a stuntman with a mass of 70kg swings from the end of a 4mlong rope that is alon
ID: 1673711 • Letter: A
Question
a stuntman with a mass of 70kg swings from the end of a 4mlong rope that is along the arc of a vertical circle. assume thathe starts from rest when the rope is horizontal find the tension inthe rope required to make the man follow his circle path A) at the begining of motion B)at a height of 1.5m above the bottom of the arc C)at the bottom of the arc a stuntman with a mass of 70kg swings from the end of a 4mlong rope that is along the arc of a vertical circle. assume thathe starts from rest when the rope is horizontal find the tension inthe rope required to make the man follow his circle path A) at the begining of motion B)at a height of 1.5m above the bottom of the arc C)at the bottom of the arcExplanation / Answer
at the 1.5 meter point, first calculate his speed. atthis point his speed can be calculated via conservation of energy. he has lost 2.5 meters, therefore his potential energy changeis 70*9.81*2.5 this must equal the change in kinetic energy.5mv^2 his speed will equal 7m/s at the bottom using the same methodhis speed will equal 8.85m/s. Also at the bottom gravity isacting directly parallel to the tension thus it is70*9.81.=686.7
To calculate the angle at which gravity is acting at the 1.5mpoint use trig to calculate the angle. sin theta * r
the angle from the bottom is 22.02 degrees so gravity is acting in the tension direction ofcos(22.0243)*9.81*70 which equals 636.588
So now we have the tension in the vine due to gravity and hisspeeds at each point so we have to calculate the tension as aresult of his speed at each point. this can be done by theequation m*v^2/r so at the 1.5 meter point it is 70*7^2/4=857.5. at the bottom it is 1355.2
add the tension required due to speed and gravity and you willhave your answer. Sorry for all the words, it is late and Iam just rambling. HOpe this helps
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