A young alien moves a small cart, containing 3 ornaments, along a track that enc

Question

A young alien moves a small cart, containing 3 ornaments, along a track that encircles a decorated tree. The mass of the cart is 1.3 kg, while that of each ornament is 0.2 kg. The diameter of the circle of track is 72 cm. The cart first travels at 6 cm/s through a station to the east of the tree. Just after it gets through the station, the youth makes it speed up at a constant rate, so that, the next time it goes through the station, it is moving 70 cm/s, and vibrating a lot! During that loop, what was the tangential acceleration (in m/s^2) of the ornament-loaded cart?
 

Explanation / Answer

Given:
r=36cm
v0 =6cm/s
v=70cm/s

First, we note that we can think of the distance of the track as just the circumfrence:
C=2r
C=2(.36m)
C=2.26m

From kinematics we can say that:

V2=Vo2+2a(x-xo)

solving for a in the previous equation gives:

((.70)2-(.06)2)/(2*2.26m)=a

*note that x-xo is the distance traveled, the circumfrence.

a=0.11 m/s2. <----- tangental acceleration

From here, if you choose to solve for the angular acceleration, that is simply given by

=a/r
=0.11/0.36
=0.31m/s2. <------- angular acceleration

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