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 1.16 g, with g = 9.80 m/s2. A 0.626 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, 2.2 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

since there is only motion in y direction,so x & z components of motion will be zero(part a,c,d,f,h,j,k,m)

(b) since air resistance is not mentioned, accn of coin will be 'g' towards ground

(e) customer has accn of 1.16g so relative to him coin is accelerating in positive y direction(upwards) with accn of .16 g [a=-g-(-1.16g)=+ 0.16g]

(g) displacement=2.2m, accn= 0.16g , initial velocity =0 (wrt customer)

S = U*T + .5*A*T^2 (equation of motion)

putting values T=(2S/A)^0.5=1.675 sec

(i) actual force on coin(gravity)= mass*g=6.1348 milli Newton

(l) appearent force=mass * appearent accn(which is 0.16g)=0.981 milli Newton

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