a.Write the general formulas for the translational KE, rotational KE, gravitational PE, spring PE. Translational KE Rotational KE Gravitational PE Spring PE b..Using any or all of those energies from Part a. that apply to this question and identifying the ground as the point of “zero height”, what is the total energy of the system initially (in terms of H, R, mp, m1, m2, and g… any or all of these may be used)? Using any of those energies from Part a. that apply to this question and identifying the ground as the point of “zero height”, what is the total energy of the system just as block m2 is hitting the floor (in terms of H, R, mp, m1, m2, and g… any or all of these may be used)?
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).
- Blocks of mass m1 and m2 are connected by a massless string that pulls over the pulley in the figure. The table is frictionless. The pulley is a frictionless disk, but it does have mass Mp and radius R (Idisk=1/2MR2). Consider that m2 is initially hanging at rest H meters above the ground.
a.Write the general formulas for the translational KE, rotational KE, gravitational PE, spring PE.
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Translational KE
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Rotational KE |
Gravitational PE |
Spring PE |
b..Using any or all of those energies from Part a. that apply to this question and identifying the ground as the point of “zero height”, what is the total energy of the system initially (in terms of H, R, mp, m1, m2, and g… any or all of these may be used)?
Using any of those energies from Part a. that apply to this question and identifying the ground as the point of “zero height”, what is the total energy of the system just as block m2 is hitting the floor (in terms of H, R, mp, m1, m2, and g… any or all of these may be used)?
c.If H=50.0 cm, R=4.00 cm, Mp = 2.00 kg, m2 = 10.0 kg, and m1 = 4.00 kg, using Conservation of Energy (there is no work done by non-conservative forces in the system of the two blocks and the pulley), find the final speed of m2 just as it reaches the ground (in terms of H, R, mp, m1, m2, and g… any or all of these may be used).
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