course Phy 201 xoF assignment #012
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17:07:15 Query set 3 #'s 13-14 If an object of mass m1 rests on a frictionless tabletop and a mass m2 hangs over a good pulley by a string attached to the first object, then what forces act on the two-mass system and what is the net force on the system? What would be the acceleration of the system? How much would gravitational PE change if the hanging mass descended a distance `dy?
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RESPONSE --> The force of gravity on the hanging mass is the force acting on the system, and Fnet is therefore equal to m2 * 9.8 m/s^2, which is also the weight of the hanging mass. Acceleration is equal to Fnet divided by the total mass of the system which is m1 + m2. The gravitational `dPE is equal and opposite to the weight of the hanging mass multiplied by distance the mass descended `dy.
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17:11:28 ** The net force on the system is the force of gravity on the suspended weight: Fnet = m2*9.8m/s/s Gravity also acts on m1 which is balanced by force of table on m1, so this force makes no contribution to Fnet. Acceleration=net force/total mass = 9.8 m/s^2 * m2 / (m1+m2). If the mass m2 descends distance `dy then gravitational PE decreases by - m2 g * `dy. COMMON MISCONCEPTIONS AND INSTRUCTOR COMMENTS: The forces acting on the system are the forces which keep the mass on the table, the tension in the string joining the two masses, and the weight of the suspended mass. The net force should be the suspended mass * accel due to gravity + Tension. INSTRUCTOR COMMENT: String tension shouldn't be counted among the forces contributing to the net force on the system. The string tension is internal to the two-mass system. It doesn't act on the system but within the system. Net force is therefore suspended mass * accel due to gravity only 'The forces which keep the mass on the table' is too vague and probably not appropriate in any case. Gravity pulls down, slightly bending the table, which response with an elastic force that exactly balances the gravitational force. **
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RESPONSE --> ok
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17:17:03 How would friction change your answers to the preceding question?
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RESPONSE --> Fnet will change when friction is accounted for in the preceding question as follows: Fnet = F1 - fFrict where F1 is the Fnet calculated without the friction and where fFrict is equal to the frictional component * weight of m1 (weight being calculated as a product of m * gravity; here being m1 * 9.8 m/s^2). Then all quantities attained by the original Fnet (which is F1 here), will need to be recalculated using the new Fnet.
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17:17:53 **Friction would act to oppose the motion of the mass m1 as it slides across the table, so the net force would be m2 * g - frictional resistance. **
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RESPONSE --> ok
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17:29:29 Explain how you use a graph of force vs. stretch for a rubber band to determine the elastic potential energy stored at a given stretch.
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RESPONSE --> Using a graph of Force vs. rubber band stretch, work required to stretch the rubber band can be found by calculating the area under the curve, and therefore, neglecting any thermal losses, `dPE will equal this work.
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17:30:10 ** If we ignore thermal effects, which you should note are in fact significant with rubber bands and cannot in practice be ignored if we want very accurate results, PE is the work required to stretch the rubber band. This work is the sum of all F * `ds contributions from small increments `ds from the initial to the final position. These contributions are represented by the areas of narrow trapezoids on a graph of F vs. stretch. As the trapezoids get thinner and thinner, the total area of these trapezoids approaches, the area under the curve between the two stretches. So the PE stored is the area under the graph of force vs. stretch. **
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RESPONSE --> ok
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17:52:31 STUDENT QUESTIONS: Does the slope of the F vs stretch graph represent something? Does the area under the curve represent the work done? If so, is it work done BY or work done ON the rbber bands?
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RESPONSE --> Slope of a F vs stretch graph would represent the rate at which force changes in relation to change in stretch, which ends up in units of mass per second squared, and I can't think of anything that type of unit would represent. The area under the curver represents the work done ON the rubber band since it adds to the rubber bands potential energy.
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17:54:07 ** Slope isn't directly related to any physical quantity. The area is indeed with work done (work is integral of force with respect to displacement). If the rubber band pulls against an object as is returns to equilibrium then the force it exerts is in the direction of motion and it therefore does positive work on the object as the object does negative work on it. If an object stretches the rubber band then it exerts a force on the rubber band in the direction of the rubber band's displacement, and the object does positive work on the rubber band, while the rubber band does negative work on it. **
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RESPONSE --> ok
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