course Phy 231 {?????????????assignment #015
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08:24:59 Set 4 probs 1-7 If we know the net force acting on an object and the time during which the force acts, we can find the change in what important quantity?
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RESPONSE --> If we know Fnet and 'dt, we can find what's called the ""Impulse"" of an object. The impulse of an object is essentially the change in momentum of that object. confidence assessment: 3
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08:25:36 ** You can find the change in the momentum. Fnet * `ds is change in KE; Fnet * `dt is change in momentum. **
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RESPONSE --> OK self critique assessment: 3
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08:26:12 What is the definition of the momentum of an object?
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RESPONSE --> The momentum of an object is the product of mass and velocity of that object confidence assessment: 3
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08:26:42 ** momentum = mass * velocity. Change in momentum is mass * change in velocity (assuming constant mass). UNIVERSITY PHYSICS NOTE: If mass is not constant then change in momentum is change in m v, which by the product rule changes at rate dp = m dv + v dm. If mass is constant `dm = 0 and dp = m dv so `dp = m * `dv. **
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RESPONSE --> OK self critique assessment: 3
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08:29:37 How do you find the change in the momentum of an object during a given time interval if you know the average force acting on the object during that time interval?
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RESPONSE --> To find the change in momentum (impulse), you multiply the Fnet and the 'dt. confidence assessment: 3
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08:29:47 ** Since impulse = ave force * `dt = change in momentum, we multiply ave force * `dt to get change in momentum. **
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RESPONSE --> OK self critique assessment: 3
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08:45:52 How is the impulse-momentum theorem obtained from the equations of uniformly accelerated motion and Newton's Second Law?
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RESPONSE --> We know from Newton's 2nd law that F = m * a We also know that a = 'dv / 'dt Therefore, F = m * 'dv/'dt, so F * 'dt = m * 'dv m * 'dv = change in momentum, which is equivalent to F * 'dt which = impulse, which = change in momentum confidence assessment: 3
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08:47:12 ** First from F=ma we understand that a=F/m. Now if we take the equation of uniformly accelerated motion vf= v0 + a'dt and subtract v0 we get vf-v0 = a'dt. Since vf-v0 = 'dv, this becomes 'dv = a'dt. Now substituting a=F/m , we get 'dv = (F/m)'dt Multiplying both sides by m, m'dv = F'dt **
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RESPONSE --> OK! We went about it in two different ways, but achieved the same result... self critique assessment: 3
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08:52:37 If you know the (constant) mass and the initial and final velocities of an object, as well as the time required to change from the initial to final velocity, there are two strategies we can use to find the average force exerted on the object. What are these strategies?
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RESPONSE --> Knowing the v0 and vf of the object, as well as the 'dt, we can easily calculate the acceleration of the object ('dv / 'dt ). Since the mass is also known, we can then calculate Fnet = m * a. Another approach would be to use the equation: vf^2 = v0^2 + 2 a 'dt, but substitute F / m for a, giving: vf^2 = v0^2 + 2 ( F / m ) 'dt solving for F, we get: [ 1/2 * ( vf^2 - v0^2 ) * m ] / 'dt NOTE: 1/2 m v^2 = KE, so essentially we end up with KE / 'dt = Fnet confidence assessment: 3
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08:53:44 ** The impulse-momentum theorem for constant masses is m `dv = Fave `dt. Thus Fave = m `dv / `dt. We could alternatively find the average acceleration aAve = (vf - v0) / `dt, which we then multiply by the constant mass to get Fave. **
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RESPONSE --> OK Your first solution was not something I had mentioned, but I do understand that concept. self critique assessment: 2
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09:40:48 Class notes #14. How do we combine Newton's Second Law with an equation of motion to obtain the definition of energy?
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RESPONSE --> I believe this may be what I had done earlier... we know F = m * a, and we know vf^2 = v0^2 + 2 a 'dt therefore, we can say: a = [ 1/2 (vf^2 - v0^2) ] / 'dt or stated in terms of a = F /m: F = [ 1/2 m v^2 ] / 'dt because we know 1/2 m v^2 = KE, we can then state: F = KE / 'dt, or F * 'dt = KE confidence assessment: 2
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09:42:49 ** a = F / m. vf^2 = v0^2 + 2 a `ds. So vf^2 = v0^2 + 2 (Fnet / m) `ds. Multiply by m/2 to get 1/2 mvf^2 = 1/2 m v0^2 + Fnet `ds so Fnet `ds = 1/2 m vf^2 - 1/2 m v0^2--i.e., work = change in KE. **
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RESPONSE --> Ahhhhh! Darn it... I stated 'dt, rather than 'ds - I know better than that!! so I should have gotten Fnet * 'ds = KE, rather than Fnet * 'dt = KE, which I know is incorrect The slightest errors can really upset your equations - I have to be careful about that... self critique assessment: 2
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09:55:40 What is kinetic energy and how does it arise naturally in the process described in the previous question?
