Physics Question & Answer Key

Question:

Two identical ice skaters are holding onto opposite ends of a very long spring with 

a spring constant of 650 N/m. While spinning in a circle, the skaters frequency of 

revolution is measured to be 0.85 Hz. Calculate the mass of the skaters. 


Answer:

f = (1/2 π)(√ k/m)

0.85 = (1/2 π)(√ 650/m)  

m = 22.8 kg 

22.8 x 2 = 45.6 kg  (the mass need to double since circular motion is the resultant 

of two perpendicular SHM with the same frequency and amplitude and phase 

difference of π/2.)

Physics Question & Answer Key

Question:

A car traveling at constant speed negotiates a frictionless banked curved. Calculate the speed of the car when the road is banked at 20 degrees and the radius of its path is 50 meters.

Answer:

When the road is banked at angle 20 degrees,
The normal force is inclined at angle 20 degrees to the vertical
Its horizontal component
mg sin 20 = centripetal force = mv^2/r
Its vertical Component balances the weight 
mg cos 20 = mg 
Dividing the first by the second equation
tan 20 = v^2/(rg)
v^2 / 50 = (9.8)(tan 20)
v = 13.35 m/s