A 48.0 kg ballet dancer stands onher toes during a performance with four square
ID: 1726594 • Letter: A
Question
A 48.0 kg ballet dancer stands onher toes during a performance with four square inches (26.0cm2) in contact with the floor. What is the pressureexerted by the floor over the area of contact in the followingcases? (a) if the dancer is stationary (b) if the dancer is leaping upwards with an acceleration of5.00 m/s2A 48.0 kg ballet dancer stands onher toes during a performance with four square inches (26.0cm2) in contact with the floor. What is the pressureexerted by the floor over the area of contact in the followingcases? (a) if the dancer is stationary (b) if the dancer is leaping upwards with an acceleration of5.00 m/s2
Explanation / Answer
Mass, M = 48 kg Area of contact, A = 26 cm^2 = 26 X 10 -4 m^2 (a) Stationary: Force, F = Weight = M g = 48 * 9.8 = 470.4 N Pressure, P = F / A = 470.4 / 26 X 10 -4 = 18.1 X 10 4 Pa = 1.8 X 10 5 Pa (b) Leapingupwards: Acceleration, a = 5 m/s^2 Apparent weight, W' = M ( g + a ) = 48 ( 9.8 + 5 ) = 48 * 14.8 = 710.4 N Force, F = 710.4 N Pressure, P = F / A = 710.4 / 26 X 10 -4 = 27.3 X 10 4 Pa = 2.7 X 10 5 Pa
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