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course Phy 201
`q001. For each of the given objects on the various inclines find the parallel and perpendicular components of the object's weight as a percent of its weight, using the sine and cosine functions. Compare with the estimates you made previously.A car weighing 20 000 Newtons on an incline making angle 12 degrees with horizontal.
The sine is -.819 and the cosine is -.574, the estimate for the x axis is about 30% and for the y axis it is about 85%.
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A hotwheels car of weight 80 000 dynes on an incline whose angle with horizontal is 20 degrees.
The sine is -.906 and the sine is -.423, the estimate for the x axis is about 40% and for the y axis it is about 90%.
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A block of weight 30 pounds on a 37 degree incline.
The sine is -.766 and the cosine is -.643, the estimate for the x axis is about 35% and for the y axis it is about 85%.
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`q002. Your answers to this question will be based on the results you got using the sines and cosines, and will differ from those you obtained previously using estimates. If the car in the first question experiences a frictional force which is 2% of the perpendicular component of its weight, then what is the magnitude of the frictional force?
The magnitude of the frictional force is 400N.
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If the car is coasting downhill what is the sum of the parallel component of its weight and the frictional force?
Since it is going downhill the sum is -19,600 because I made the 20,000N negative.
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If the car is coasting uphill what is the sum of the parallel component of its weight and the frictional force?
The sum would be 19,600 because I made the 20,000N positive since it was going uphill.
@& 19600 is the perpendicular component of the weight.
From your sketch it should be clear that the parallel component is much smaller than the weight.*@
@& You should have calculated this as 20 000 N * cos(258 degrees).*@
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`q003. Again your results will be based on the calculations you did in the first question, and should be compared to your previous estaimtes.
If the hotwheels car in the first question is attached by a light thread to a washer weighing 20 000 dynes and suspended over a pulley at the lower end of the ramp, then if friction is ignored what is the net force acting in the direction down the ramp?
The net force would be 980,000N, I found this answer by doing the following, 9.8m/s^2 * (80,000 dynes + 20,000 dynes).
@& You would multiply 9.8 m/s^2 by the mass to get the weight.
However 20 000 dynes is the weight, and you don't multiply the weight by the acceleration of gravity to get the force. The weight is already the force of gravity on the object.*@
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Answer the same question assuming that the washer is suspended from a pulley at the top of the ramp.
The net force would be 588,000, I did the same thing but instead of 100,00 dynes I used 60,000 dynes.
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`q004. Once more base your answers on the results obtained for the first question, and compare your results with your previous estimate-based results.
How much frictional force would it take to hold the block in the first question stationary on the incline?
The frictional force would be -.7986N.
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What is this force as a percent of the weight of the block?
The frictional force as a percentage of the weight of the block is 1.3270%.
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`q005. Sound in air travels at about 340 m/s. If you drop a rock down a well which is 40 meters deep, how much time will elapse between the drop and hearing the sound of the splash?
About .12s, I found that by finding how far it would fall in .01s that is 3.4m then I divided 3.4 into 40 getting 11.76.
@& 3.4 m is how far the sound would travel in .01 second.
The rock starts from rest, drops 40 meters, accelerating at 9.8 m/s^2. How long does that take?
How long does it then take the sound to travel back up the well?*@
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`q006. A rock of mass 2 kilograms is tossed upward at 6 meters per second, being released at a height of 4 meters above the ground. Assume that air resistance has no significant effect on its motion.
How long after being released will it reach the ground?
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What will be its kinetic energy at the instant it reaches the ground?
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What was its kinetic energy when just after its release?
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How much work did gravity do on the ball between release and striking the ground?
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How much work did gravity do on the ball between release and reaching its maximum altitude?
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How much work did gravity do on the ball as it fell from its maximum altitude to the ground?
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@& Start by identifying the interval you wish to analyze. Then identify which of the quantities v0, vf, `dt, a and `ds you know.