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RESPONSE --> KE is the energy that is obtained by accelerating a mass over a given interval. KE naturally arises when a force acclerates (changes its velocity over a given time interval) an object with a given mass. An example would be where an object is suspended in air and then is released. The object accelerates downward as the force of gravity acts on the object with given mass. KE is gained as the object moves downward. confidence assessment: 2
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09:57:20 ** KE is the quantity 1/2 m v^2, whose change was seen in the previous question to be equal to the work done by the net force. **
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RESPONSE --> OK I understand the KE = 1/2 m v^2 principle I now equate KE as the work done by the Fnet self critique assessment: 2
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09:58:29 What forces act on an object as it is sliding up an incline?
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RESPONSE --> Frictional force and gravitational force act on an object as it slides up an incline. confidence assessment: 3
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10:07:07 ** Gravitational force can be broken into two components, one parallel and one perpendicular to the ramp. The normal force exerted by the ramp is an elastic force, and unless the ramp breaks the normal force is equal and opposite to the perpendicular component of the gravitational force. Frictional force arises from the normal force between the two surfaces, and act in the direction opposed to motion. The gravitational force is conservative; all other forces in the direction of motion are nonconservative. COMMON ERROR: The Normal Force is in the upward direction and balances the gravitational force. COMMENT: The normal force is directed only perpendicular to the incline and is in the upward direction only if the incline is horizontal. The normal force cannot balance the gravitational force if the incline isn't horizontal. Friction provides a component parallel to the incline and opposite to the direction of motion. **
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RESPONSE --> OK So to go a step further, gravitational force can be broken down into a force parallel to the ramp and a force perpendicular to the ramp. The normal force is equal and opposite to the perpendicular component of gravity. The frictional force arises from the normal force between the two surfaces. So does this mean there is still a parallel component of gravity that is acting against the object?
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10:35:43 For an object sliding a known distance along an incline how do we calculate the work done on the object by gravity? How do we calculate the work done by the object against gravity?
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RESPONSE --> to calculate the work done by gravity against the object we can multiply the Fnet * 'ds The work done by the object against gravity should be equal and opposite, since gravity is a conservative force confidence assessment: 2
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10:37:36 ** The gravitational force is m * g directly downward, where g is the acceleration of gravity. m * g is the weight of the object. If we know change in vertical position then we can simply multiply weight m * g with the vertical displacement `dy, being careful to keep track of which is positive and/or negative. Alternatively it is instructive to consider the forces in the actual direction of motion along the incline. For small inclines the component of the gravitational force which is parallel to the incline is approximately equal to the product of the weight and the slope of the incline, as seen in experiments. The precise value of the component parallel to the incline, valid for small as well as large displacements, is m g * sin(theta), where theta is the angle of the incline with horizontal. This force acts down the incline. If the displacement along the incline is `ds, measured with respect to the downward direction, then the work done by gravity is the product of force and displacement, m g sin(theta) * `ds. If `ds is down the incline the gravitational component along the incline is in the same direction as the displacement and the work done by gravity on the system is positive and, in the absence of other forces in this direction, the KE of the object will increase. This behavior is consistent with our experience of objects moving freely down inclines. If the displacement is upward along the incline then `ds is in the opposite direction to the gravitational force and the work done by gravity is negative. In the absence of other forces in the direction of the incline this will result in a loss of KE, consistent with our experience of objects coasting up inclines. The work done against gravity is the negative of the work done by gravity, positive for an object moving up an incline (we have to use energy to get up the incline) and negative for an object moving down the incline (the object tends to pick up energy rather than expending it) **
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RESPONSE --> OK I think I was correct, though I didn't note that Fnet was equal to m * g I also assumed the object was free-hanging, and not on an incline self critique assessment: 2
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10:44:34 For an object sliding a known distance along an incline how do we calculate the work done by the object against friction? How does the work done by the net force differ from that done by gravity?
