Problem 7: A high school physics instructor catches one of his students chewing
ID: 1565409 • Letter: P
Question
Problem 7: A high school physics instructor catches one of his students chewing gum in class. He decides to discipline the student by asking that he stick the gum to a fan and calculate how fast the fan is moving when the gum gets thrown off. The label says that the diameter of the fan is d 39 cm, and at full speed it turns at a rate of f 45 revls, and that the fan is guaranteed to accelerate uniformly. The fan takes t 11sto go from rest to full speed. Randomized Variables d 39 cm f 45 rev/s 11 s Part (a) Calculate the maximum the angular velocity of the fan omax, in radians per second. Numeric Anumeric value is expected and not an expression. Comax Part (b) Surprisingly, the gum seems to remain stuck to the fan at this speed. Calculate the angular acceleration of the gum a, in radians per square second, as the fan is speeding up. Numeric A numeric value is expected and not an expression Part (c) Calculate the tangential component of the acceleration of the gum atan, in meters per square second, as the fan is speeding up. Numeric A numeric value is expected and not an expression. atan Part (d) What is the magnitude of the centripetal acceleration of the gum arad, in meters per square second, when the fan reaches full speed? Numeric A numeric value is expected and not an expression. arad Part (e) What is the direction of the centripetal acceleration of the gum, as the fan is turning at top speed? Multiple Choice 1) Radially inward. 2) There is no radial component of the acceleration. 3) In the direction of rotation. 4) Radially outward. 5) Opposite the direction of rotation. Part (f Calculate the tangential component of the acceleration of the gum atan.f in meters per square second, when the fan is at full speed. Numeric Anumeric value is expected and not an expression. tan,Explanation / Answer
a) w_max = 45 rev/s
= 45*2*pi rad/s
= 282.7 rad/s
b) alfa = (wf - wi)/t
= (282.7 - 0)/11
= 25.7 rad/s^2
c) a_tan = r*alfa
= (d/2)*alfa
= (0.39/2)*25.7
= 5.01 m/s^2
d) a_rad = r*w^2
= (d/2)*w^2
= (0.39/2)*282.7^2
= 1.56*10^4 m/s^2
e) 1) radially inward
f) a_tanf = 0 (since alfa = 0, when the the fan spins with maximum speed)
g) v = r*w
= (d/2)*w
= (0.39/2)*282.7
= 55.1 m/s