3. In this question you will do some algebra to determine two relations that you will need for Part 2 of this lab. Write down Eq. 11 twice. In the first statement, set the rotational kinetic energy term equal to zero (i.e. 1w² = 0) - call this your "No Krot model". Leave the second as it is written in Eq. 11- call this your "Krot model". For both models, solve for v in terms of g, h, and a. In the Krot model, you will need to use I = kMR² (Eq. 3) and w = : "/r. The solution for the Krot model will have a k term as well. Once you have solved for v, use the kinematic relation, v = at, and the trigonometric relationship, h = L sin 0, solve for t for both models separately. NOTE: L is the length of the incline plane. NOTE: a is different for the two models (refer to the "Rotational Mechanics" discussion in the introduction): In the "No Krot model", a = g sin 0 (remember the Newton's 2nd Law lab) In the "Krot model", a is given by equation 8 These two solutions represent the predicted time it will take an object to descend a height, h, down an inclined plane when you assume all kinetic energy in the system is translational (No Krot model) and when you assume the kinetic energy is distributed between translational and rotational motion (Krot model).
3. In this question you will do some algebra to determine two relations that you will need for Part 2 of this lab. Write down Eq. 11 twice. In the first statement, set the rotational kinetic energy term equal to zero (i.e. 1w² = 0) - call this your "No Krot model". Leave the second as it is written in Eq. 11- call this your "Krot model". For both models, solve for v in terms of g, h, and a. In the Krot model, you will need to use I = kMR² (Eq. 3) and w = : "/r. The solution for the Krot model will have a k term as well. Once you have solved for v, use the kinematic relation, v = at, and the trigonometric relationship, h = L sin 0, solve for t for both models separately. NOTE: L is the length of the incline plane. NOTE: a is different for the two models (refer to the "Rotational Mechanics" discussion in the introduction): In the "No Krot model", a = g sin 0 (remember the Newton's 2nd Law lab) In the "Krot model", a is given by equation 8 These two solutions represent the predicted time it will take an object to descend a height, h, down an inclined plane when you assume all kinetic energy in the system is translational (No Krot model) and when you assume the kinetic energy is distributed between translational and rotational motion (Krot model).
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
Question
Transcribed Image Text:3. In this question you will do some algebra to determine two relations that
you will need for Part 2 of this lab. Write down Eq. 11 twice. In the first
statement, set the rotational kinetic energy term equal to zero
(i.e. lw? = 0) –- call this your "No Krot model". Leave the second as it is
written in Eq. 11– call this your "Krot model". For both models, solve for v
in terms of g, h, and a. In the Krot model, you will need to use I
(Eq. 3) and w =
KMR2
/r. The solution for the Krot model will have a k term as
well.
Once you have solved for v, use the kinematic relation, v =
and the trigonometric relationship, h
both models separately.
at,
= L sin 0, solve for t for
NOTE: L is the length of the incline plane.
NOTE: a is different for the two models (refer to the
"Rotational Mechanics" discussion in the introduction):
In the "No Kpot model", a = g sin 0 (remember the Newton's 2nd Law
lab)
In the "Krot model", a is given by equation 8
These two solutions represent the predicted time it will take an object
to descend a height, h, down an inclined plane when you assume all
kinetic energy in the system is translational (No Krot model) and when
you assume the kinetic energy is distributed between translational and
rotational motion (Krot model).
Transcribed Image Text:We can also then write a statement of conservation of energy for the system
that you will investigate in this lab, where an object is released from rest at a
specific height, h, above its end point and we assume all the potential energy
initially in the system is translated into kinetic energy when it reaches its final
position.
1
1
mv² +=Iw²
2
Uinitial = Kfinal
Eq. 11
- or -
Using kinematics and the relationship above, we can calculate the velocity
of an object rolling down an incline by:
|2Lg sin 0
(1+ k)
2Lg sin e
Vt =
V2al
Eq.8
+
MR2
where L is the length of the incline.
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