*) write out the solution on paper step by step ; *) clearly show all steps usin

Question

*) write out the solution on paper step by step;
*) clearly show all steps using variable notation and algebraic manipulation whenever possible;
*) express the solution in symbolic form; and
*) substitute numerical values in the last step (not the first) so as to obtain the numerical results.

7.42 CP Riding a Loop-the Figure P7.42 Loop A car in an amusement park ride rolls without friction around a track (Fig. P7.42 The B car starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. Ca) What is the minimum value of h (in terms of R such that the car moves around the loop without falling off at the top (point B? (b) If h E 3.50R and R 14.0 m compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter. Show these acceleration components in a diagram, approximately to scale

Explanation / Answer

at point B

mg - N = mv^2/R

for minimum v

N = 0

mg = mv^2/R

v = sqrt(gR)

total energy at A = total energy at B

m*g*h = (1/2)*m*v^2 + m*g*2R

m*g*h = (1/2)*m*g*R + 2*m*g*R

h = (5/2)*R = 2.5*R

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(b)

from energy conservation

total energy at A = total energy at C

m*g*h = (1/2)*m*v^2 + m*g*R

g*h = (1/2)*v^2 + g*R

9.8*3.5*14 = ((1/2)*v^2) + (9.8*14)

v = 26.2 m/s

=======================

radial acceleration ar = v^2/R = 26.2^2/14 = 49 m/s^2

tangential acceleration at = -g = -9.8 m/s^2

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