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RESPONSE --> work done by the object against friction is equal to Fnet (which = m * a - Ffrict) * 'ds the work done by Fnet differs from work done by gravity, because we have to take into account the frictional force acting on the object as well. The force of gravity will be acting against the object if it is moving up the incline and will be acting with the direction of motion of the object if it is moving down the incline. The frictional force will always be acting against the direction of motion of the object. confidence assessment: 2
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10:49:39 ** The work done against friction is the product of the distance moved and the frictional force. Since the force exerted by friction is always opposed to the direction of motion, the force exerted by the system against friction is always in the direction of motion so the work done against friction is positive. The net force on the system is sum of the gravitational component parallel to the incline and the frictional force. The work done by the net force is therefore equal to the work done by gravity plus the work done by the frictional force (in the case of an object moving up an incline, both gravity and friction do negative work so that the object must do positive work to overcome both forces; in the case of an object moving down an incline gravity does positive work on the system while friction, as always, does negative work on the system; in the latter case depending on whether the work done by gravity on the system is greater or less than the frictional work done against the system the net work done on the system may be positive or negative) **
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RESPONSE --> OK! self critique assessment: 3
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11:09:39 Explain why the restoring force on a simple pendulum is in nearly the same proportion to the weight of the pendulum as its displacement from equilibrium to its length, and explain which assumption is made that makes this relationship valid only for displacements which are small compared to pendulum length.
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RESPONSE --> The ratio of net force to weight is = ratio of 'ds to the length of the pendulum though I can not specifically state why.... confidence assessment: 0
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11:17:23 ** In terms of similar triangles: The reason the approximation only works for small displacements is because the sides used on one triangle are not the same as the sides used on the other. From the triangle we see that the restoring force and the weight are at right angles, while the length and horizontal displacement of the pendulum from equilibrium are the hypotenuse and the horizontal leg of a triangle and hence are not at right angles. For small angles the two long sides of the triangle are approximately equal so the discrepancy doesn't make much difference. For larger angles where the two long sides are significantly different in length, the approximation no longer works so well. In terms of components of the vectors: The tension force is in the direction of the string. The component of the tension force in the horizontal direction is therefore seen geometrically to be in the same proportion to the total tension as the length of the pendulum to the horizontal displacement (just draw the picture). The vertical component of the tension force must be equal to the weight of the pendulum, since the pendulum is in equilibrium. If the displacement is small compared to the length the vertical component of the tension force will be very nearly equal to the tension force. So the previous statement that 'The component of the tension force in the horizontal direction is therefore seen geometrically to be in the same proportion to the total tension as the length of the pendulum to the horizontal displacement' can be replaced by the statement that 'The component of the tension force in the horizontal direction is therefore seen geometrically to be in the same proportion to the weight of the pendulum as the length of the pendulum to the horizontal displacement. **
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RESPONSE --> OK So the reason it only works for small displacements is because we are working with triangles, and smaller triangles are closer to having a right angle (which is needed) than larger displacements which result in non-right angle triangles. self critique assessment: 2
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11:17:35 prin and gen phy: 6.4: work to push 160 kg crate 10.3 m, horiz, no accel, mu = .50.
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RESPONSE --> skip, diff class confidence assessment: 3
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11:17:40 The net force on the crate must be zero, since it is not accelerating. The gravitational force on the crate is 160 kg * 9.8 m/s^2 = 1570 N, approx. The only other vertical force is the normal force, which must therefore be equal and opposite to the gravitational force. As it slides across the floor the crate experiences a frictional force, opposite its direction of motion, which is equal to mu * normal force, or .50 * 1570 N = 780 N, approx.. The only other horizontal force is exerted by the movers, and since the net force on the crate is zero the movers must be exerting a force of 780 N in the direction of motion. The work the movers do in 10.3 m is therefore work = Fnet * `ds = 780 N * 10.3 m = 8000 N m = 8000 J, approx..
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RESPONSE --> skip, diff class self critique assessment: 3
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11:17:44 gen phy prob 6.9: force and work accelerating helicopter mass M at .10 g upward thru dist h.
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RESPONSE --> skip, diff class confidence assessment: 3
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11:17:49 To accelerate the helicopter at .10 g it must experience net force Fnet = mass * acceleration = M * .10 g = .10 M g. The forces acting on the helicopter are its upward thrust T and the downward pull - M g of gravity, so the net force is T - M g. Thus we have T - M g = .10 M g, and the upward thrust is T = .10 M g + M g = 1.10 M g. To exert this force through an upward displacement h would therefore require work = force * displacement = 1.10 M g * h = 1.10 M g h.
