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course phy 201
10/27 10:30 pm
`q001. Report your data and the procedure used to obtain it.General College Physics Students: For each object, you observed a slope on which the object would eventually come to rest if given a slight push, and another slope on which the object would continue moving if given a slight push. So you had a range of slopes, such that for some slope in the range the object would neither speed up nor slow down when given a slight push. That is, for some slope in the range, the acceleration of the object on the incline was zero.
What was this range of slopes for each object?
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Domino: 0.19 - 0.31
Magnet: 0.29 - 0.34
Toy car: 0.0066 - 0.013
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You haven't reported your data, but your slopes appear to be very plausible.
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`q002. A mass of 12 kg is lifted from the floor to a height of 5 meters above the floor.
How much force does gravity exert on the mass?
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117.6 Newtons
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Does gravity do positive or negative work on the mass?
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negative
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What is the work done by gravity on the mass?
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-588 Joules
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What is the change in the gravitational potential energy of the mass?
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588 Joules
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What definitions were used in solving this problem?
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definition of work, definition of potential energy
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`q003. The 12 kg mass in the preceding is raised from the floor until its gravitational potential energy is 2000 Joules. How high was it raised?
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2000 Joules = ds * force; force = 9.8 * 12; force = 117.6 newtons; 2000 Joules / 117.6 newtons = roughly 17 meters;
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If the object is released from rest and allowed to fall back to the floor, what will be its kinetic energy when it reaches the floor, assuming that no energy is lost to air resistance?
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2000 Joules
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In this case, how fast will it be traveling when it reaches the floor?
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KE = ½ m * v^2; 2000 = 6 * v^2; 333.33 = v^2; 18.25 = v; 18.25 m/s;
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What will be its kinetic energy when it reaches the floor if during its fall the average force of air resistance is 10 Newtons?
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117.6 - 10 = 107.6 newtons; 107.6 newtons * 17 meters = 1829.2 Joules;
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In this case, how fast will it be traveling when it reaches the floor?
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1829.2 = 6 * v^2; 304.86 = v^2; v = roughly 17.5 m/s;
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What definitions were used in solving this problem?
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definition of work, definition of Kinetic energy, change in KE = work done.
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`q004. An incline rises from left to right, making an angle of 20 degrees with horizontal. A block of mass 12 kg rests on the incline.
What is the angle of the weight vector of that block relative to an x axis which is parallel to the incline?
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290 degrees
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If the incline rises from left to right, the x axis will be directed at 20 degrees above horizontal, which is closer (in the counterclockwise direction) to the downward vertical than before. So the angle will be 250 degrees.
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What is the weight of the mass?
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117.6 Newtons
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What are the components of the weight in the x and the y directions?
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x = cos(290) * 117.6 = 40.2 Newtons
y = sin(290) * 117.6 = -110.5 Newtons;
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If there is no friction present, what acceleration will result from the x component of the weight?
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3.35 m/s^2
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Why doesn't the y component of the weight result in an acceleration in the y direction?
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because the incline presents an equal and opposite force to the y force; if it didn’t, then the incline would break.
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If friction exerts a force opposing motion down the incline equal to 25% of the magnitude of the y component of the weight, then what will be the net force accelerating the block down the incline, and what will be its acceleration?
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force of friction: - 27.625 newtons; net force: 12.575 newtons; acceleration: 1.05 m/s^2;
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What definitions, laws and principles were used in solving this problem?
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definition of force, force on slope, definition of friction;
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`q005. If the block in the preceding travels 15 meters along the incline, by how much does its altitude change?
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hyptotenuse: 15 meters; horizontal distance: 14.1 meters; vertical distance: 5.13 meters; change in altitude: roughly 14 meters;
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Altitude is vertical, not horizontal. The change in altitude will be about 5 meters.
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If the block slides 15 meters down the incline, is the gravitational force in the direction of motion, or only partly in the direction of motion?
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The full gravitational force is only partially in the direction of motion;
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What is the component of gravity in the direction of motion?
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40.2 newtons;
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How much work does gravity therefore do on the block, and what is its change in gravitational potential energy?
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40.2 newtons * 5.13 meters = 206.2 Joules; work done: 206.2 Joules; change in potential energy: -206.2 Joules;
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5.13 meters is in the vertical direction; the 40.2 Newtons force is in the x direction.
You can multiply the force in the vertical direction by the component of gravity in the vertical direction (the latter, since the gravitational force is vertical, being the full force exerted by gravity), or you can multiply the component of the force in the x direction by the displacement in that direction.
You should do both, and verify that the two calculations give you identical results.
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If no nonconservative forces act, what must be the change in its kinetic energy?
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206.2 Joules
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How fast will it be moving at its final kinetic energy?
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206.2 = 6 * v^2; 34.37 = v^2; 5.86 = v; 5.86 m/s;
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If you multiply the weight of the block by the altitude change you calculated in the first of the questions in this problem, what is your result?
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12 * 5.13 = 61.56 kg m
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The weight of the block is a force, not a mass.
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What definitions, laws and principles were used in solving this problem?
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trigonometric identities, definition of work, definition of KE, vector forces;
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`q006. If the frictional force on the block in the preceding questions is equal and opposite to the x component of the weight, then what is the frictional force as a percent of the y component of the weight?
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force: -40.2 newtons; y component: -110.5 newtons; 36.4%
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What is the frictional force as a percent of the normal force?
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force: -40.2 newtons; normal force: 117.6 newtons; 34.1%
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How will the block behave under these conditions if given a slight push down the incline?
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it will slide a little, then come to a stop.
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If the forces are in balance, then the object will be in equilibrium, which means that its acceleration is zero.
The object would therefore continue moving at constant velocity.
In the real world, of course, friction isn't all that smooth, so the object's velocity would fluctuate a bit; it's possible, if the fluctuations are greater than the velocity you give the object, that the object could come to rest.
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What definitions, laws and principles were used in solving this problem?
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algebra percentiles, definition of friction
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Percents, not percentiles.
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`q007. Give a brief synopsis of what you learned by using the assigned PHeT program.
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I did the basic movement exercises, as well as the one pertaining to molecules in water. While I learned nothing new from the movement (it was stuff that had all been covered in class), the fluid molecules was somewhat interesting. I new most of what was there, but had never seen it displayed as such. This included the increased conductivity of salty water, while sugar did nothing, as well as the dissolving of sodium chloride (salt) while sucrose (sugar) did not.
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You're in pretty good shape here, but be sure to see my notes for at least one situation you didn't get right.
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