badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12

                        

A heavy chain with a mass per unit length ? is pulled by the constant force F along a horizontal surface consisting of a smooth section and a rough section.The chain is initially at rest on the rough surface with x=0 .If the coefficient of kinetic friction between the chain and rough surface is µ , determine the velocity of the chain when x=L . I am applying work energy theorem . Work done by constant Force will be Force × displacement of centre of mass i.e FL but not able to find work done by friction .The friction force at an instant when chain length x lies on the rough surface should be µ?xg.This force is continuously decreasing .i feel calculus is involved here but i am unable to apply it.Please help me .thanks.

8 years ago

Answers : (1)

Vishal
12 Points
							The chain is initially at rest, soKEo=0KEo=0The force of friction is given byf(x)=μρ(L−x)gf(x)=μρ(L−x)gThe net force on the chain is∑F=F−μρ(L−x)g∑F=F−μρ(L−x)gWork done on the chain is the integral of force over distance, soW=∫L0F−μρ(L−x)gdxW=∫0LF−μρ(L−x)gdxIntegrate and getW=FL−12μρgL2W=FL−12μρgL2Use Work-Energy TheoremKEf=KEo+WKEf=KEo+Wand final kinetic energy isKEf=FL−12μρgL2KEf=FL−12μρgL2Kinetic Energy equationKEf=12mv2f=12(ρL)v2f=FL−12μρgL2KEf=12mvf2=12(ρL)vf2=FL−12μρgL2Solve for final velocityvf=2Fρ−μgL−−−−−−−−−√
						
3 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details