SlideShare une entreprise Scribd logo
1  sur  2
Problem #1 (20pts) Two weights of differing masses mi and m: (where m is larger than ms ) are
connected string that passes over a frictionless pulley in the shape of a uniform cylinder of mass
a moment of inertia 1-(1/2) M.R. There is no slipping between the string system is initially at
rest. M, radius R, and the pulley. The a) Find a beautiful algebraic expression for the magnitude
of the lincar spsed v of mi afher having descended a distance h from the starting point. Neglest
air dnug & E M with b) Find the an al?ebraic espression for the lisar asslanation a of tho system
2. for each one of the tonsions. Ti and T, in each cable. c) Find an algebraic expression initial:
MR n2 Page 2 of 2
Solution
On the right side of the pulley,
m1g - T1 = m1*a
T2 - m2g = m2*a
(T1 - T2)*R = 0.5*M*R^2*alpha
and R*alpha = a
So (T1 -T2) = 0.5*M*a
So Adding the first and second equation gives,
(m1 - m2)*g -(T1 -T2) = (m1 +m2)*a
So a = (m1 -m2)*g/(m1 + m2 +M/2)
v^2 = 2*a*h = 2*h*(m1 -m2)*g/(m1 + m2 +M/2)
v = sqrt(2*h*(m1 -m2)*g/(m1 + m2 +M/2))
T1 = m1*(g-a) = m1*g*(1 - (m1-m2)/(m1 + m2 +M/2))
T2 = m2*(g+a) = m2*g(1+ (m1-m2)/(m1 + m2 +M/2))
Problem #1 (20pts) Two weights of differing masses mi and m- (where m.docx

Contenu connexe

Plus de helenc18

The sound strikes the cantina walls and bounces off at the same angle.docx
The sound strikes the cantina walls and bounces off at the same angle.docxThe sound strikes the cantina walls and bounces off at the same angle.docx
The sound strikes the cantina walls and bounces off at the same angle.docx
helenc18
 
The sale of stock and the sale of bonds are reported as financing acti.docx
The sale of stock and the sale of bonds are reported as financing acti.docxThe sale of stock and the sale of bonds are reported as financing acti.docx
The sale of stock and the sale of bonds are reported as financing acti.docx
helenc18
 
Prepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docx
Prepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docxPrepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docx
Prepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docx
helenc18
 

Plus de helenc18 (19)

The total electromagnetic power emitted by the sun is 3-8 x 1026 W- Th.docx
The total electromagnetic power emitted by the sun is 3-8 x 1026 W- Th.docxThe total electromagnetic power emitted by the sun is 3-8 x 1026 W- Th.docx
The total electromagnetic power emitted by the sun is 3-8 x 1026 W- Th.docx
 
The Tinsley Company exchanged land that it had been holding for future.docx
The Tinsley Company exchanged land that it had been holding for future.docxThe Tinsley Company exchanged land that it had been holding for future.docx
The Tinsley Company exchanged land that it had been holding for future.docx
 
The State of Rhode Island publishes its budget and the various support.docx
The State of Rhode Island publishes its budget and the various support.docxThe State of Rhode Island publishes its budget and the various support.docx
The State of Rhode Island publishes its budget and the various support.docx
 
The SRLY rules for consolidated tax returns are designed to keep corpo.docx
The SRLY rules for consolidated tax returns are designed to keep corpo.docxThe SRLY rules for consolidated tax returns are designed to keep corpo.docx
The SRLY rules for consolidated tax returns are designed to keep corpo.docx
 
The sound strikes the cantina walls and bounces off at the same angle.docx
The sound strikes the cantina walls and bounces off at the same angle.docxThe sound strikes the cantina walls and bounces off at the same angle.docx
The sound strikes the cantina walls and bounces off at the same angle.docx
 
The six platforms below are initially at rest in deep space- The indic.docx
The six platforms below are initially at rest in deep space- The indic.docxThe six platforms below are initially at rest in deep space- The indic.docx
The six platforms below are initially at rest in deep space- The indic.docx
 
The rise of various digital communication methods in the past decade h.docx
The rise of various digital communication methods in the past decade h.docxThe rise of various digital communication methods in the past decade h.docx
The rise of various digital communication methods in the past decade h.docx
 
The reason that the increase in population growth in the 19th and 20th.docx
The reason that the increase in population growth in the 19th and 20th.docxThe reason that the increase in population growth in the 19th and 20th.docx
The reason that the increase in population growth in the 19th and 20th.docx
 
The sale of stock and the sale of bonds are reported as financing acti.docx
The sale of stock and the sale of bonds are reported as financing acti.docxThe sale of stock and the sale of bonds are reported as financing acti.docx
The sale of stock and the sale of bonds are reported as financing acti.docx
 
Precipitation volumetric analysis involves formation reactions of solu.docx
Precipitation volumetric analysis involves formation reactions of solu.docxPrecipitation volumetric analysis involves formation reactions of solu.docx
Precipitation volumetric analysis involves formation reactions of solu.docx
 
POST-LAB QUESTIONS 1- Based on your observations- what aimilarities di.docx
POST-LAB QUESTIONS 1- Based on your observations- what aimilarities di.docxPOST-LAB QUESTIONS 1- Based on your observations- what aimilarities di.docx
POST-LAB QUESTIONS 1- Based on your observations- what aimilarities di.docx
 
Portman Corporation has retained earnings of $675-000 at January 1- 20.docx
Portman Corporation has retained earnings of $675-000 at January 1- 20.docxPortman Corporation has retained earnings of $675-000 at January 1- 20.docx
Portman Corporation has retained earnings of $675-000 at January 1- 20.docx
 
