Newtons Laws EX 14

Helena Dedic

For a real rope with mass, tension is not constant throughout the rope.

To find the tension at the midpoint of the rope, we isolate the system of the object and the bottom half of the rope.

$T_{mid}-W=ma$

$T_{mid}-2.1N=0.215kg(4m/s^{2})$

$T_{mid}=2.1N+0.86N=2.96N$

To find the tension at the top of the rope, we would isolate the system of the object alone.

$T_{bottom}-W=ma$

$T_{bottom}-0.2kgx9.8N/kg=0.2kg(4m/s^{2})$

$T_{bottom}=1.96N+0.8N=2.76N$

To find the tension at the bottom of the rope, we would look at the system of the object and the whole rope.

$T_{top}-W=ma$

$T_{top}-0.23kgx9.8N/kg=0.23kg(4m/s^{2})$

$T_{top}=2.25N+0.92N=3.17N$

You can see that the tension in the rope increases from the bottom to the top.