HY $203$ Homework #$12$

NAME:

$2.$ Six forces act on a block of mass $M=8kg$ which is initially at rest at the origin on a frictionless horizontal xy$-$plane. Of these six, the weight force is $(0,0,-Mg),$ the normal force is $(0,0,N),$ and the other four are:

vec$(F_1)=(4,-4,0),$vec$(F_2)=(5,13,0),$vec$(F_3)=(-3,-10,0),$vec$(F_4)=(-1,2,0),$

all in N$.$ Later, the block is observed to have displaced in a straight line to $(10,0,0)m.$

a$)$ Determine the work done by each of the six forces through the displacement.

$W_{Mg}=$

$W_N=$

$W_{F_1}=$

$W_{F_2}=$

$W_{F_3}=$

$W_{F_4}=$

b$)$ Add your answers from part a to find the total work done.

c$)$ Add the forces to get the total net force acting on the block $($in component form$).$

d$)$ Determine the total work done using the displacement and your answer from part c$.$

e$)$ Determine the speed of the block when it reached $(10,0,0)m.$