Please show all work, thanks! A robo anm moves so than P in a circle about point

Question

Please show all work, thanks!

A robo anm moves so than P in a circle about point B, which is not 2. Knowing that P starts from rest, and its speed increases at a constant rate 12 mm/s of a. The magnitude of the acceleration when sec. the of the acceleration to be 100 mm 3 For the child walking on the merry-go-round shown below. with a emntant speed 2 ft/s and constant an velocity of the memy go-mand of w El Askaming the child starts at the at o see. and walks in a straight line sowards Calculate the velocity componen calculate the accelerat 3.5 see making sure label each

Explanation / Answer

2)
a) at t = 3 sec, the speed v = a*t = 12*3 = 36 mm/s

The radius is 0.8 m(not clearly visible in the image)

So the centripital acceleration = v^2/r = 36^2/800 = 1.62 mm/s^2

The tangential acceleration = 12 mm/s^2

So the net acceleration will be,

a = sqrt(12^2+1.62^2) = 12.11 mm/s^2

b) time when a = 100 mm/s^2

a^2 + ((at)^2/R)^2 = 100^2 = 10000

144 + 0.0324 t^2 = 10000

t = 551.54 sec

3) a) at t = 3.5 s distance radially travelled = 3.5*2 = 7 ft.

The tangential velocity at this point of time = omega*r = 25*(2pi/60)*7 = 18.326 ft/s

So the velocity = 2 ft/s radially and 18.326 ft/s tangentially

b) acceleration component = tangentially = v*omega = 2*25*(2pi/60) = 5.236 ft/s^2

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