Please write it in Microsoft Word- Not in handwritten form- I-'ll give.docx
Please write it in Microsoft Word- Not in handwritten form- I-'ll give.docxPlease write it in Microsoft Word- Not in handwritten form- I-'ll give.docx
Please write it in Microsoft Word- Not in handwritten form- I-'ll give.docx
 
please write carefully and explain clearly- Thank you-SolutionKsp of C.docx
please write carefully and explain clearly- Thank you-SolutionKsp of C.docxplease write carefully and explain clearly- Thank you-SolutionKsp of C.docx
please write carefully and explain clearly- Thank you-SolutionKsp of C.docx
 
Prioritize the three themes of integrated solid waste management- 1^st.docx
Prioritize the three themes of integrated solid waste management- 1^st.docxPrioritize the three themes of integrated solid waste management- 1^st.docx
Prioritize the three themes of integrated solid waste management- 1^st.docx
 
present synchronized savage code while (1) { getServingFromPot ()- ea.docx
present synchronized savage code while (1) {  getServingFromPot ()- ea.docxpresent synchronized savage code while (1) {  getServingFromPot ()- ea.docx
present synchronized savage code while (1) { getServingFromPot ()- ea.docx
 
Prepare general journal entries to record the following transactions f.docx
Prepare general journal entries to record the following transactions f.docxPrepare general journal entries to record the following transactions f.docx
Prepare general journal entries to record the following transactions f.docx
 
Prepare functional specifications for the company-'s use of the Web an.docx
Prepare functional specifications for the company-'s use of the Web an.docxPrepare functional specifications for the company-'s use of the Web an.docx
Prepare functional specifications for the company-'s use of the Web an.docx
 
Prepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docx
Prepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docxPrepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docx
Prepare a 3 to 5 paragraph briefing statement which explains the 3 mos.docx
 

Dernier

Gardella_Mateo_IntellectualProperty.pdf.
Gardella_Mateo_IntellectualProperty.pdf.Gardella_Mateo_IntellectualProperty.pdf.
Gardella_Mateo_IntellectualProperty.pdf.
MateoGardella
 
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptxSeal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
negromaestrong
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
PECB
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
ciinovamais
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
QucHHunhnh
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
heathfieldcps1
 
Making and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdfMaking and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdf
Chris Hunter
 

Dernier (20)

Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
 
Gardella_Mateo_IntellectualProperty.pdf.
Gardella_Mateo_IntellectualProperty.pdf.Gardella_Mateo_IntellectualProperty.pdf.
Gardella_Mateo_IntellectualProperty.pdf.
 
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptxSeal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
 
Z Score,T Score, Percential Rank and Box Plot Graph
Z Score,T Score, Percential Rank and Box Plot GraphZ Score,T Score, Percential Rank and Box Plot Graph
Z Score,T Score, Percential Rank and Box Plot Graph
 
fourth grading exam for kindergarten in writing
fourth grading exam for kindergarten in writingfourth grading exam for kindergarten in writing
fourth grading exam for kindergarten in writing
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
 
ICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptx
 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptx
 
PROCESS RECORDING FORMAT.docx
PROCESS      RECORDING        FORMAT.docxPROCESS      RECORDING        FORMAT.docx
PROCESS RECORDING FORMAT.docx
 
This PowerPoint helps students to consider the concept of infinity.
This PowerPoint helps students to consider the concept of infinity.This PowerPoint helps students to consider the concept of infinity.
This PowerPoint helps students to consider the concept of infinity.
 
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeMeasures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and Mode
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
 
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17  How to Extend Models Using Mixin ClassesMixin Classes in Odoo 17  How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
 
Class 11th Physics NEET formula sheet pdf
Class 11th Physics NEET formula sheet pdfClass 11th Physics NEET formula sheet pdf
Class 11th Physics NEET formula sheet pdf
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
Making and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdfMaking and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdf
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
 

Problem #1 (20pts) Two weights of differing masses mi and m- (where m.docx

  • 1. Problem #1 (20pts) Two weights of differing masses mi and m: (where m is larger than ms ) are connected string that passes over a frictionless pulley in the shape of a uniform cylinder of mass a moment of inertia 1-(1/2) M.R. There is no slipping between the string system is initially at rest. M, radius R, and the pulley. The a) Find a beautiful algebraic expression for the magnitude of the lincar spsed v of mi afher having descended a distance h from the starting point. Neglest air dnug & E M with b) Find the an al?ebraic espression for the lisar asslanation a of tho system 2. for each one of the tonsions. Ti and T, in each cable. c) Find an algebraic expression initial: MR n2 Page 2 of 2 Solution On the right side of the pulley, m1g - T1 = m1*a T2 - m2g = m2*a (T1 - T2)*R = 0.5*M*R^2*alpha and R*alpha = a So (T1 -T2) = 0.5*M*a So Adding the first and second equation gives, (m1 - m2)*g -(T1 -T2) = (m1 +m2)*a So a = (m1 -m2)*g/(m1 + m2 +M/2) v^2 = 2*a*h = 2*h*(m1 -m2)*g/(m1 + m2 +M/2) v = sqrt(2*h*(m1 -m2)*g/(m1 + m2 +M/2)) T1 = m1*(g-a) = m1*g*(1 - (m1-m2)/(m1 + m2 +M/2)) T2 = m2*(g+a) = m2*g(1+ (m1-m2)/(m1 + m2 +M/2))