[Question] Tensions/Inclined planes question

[Orson]

Hey guys, I've been struggling with this style of question. I'm now good with these on horizontal planes, but I'm still struggling with on inclined planes.

Question [NEAP 2012 U3]:
A 4WD of mass 1800kg pulls a boat on a trailer at a constant speed up a boat ramp with an incline of 18 degrees. The combined mass of the boat and trailer is 700kg.

A frictional force of 300N acts between the boat trailer and the ramp, and a frictional force of 850N acts between the 4WD and the ramp.

a) Calculate the force exerted by the boat ramp on the 4WD (I'm good with this one). 1.7*10^4 N
b) Calculate the magnitude of the tension in the coupling joining the trailer and the 4WD. 2.5*10^3 N
c) Calculate the power developed by the 4WD if it moves the boat 15 meters up the ramp in 8 seconds. 1.7*10^4 W

Thanks heaps!

[archenemy]

hey, with these types of questions (and a lot or the motion questions for that matter) it's best to draw a diagram to aid in resolving forces and the like. It's kind of late atm so I have no diagrams atm, I'll attach some (if you want) when I'm less sleep deprived...

okay so you're good with the first part so I'll skip it.

For part b, Calculate the magnitude of the tension in the coupling joining the trailer and the 4WD. , pretty much what I did was to look at the forces acting on the trailer kind of in isolation. So the question states that the 4WD and trailer are moving at constant speed, this means no acceleration which means no net force. i.e the force component acting "up" the inclined plane (in this case only from the tension in the string) is the same as the forces acting "down" the inclined plane (frictional forces + component of weight parallel to plane). Using this we have the following "equation".

Tension = Frictional force with trailer + component of weight parallel to plane
T = 300N + mass x gravity x sin(18)
T = 300 + 7000sin(18) = 2,463.11N = 2.5*10^3 N

For part c), Calculate the power developed by the 4WD if it moves the boat 15 meters up the ramp in 8 seconds., similar kind of thing except instead of focusing on the trailer only, we'll be looking at the entire 4wd setup. So Power is given by the equation: P = Work / Time; where work is Force x Distance. We have the distance and time, so we need to find the force.
Force generated (up the plane) is once again equal to the total frictional forces + total forces due to the component of weight.

Therefore:
Force 4WD = 850N + 300N + 7000sin(18) + 18000sin(18) = 8875.42N
Work = 8875.42 x 15(m) / 8 (sec) = 1.66 x 10^4W = 1.7 x 10^4 W 

Hope this helped!

[Orson]

Hope this helped!

Thanks so much! Helped me...I just revisited this question...and this really helped me!