Consider the following discussion between three students. student 1: The entring
ID: 1443726 • Letter: C
Question
Consider the following discussion between three students. student 1: The entring exertr a force that tangent to the rim of spool A. This force has no component that points torward the center of the spool, so this force does noe, affect the acceleration of the center of mass." student 2: " i diagree. The acceleration of the center of mass of the spool is affected by the string. Any of the force not used up in rotational accelaration will be given to translational acceleration. This is why the acceleration of the center of mass of spool A is less than g. Student 3: The net force on spool A is the gravitional force minus the tension foce by newton's second law, the accelration of the center of mass is the net force divided by the mass. A force will have the same effect on the motion of the center of mass regardless of whether the force causes rotational motion or not. with which student(s), if any, do you agree? Explain your reasoning. if necessary revise your description in part A of how the net force is related to forces exceted at different points on an object Discuss your answers with a tutorial instructor before continuing. D. Write down newton's second law for each spool. Express your answer in terms of the mass of each spool (m), the acceleration of the center of mass of each spool (a_am) and the individual forces acting on each spool.Explanation / Answer
Student 3 have the right explanation.
From newton 2nd law,
Fnet = ma
so each force that acts on object, affects the acceleration of centre of mass.
there are two force act on spool.
1st: Weight force (mg ) passing through the centre of spool.
2nd: Tension force, tangential to spool.
So Fnet = mg - T
and mg - T = ma
a = (mg - T)/m Or g - (T/m)
and net torque = I x alpha
force that are responsible for torque are responsible for angular acceleration.
(rotational acceleration)
and torque = r x F (cross product)
mg passes through centre hence r = 0
so torque due to weighht force = 0
andT is at distance r from centre.
torque = r T
and torque = I x alpha
r T = I alpha
alpha = rT / I
where I is moment of inertia of spool and r is radius of spool.