Three objects are connected on the table as shown below. The coefficient of kinetic friction between the block of mass$$

m$2$

$$and the table is$0\mathrm{.}430.$ The objects have masses of$$

m$1=4\mathrm{.}50$kg$,$

$$

m$2=1\mathrm{.}50$kg$,$

$$and$$

m$3=2\mathrm{.}30$kg

$$as shown, and the pulleys are frictionless.

A side view of a block of mass$$m$2$positioned at the center of a table's horizontal surface. Two diagonal pulleys each extend outward from the left and right corners of the table. Two cords are attached to block$$m$2$such that one extends from its left side while the other extends from its right side. Each chord passes over the pulley on its respective side of the table. A block of mass$$m$1$is suspended vertically from the free end of the left cord and a block of mass$$m$3$is suspended vertically from the free end of the right cord.

$($a$)$

Draw a diagram of the forces on each object. $($Submit a file with a maximum size of$15$ MB$.)$

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$($b$)$

Determine the acceleration of each object $($in m$/$s$2),$ including its direction.

$($i$)$

acceleration of object$$m$1$

magnitude$$m$/$s$2$direction$---$Select$---$up$$down

$($ii$)$

acceleration of object$$m$2$

magnitude$$m$/$s$2$direction$---$Select$---$left$$right

$($iii$)$

acceleration of object$$m$3$

magnitude$$m$/$s$2$direction$---$Select$---$up$$down

$($c$)$

Determine the tensions in the two cords. $($Enter your answers in N$.)$

left cord$$Nright cord$$N

$($d$)$

If the tabletop were smooth, would the tensions increase, decrease, or remain the same?

The tension in the left cord will decrease while the tension in the right cord will increase.The tension in the left cord will increase while the tension in the right cord will decrease.$$The tensions in the both cords will remain the same.