_{AB}=x_{BC}$

Justify your selection.

$1.{}_1=P_f$

${}_A=P_A+p_f$:$m_A$:$(m_A+m_B)V_f$

conservation $of$ momentum, derive $an$ expression for $x_{AB}in$ terms $of{m}_A,m_B,v_0,h,$ and

$($b$)$ Starting with the conservation of momentum, derive an exps which the blocks are only partially beyond the physical constants, as appropriate. Assume that is negligible. table's edge and still partially on table is ngigite.

$($c$)$ Indicate whether the expression you derived in part $($b$)$ is consistent with the relation you selected in part $($a$).$ Justify your answer.