Look at the following roller coaster diagram. Assume that an 80 Kg cart has an i

Question

Look at the following roller coaster diagram. Assume that an 80 Kg cart has an   initial velocity of 2 m/s at the top of the track at point A. The cart then rolls to the bottom of the track to point C, then to point B and finally D. Calculate the kinetic energy, potential energy, velocity, gravity, and normal acceleration at points A, B, C, and D. Assume the following: the track is frictionless, the track is flat at point A, and the track radius is 10.5m at point C and point B. (Recall that normal acceleration is an=v2/r.)

Find the kinetic energy at point C.

Find the potential energy at point C.

Find the velocity at point C.

Find the acceleration due to gravity at point C.

Find the normal acceleration at point C.

Thank you so much

Explanation / Answer

Potential energy at A, PEA = mghA = 80*9.8*27 = 21168 J

Kinetic energy at A, KEA = mvA2/2 = (80*22)/2 = 160 J

Potential energy at C, PEC = mghC = 80*9.8*1 = 784 J

From conservation of energy, we have

KEC + PEC = KEA + PEA

KEC = 160 + 21168 - 784 = 20544 J

mvC2/2 = KEC = 20544

velocity at C, vC = 22.66 m/s

Acceleration due to gravity at C = g = 9.8 m/s2

Normal acceleration at C, an = (vC2)/r = (22.66)2/10.5 = 48.91 m/s2

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