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 1.33 g, with g = 9.80 m/s². A 0.335 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, 2.6 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?

Answer 1

a)

relative to ground

a_x = 0 m/s²

b)

relative to ground, the coin is in free fall. hence

a_y = - 9.8 m/s²

c)

relative to ground

a_z = 0 m/s²

d)

relative to customer

a_x = 0 m/s²

e)

relative to customer

a_y = - (1.33 g - g)

a_y = - (0.33) (9.8)

a_y = - 3.2 m/s²

f)

relative to customer

a_z = 0 m/s²

g)

y = vertical displacement = - 2.6 m

v_oy = initial velocity = 0 m/s

a_y = - 3.2 m/s²

t = time of travel

Using the equation

y = v_oy t + (0.5) a_y t²

- 2.6 = (0) t + (0.5) (- 3.2) t²

t = 1.3 sec