
Applied Math Applied Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 14th, 2017, 11:46 AM  #1 
Newbie Joined: Jun 2017 From: Ferndown Posts: 2 Thanks: 0  Inclined plane problem (work done)
Hi guys, I have a question here that I am struggling with and it goes as follow: A train of mass 250 tonnes starts from rest and accelerates up an incline of 1/100 attaining a speed of 45 km/h after travelling 250m. If the frictional resistance to motion is constant at 30kN calculate the work done by the train's engine using the principle of conservation of energy. I have converted the speed to be be 12.5 m/s and tonnes into kg by x10^3. I think that the height is 2.5m as for every 100m it increases 1m and the total distance is 250m so 250/100 = 2.5m. With this I calculated work done against gravity to be 6125000j (250x10^3 x 9.8 x 2.5). Frictional work done I calculated as 30,000 x 250 to get 7500000N. But I am now stuck from where to go on from here :/ I may just be being stupid, but any help would be greatly appreciated Thanks Last edited by skipjack; June 15th, 2017 at 12:05 PM. 
June 14th, 2017, 04:34 PM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416  Quote:
net work = (net force)(displacement) = change in Kinetic Energy $(F_e  f  Mg\sin{\theta})\Delta x = \dfrac{1}{2}M(v_f^2v_0^2)$ $F_e \cdot \Delta x = \dfrac{1}{2}M(v_f^2v_0^2) + (f + Mg\sin{\theta}) \Delta x$ $M$ = 250 metric tons = 250000 kg $v_f = 45 \, km/hr = 12.5 \, m/s$ $g = 9.8 \, m/s^2$ $\sin{\theta} = \dfrac{1}{\sqrt{10001}}$ $F_e \cdot \Delta x = \dfrac{1}{2}(250k)(12.5^20) + (30k + 250k \cdot g\sin{\theta})(250)$ $F_e \cdot \Delta x \approx 3.32 \times 10^7 \, J$  
June 15th, 2017, 09:18 AM  #3 
Newbie Joined: Jun 2017 From: Ferndown Posts: 2 Thanks: 0 
ah I see! Thank you very much for your help!


Tags 
conservation, energy, inclined, inclined plane, plane, problem, work, work done 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The resistance force of an inclined plane.  Mr Davis 97  Physics  5  April 11th, 2015 11:30 PM 
Solid hemisphere resting on an inclined plane  john Cartwell  Applied Math  0  October 28th, 2014 11:41 AM 
HELP !! Masses on inclined plane with pulley and friction !!  GBR1026  Physics  1  March 25th, 2013 06:15 AM 
Inclined Plane  proglote  Physics  0  October 9th, 2011 03:54 PM 
HELP !! Masses on inclined plane with pulley and friction !!  GBR1026  Applied Math  0  December 31st, 1969 04:00 PM 