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RESPONSE --> skip, diff class self critique assessment: 3
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11:31:23 **** Univ: 6.58 (6.50 10th edition). chin-up .40 m, 70 J/kg of muscle mass, % of body mass in pullup muscles of can do just 1. Same info for son whose arms half as long.
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RESPONSE --> OK, I'm unable to find this in my book (12th edition), so here's my best shot an adult with arms .40 m long does a chin-up which takes 70 Joules/kg of muscle mass. What % of body mass is required to do 1? 'dWnet = Fnet * 'ds 70 Joules = m * 9.8 m/s^2 * .40 m 70 Joules = m 3.92 m^2/s^2 m = 17.86 kg If arms were only 0.20 m: 70 Joules = m * 1.96 m^2/s^2 m = 35.714 kg Fnet = m * a confidence assessment: 1
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11:33:01 ** For each kg of mass the weight is 1 kg * 9.8 m/s^2 = 9.8 N. Work done to lift each kg of mass .4 m would then be 9.8 N * .4 m = 3.92 J. The chin-up muscles generate 3.92 J per kg, which is 3.92 / 70 of the work one kg of muscle mass would produce. So the proportion of body mass in the pullup muscles is 3.92 / 70 = .056, or 5.6%. For the son each kg is lifted only half as far so the son only has to do half the work per kg, or 1.96 J per kg. For the son the proportion of muscle mass is therefore only 1.96 / 70 = 2.8%. The son's advantage is the fact that he is lifting his weight half as high, requiring only half the work per kg. **
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RESPONSE --> OK Interesting...I came up with 3.92 as part of it, but I then divided 70 by 3.92 for the answer. I suppose I should have divided 3.92 by 70 to get the correct answer. This essentially means I set up the original equation incorrectly. self critique assessment: 2
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11:48:13 Univ. 6.72 (6.62 10th edition). net force 5 N/m^2 * x^2 at 31 deg to x axis; obj moves along x axis, mass .250 kg, vel at x=1.00 m is 4.00 m/s so what is velocity at x = 1.50 m?
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RESPONSE --> Yikes....I can not discern what is being asked here... It sounds like: an object with Fnet = 5 N/m^2 * x^2 moves along an incline at 31 degrees. The object has mass = 0.250 kg and has v = 4 m/s at x=1 m. What is the v at x=1.5 m? Fnet = 5 N/m^2 * x^2 Fnet = m * a 5 N/m^2 * x^2 = 0.25 kg * a a = 20 x^2 N/kg m^2 At x = 1.5 m: a = 20 * (1.5 m)^2 N/kg m^2 a = 20 * 2.5 m^2 N / kg m^2 a = 45 [ m^2 kg m/s^2 ] / kg m^2 a = 45 m/s^2 m = 0.25 kg v0 = 4 m/s vf = ? a = 45 m/s^2 'ds = 1.5 - 1.0 = 0.5 m vf^2 = v0^2 + 2 a 'ds vf = sqrt[ (4 m/s)^2 + 2 (45 m/s^2) 0.5 m ] vf = sqrt[ 16 m^2/s^2 + 45 m^2/s^2 ] vf = sqrt[ 61 m^2/s^2 ] = +- 7.81 m/s because the accleration was positive, we can say the vf was also positive, so vf = 7.81 m/s confidence assessment: 3
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11:49:32 ** Force is variable so you have to integrate force with respect to position. Position is measured along the x axis, so you integrate F(x) = - k / x^2 with respect to x from x1 to x2. An antiderivative of - k / x^2 is k / x so the integral is k / x2 - k / x1. If x2 > x1, then k / x2 < k / x1 and the work is negative. Also, if x2 > x1, then motion is in the positive x direction while F = - k / x^2 is in the negative direction. Force and displacement in opposite directions imply negative work by the force. For slow motion acceleration is negligible so the net force is practically zero. Thus the force exerted by your hand is equal and opposite to the force F = - k / x^2. The work you do is opposite to the work done by the force so will be - (k / x2 - k / x1) = k/x1 - k/x2, which is positive if x2 > x1. This is consistent with the fact that the force you exert is in the opposite direction to the force, therefore in the positive direction, as is the displacement. Note that the work done by the force is equal and opposite to the work done against the force. **
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RESPONSE --> ?? I'm unsure if the answer relates to the question - perhaps I completely misunderstood because I was making assumptions about what the question was asking.... self critique assessment: 1
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