A 1000 kg roller coaster cart moving to the right passes point 1 at a speed of 2

Question

A 1000 kg roller coaster cart moving to the right passes point 1 at a speed of 20 m/s. It then travels over the top of a hill that is shaped like a vertical circle of radius 10 m. Point 4 is 20 m above point 1. Suppose the cart barely makes it to point 4 before stopping. If friction and air resistance are not negligible, what is the total work done on the cart by friction and air resistance?

I defined height=h=20m, velocity=v=20m/s, and mass=m=1,000kg

using the conservation of energy, K=U+W. Where K is kinetic energy U is potential energy and W is work. Im assuming initially all the energy is kinetic and the final energy is the sum of the potential energy and work.

plugging the variables into this equation I got

.5mv^2=mgh+w

.5mv^2-mgh=w

200,000-196200=W

with one sig fig W=4,000N.

Does this look right?

Explanation / Answer

since the coaster travelling from point 1 to point 4

total energy at point 4 is E4 = K+U = 0+m*g*h = 1000*9.81*20 = 196200 J

toptal energy at point 1 is E1 = K+U= 0.5*m*v^2 + 0 = 0.5*1000*20*20 = 200000 J

work done by friction and air resistance is W = E4-E1 = 196200 -200000 = -3800 J

negatice sign represents lost in energy due to friction and air resistance

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