Homework Help: Solve Physics & Math Problems with Answers

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SUMMARY

This discussion focuses on solving various physics problems related to mechanics, including the motion of objects in circular paths and energy conservation. Key problems include determining the minimum height for an object to remain on a track (Problem 44), calculating work done by air resistance on a paratrooper (Problem 71), and analyzing the dynamics of a swinging student (Problem 85). The solutions employ principles such as energy conservation and centripetal force, providing clear methodologies for each scenario.

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Stephanie
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I've tried these problems but I need some help.

44. a small mass m slides without fritction around the looped apparatus show in the picture below. If the object is to remain on the track, even at the top of the circle (whose radius is r), from what minimum height H must it be released?

http://i75.photobucket.com/albums/i319/Thepalaceguild/draw.jpg

71. A paratrooper fell 370m after jumping from an aircraft without his parachute opening. He landed in a snowback, creating a crater 1.1m deep, but survived with only minor injuries. Assuming the paratroopers mass was 80kg and his terminal velocity was 30m/s, estimate the work done on him by air resistance as he fell.

74. In a film of Jesse Owens's famous long jump in the 1936 Olympics, it is observed that his center of mass rose 1.1m from launch point to the top of the arc. What minimum speed did he need at launch if he was also noted to be traveling at 6.5m/s at the top of the arc?

76. A ball is attached to a horizontal cord of length L, whose other end is fixed, (picture below). (a) If the ball is released, what will be its speed at the lowest point of its path?(b)A peg is located a distance H directly below the point of attachment of the cord. If H=.8L, what will be the speed of the ball when it reaches the top of its circular path about the peg?

http://i75.photobucket.com/albums/i319/Thepalaceguild/draw2.jpg

81. Water flows over a dam at the rate of 550 Kg/s and falls vertically 80m before striking the turbine blades. Calculate: the rate at which mechanical energy is transferred to the turbine blades, assuming 60% efficiency.

85. A 75Kg student runs at 5.0 m/s, grabs a rope, and swings out over a lake. He releases the rope when is velocity is zero. (a) What is the angle (-)(theta) when he releases the rope? (b) What is the tension in the rope just before he releases it? (c) What is the maximum tention in the rope?


Thanks to all who respond. ^_^
 
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Stephanie said:
I've tried these problems but I need some help.

Well, if you're stuck somewhere, you could perhaps point out where the problem is.
 
44.
N + mg = mv^2 /r -at the top of the loop
N goes to zero and
mg = (mv^2)/r

so v minimum = √rg

now use energy conservation
mgh + 0 = 0.5m(√rg)^2
h = 0.5r

and your H = 2r+ h = 2.5*r
 

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