conservation of energy problem

[vinn1ev]

ive got the below question. ive calculated the force required to pull the boat up the incline but how do i factor in the coefficient of friction (my working out is below too)

 

[Deleted member 4993]

ive got the below question. ive calculated the force required to pull the boat up the incline but how do i factor in the coefficient of friction (my working out is below too)
View attachment 27930
View attachment 27931

You need to draw the Free-Body-Diagram of the mass - which will be subjected to

tensile force from the cable (T),​

​

gravity force (mg),​

​

Normal force (N),​

​

frictional force (µN) and​

​

inertial force (ma).​

I would select x-axis parallel to the slip-way (positive going up). Now apply D 'Alembert's Principle and solve.

 

[skeeter]

[MATH]F_{net} = ma = F_c - mg\sin{\theta} - \mu mg \cos{\theta}[/MATH]
[MATH]v_f^2 = v_0^2 + 2a \Delta x \implies a = \frac{v_f^2 - v_0^2}{2 \Delta x}[/MATH]

 

[vinn1ev]

sorry for being dumb but i dont get any of that lol

 

[skeeter]

sorry for being dumb but i dont get any of that lol

In post #2, Khan mentioned a free-body diagram of the forces acting on the boat. (attached) The net force is up and parallel to the incline.
I posted the relevant equation to find the acceleration necessary to move 25 m up the incline with an initial speed of 0 m/s and final speed of 1.2 m/s.
The force of friction is [MATH]f = \mu \cdot N[/MATH], where [MATH]N = mg\cos{\theta}[/MATH]
With that acceleration, you can use the net force equation to determine the force of the cable necessary to achieve that acceleration.