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Phys 1001 Exam 3 Comprehensive Review Problem (The exam problems won't be this long/complicated) In the contraption shown below, a cord unwinds from a cylinder, then passes over a non-ideal pulley, and then attaches to a hanging box. The cylinder can be considered a uniform solid disk with mass mc = 5.00 kg and radius rc = 40.0 cm. The pulley is also a uniform solid disk with mass mp = 2.00 kg and rp = 20.0 cm (the pulley is non-ideal because it will have rotational inertia). Both the cylinder and the pulley turn without friction, and there is no slipping between the cord and the pulley surface. The box has mass m = 3.00 kg. The box is released from rest and accelerates downward as the cord unwinds from the cylinder. a) Use conservation of mechanical energy to find the linear speed of the box when it has descended 2.50 m. Then find the angular speeds (ωc and ωp) of the cylinder and the pulley (they will be different from each other since they have different radii). b) Use a linear constant acceleration formula to find the linear acceleration of the box. Then find the angular accelerations (αc and αp) of the cylinder and the pulley. c) Use Newton's 2nd law equations (in linear or rotational form as appropriate) to find the tension in the horizontal portion of the cord (T) and the tension in the vertical portion of the cord (T) (the tension will not be the same on each side of the pulley since it's not an ideal pulley). Include free-body diagrams. Pulley Cylinder Box 

          Phys 1001 Exam 3 Comprehensive Review Problem (The exam problems won't be this long/complicated)

In the contraption shown below, a cord unwinds from a cylinder, then passes over a non-ideal pulley, and then attaches to a hanging box. The cylinder can be considered a uniform solid disk with mass mc = 5.00 kg and radius rc = 40.0 cm. The pulley is also a uniform solid disk with mass mp = 2.00 kg and rp = 20.0 cm (the pulley is non-ideal because it will have rotational inertia). Both the cylinder and the pulley turn without friction, and there is no slipping between the cord and the pulley surface. The box has mass m = 3.00 kg. The box is released from rest and accelerates downward as the cord unwinds from the cylinder.

a) Use conservation of mechanical energy to find the linear speed of the box when it has descended 2.50 m. Then find the angular speeds (ωc and ωp) of the cylinder and the pulley (they will be different from each other since they have different radii).

b) Use a linear constant acceleration formula to find the linear acceleration of the box. Then find the angular accelerations (αc and αp) of the cylinder and the pulley.

c) Use Newton's 2nd law equations (in linear or rotational form as appropriate) to find the tension in the horizontal portion of the cord (T) and the tension in the vertical portion of the cord (T) (the tension will not be the same on each side of the pulley since it's not an ideal pulley). Include free-body diagrams.

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phys 1001 exam 3 comprehensive review problem the exam problems wont be this longcomplicated in the contraption shown belowa cord unwinds from a cylinderthen passes over a non ideal pulleyan 30202

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University Physics with Modern Physics
Hugh D. Young 14th Edition
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Phys 1001 Exam 3 Comprehensive Review Problem (The exam problems won't be this long/complicated) In the contraption shown below, a cord unwinds from a cylinder, then passes over a non-ideal pulley, and then attaches to a hanging box. The cylinder can be considered a uniform solid disk with mass mc = 5.00 kg and radius rc = 40.0 cm. The pulley is also a uniform solid disk with mass mp = 2.00 kg and rp = 20.0 cm (the pulley is non-ideal because it will have rotational inertia). Both the cylinder and the pulley turn without friction, and there is no slipping between the cord and the pulley surface. The box has mass m = 3.00 kg. The box is released from rest and accelerates downward as the cord unwinds from the cylinder. a) Use conservation of mechanical energy to find the linear speed of the box when it has descended 2.50 m. Then find the angular speeds (ωc and ωp) of the cylinder and the pulley (they will be different from each other since they have different radii). b) Use a linear constant acceleration formula to find the linear acceleration of the box. Then find the angular accelerations (αc and αp) of the cylinder and the pulley. c) Use Newton's 2nd law equations (in linear or rotational form as appropriate) to find the tension in the horizontal portion of the cord (T) and the tension in the vertical portion of the cord (T) (the tension will not be the same on each side of the pulley since it's not an ideal pulley). Include free-body diagrams. Pulley Cylinder Box
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Transcript

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00:01 Oh, here we have to solve the following problem.
00:03 Disc has a mass of 2 .6 kilograms.
00:08 Let's call it mp, which stands for the pulley.
00:14 And the stone has a mass of 1 .9 kilograms.
00:23 In question a, we have to find how far the stone must fall, so the kinetic energy of the pulley is four and a half joules.
00:38 Let's calculate it.
00:41 So it means that this mgh, decreasing potential energy of the stone, must be equal to the kinetic energy of the stone plus rotational energy of the pulley.
00:57 Now let's rewrite it.
01:08 And here let's basically look at the kinetic energy of the pulley.
01:14 That's i omega squared over 2, which is mass of the pulley, its squared radius over 2, times one half times v squared over r squared.
01:36 So then v squared is for kinetic energy of the pulley over mass of the pulley.
01:44 Now let's write down the formula for the changing potential energy of the stone.
02:00 And let's simplify this.
02:15 Now let's calculate the height h...
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