Q) a barge is pulled along a straight canal by a horse on the tow rope. the barge and the horse move in parallel straight lines 5m apart. the tow rope is 13m long and it remains taut and horizontal. the horse and the barge each move at a constant speed of 0.78m/s and the towrope has a constant tension of 400N. calculate the work done by the horse on the barge in 10 minutes.
answer: 173 kJ
2007-04-07 01:14:08 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The work done by the horse is the force it is applying times the distance moved in the direction of the force.
In ten minutes (600 seconds) the distance the barge moves is 0.78*600 m = 468m.
If you draw a right angled triangle you can see that the cosine of the angle between the direction of motion and the direction the force is applied is 12/13 (the triangle is a 5-12-13 pythagorean triple)
So, the force applied in the direction of motion of the barge is 400* 12/13 N.
Multiply this by the distance travelled and you get 172800J which is about 173kJ.
2007-04-07 01:44:13 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The angle@between the force and the displacement is
sin @= 5/13 and the displacement is 0.78*600 m ( you must express all in the same unit of time)
cos@= sqrt( 1-25/169) = 12/13
so as
work = force(in the direction of displacement)*displacement
= 400*0.78*600*12/13=172.8 kJ
2007-04-07 07:09:16 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