A customer sits in an amusement park ride in which the compartment is to be pull

Question

A customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a y axis with an acceleration magnitude of 1.59 g, with g = 9.80 m/s2. A 0.697 g coin rests on the customer's knee. Once the motion begins and in unit-vector notation, what are projections of the coin's acceleration relative to the ground on (a)x-axis, (b)y-axis, (c)z-axis and relative to the customer on (d)x-axis, (e)y-axis, (f)z-axis? (g) How long does the coin take to reach the compartment ceiling, 2.3 m above the knee? What are projections of the actual force on the coin on (h)x-axis, (i)y-axis, (j)z-axis and projections of the apparent force according to the customer's measure of the coin's acceleration on (k)x-axis, (l)y-axis, (m)z-axis?

Explanation / Answer

projections of coins acceleration reletive to ground:

a) zero b) -g c) zero

relative to customer:

d) zero since both don't have any motion along x and z axis.

e) (1.59g-g) = + 0.59g

f) Zero

g) we have ,

s= ut + 0.5at^2

u ie initial velocity =0

2.3 = 0.5 * 0.59 * 9.8 t^2

so, t = 0.892 sec

projections of actual force ( i.e wrt ground) :

h) zero

i) mg = 0.697*9.8 = 6.83 N along negative y axis

j) zero

projection of apparent force a/c to customer:

k) zero

l) 0.697* 0.59* 9.8 = 4 along positive y axis

m)zero

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