A kangaroo, a wallaby, a wombat, and a bandicoot travel to Innsbruck, Austria on

Question

A kangaroo, a wallaby, a wombat, and a bandicoot travel to Innsbruck, Austria on holiday where they decide to take a bobsled ride. They cruise through their first turn, which is banked at an angle of theta=50 degrees, with a constant linear speed of 29.5 m/s. The track is frictionless, and a centripetal force of 2250 N acts on the combination of marsupials and bobsled.

Note: This is a uniform circular motion problem. When you draw the free-body diagram, you should have a radial and vertical axis. The acceleration will be centripetal acceleration directed radially inward for which you have an expression on your formula sheet.

(a.) What is the radius (in meters) of their first turn?

(b.) What is the combined mass of the marsupials and bobsled?

Explanation / Answer

Given theta = 50

v = 29.5 m/s

the condition of banking of road without friction is

tan(theta) = v^2 / rg

tan(50) = 29.5^2 / (r * 9.8)

r = 74.51 m

b)

we have m * v^2 / r = 2250

m * 29.5^2 / 74.51 = 2250

m = 192.64 kg

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