Circus attraction - How far does this sled move up an incline

AI Thread Summary
In a circus scenario, a monkey and sled with a combined mass of 20 kg start moving up a 20-degree incline at 4 m/s. The discussion focuses on calculating how far they travel up the incline, considering the effects of gravitational potential energy and friction, with a coefficient of friction of 0.20. The participant struggles to formulate the correct equations, recognizing that the monkey gains potential energy while losing kinetic energy due to friction. A force diagram is suggested to clarify the forces at play, leading to the equation f parallel - force friction = ma. The participant is exploring the relationship between potential gravitational energy, work done against friction, and kinetic energy to solve the problem using energy principles.
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Homework Statement


In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 4 m/s up a 20 degree inclined track. The combined mass of monkey and sled is 20 kg and the coefficient of friction between the sled and incline is .20. How far up the incline do the monkey and sled move?

Homework Equations


Potential energy gravity = mg(delta h)
Work of Friction = force x X
Kinetic energy = .5mv2
F perpendicular = fgcostheta
F parallel = fgsintheta

The Attempt at a Solution


I'm having the most trouble just coming up with the equation to use. As the monkey moves up he gains potential gravitational energy. He also loses some kinetic energy to the work of friction. I'm also not sure what to plug in for work of friction.
 
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its best to draw a force diagram before you go any farther.

draw a ramp inclined at 20 degrees, draw your force normal applied force and force of gravity. From that you should have an idea of where to start
 


I drew that and I came up with
f parallel - force friction = ma
I substituted and solved and got a=1.51 m/s
I'm not sure what to do from here. I know I could use kinematics to solve but I'm trying to do it using energy. Would the equation be Potential gravitational energy - work of friction = kinetic energy?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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