Then use the equations of motion to find the motion quantities you don't know.*@
`q007. A hotwheels car of mass 50 grams rolls down a ramp inclined at 30 degrees from horizontal.
How much force does gravity exert on it?
The force that gravity exerts on it is -.86603.
@& This looks like the sine of either 250 degrees or 300 degrees. It's not a force, it's a component of the weight as a percent of the weight.*@
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What is the component of the gravitational force parallel to the incline?
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If friction is negligible, what therefore will be the acceleration of the car?
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`q008. A rubber band breaks when its tension reaches 20 Newtons. The rubber band is used to accelerate a 1.2 kg mass upward, with gradually increasing acceleration. When the acceleration reaches a certain value the rubber band breaks. What is that acceleration?
The acceleration that will break the rubber band is 16.6 N/kg.
@& What force acts on the mass, in addition to the tension?
If the tension is 20 Newtons, then what is the net force on the 1.2 kg mass?
With that net force, what is the acceleration of the mass?
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`q009. Two dominoes are stacked, one on top of the other. The maximum frictional force exerted between the dominoes is 10% of the weight of the top domino. The bottom domino is attached to a rubber band chain, which is stretched to some length before the dominoes are released. This is repeated, slightly increasing the length of the rubber band chain with each repetition, until the top domino slides off.
What acceleration was necessary to cause this to occur?
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Will the top domino begin to slide shortly after the moment of release, or does this occur a bit later?
I think that it will begin side a little bit after the moment of release but it will only be a little bit.
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`q010. A spring exerts an average force of 3 Newtons on a 100-gram toy car, initially at rest, as the car moves 10 centimeters. Other forces in the direction of the car's motion are not significant, nor is the mass of the spring.
How fast will the car be moving at that point?
The car will begin accelerating at .03m/s^2.
@& You're thinking correctly, except that would the the acceleration of a 100-kg car, not a 100-gram car.
Be sure your units work out.*@
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Assuming that the spring's force is conservative, by how much did its potential energy change during this interval?
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@& We covered the definition of PE in greater depth today in class. Use the definition to find the change in the PE.*@
`q011. A 100-gram steel ball observed to be moving at 80 cm/s collides with a marble of mass 30 kg, which is initially at rest. Immediately after the collision the ball is observed to be moving at 60 cm/s and the marble at 66 cm/s.
What is the total momentum of the two objects before collision?
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@& What is the definition of momentum?
What does that tell you about the given situaiton?*@
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What is their total momentum after collision?
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What was the change in the momentum of the steel ball?
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What was the change in the momentum of the marble?
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How much total kinetic energy was present before the collision?
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How much total kinetic energy was present after the collision?
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Estimate how long the steel ball and the marble would have been in contact.
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Based on your estimate what average force was exerted by the ball on the marble, and what average force by the marble on the ball?
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`q012. An object moving at velocity v along the arc of a circle of radius r is being accelerated toward the center of the circle, with acceleration a_centripetal = v^2 / r. Note that 'centripetal' means 'toward the center'.
A domino of mass 15 grams is balanced each end of a metal strap of length 40 cm, which is rotating about its center at a rate that gives the domino a speed of 10 cm / second.
What is the centripetal acceleration of the domino?
The centripetal acceleration is 5 cm/second^2.
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What is the centripetal force on the domino?
It CA is 75g cm^2/s.
@& You mean g cm/s^2.*@
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Where does this centripetal force come from?
It comes from the rotation of the metal strap.
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How fast would the domino have to be moving in order for its centripetal acceleration to be 1.5 m/s^2?
The domino would have to be moving at about 5.5 cm/s.
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How fast would the domino have to be moving in order for the centripetal force to be 10% of its weight?
It would have to be moving at a velocity of .1cm/s.
@& You got the centripetal force questions right up to this one, but this isn't right. At .1 cm/s what would be the centripetal acceleration and the centripetal force? The latter would be much less than 10% of its weight.*@
@& Good work on some problems; see my notes on others and submit a revision as indicated.
&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you. &#
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